Holt Algebra 1

8-4 Factoring ax2 + bx + c

Warm Up

Find each product.

1. (x – 2)(2x + 7)

2. (3y + 4)(2y + 9)

3. (3n – 5)(n – 7)

Find each trinomial.4. x2 +4x – 325. z2 + 15z + 366. h2 – 17h + 72

6y2 + 35y + 36

2x2 + 3x – 14

3n2 – 26n + 35

(z + 3)(z + 12) (x – 4)(x + 8)

(h – 8)(h – 9)

Holt Algebra 1

8-4 Factoring ax2 + bx + c

Simplify and write the

answer in scientific notation

10

35 10

Holt Algebra 1

8-4 Factoring ax2 + bx + c

Factor quadratic trinomials of the form ax2 + bx + c.

Objective

Holt Algebra 1

8-4 Factoring ax2 + bx + c

In the previous lesson you factored trinomials of the form x2 + bx + c. Now you will factor trinomials of the form ax + bx + c, where a ≠ 0.

Holt Algebra 1

8-4 Factoring ax2 + bx + c

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

2Factor 2 7 3x x

22x

3

26x

7x6x x

6x

x

2x

x

3

1

2 1 3x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

Factor 6x2 + 11x + 4

26x

4

224x

11x8x 3x

8x

3x

2x

3x

4

1

2 1 3 4x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

6x2 + 11x + 3

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

26x

3

218x

11x9x 2x

9x

2x

3x

2x

3

1

3 1 2 3x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

3x2 – 2x – 8

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

23x

8

224x

2x4x6x

4x

6x

3x

x

2

4

3 4 2x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

2x2 + 17x + 21

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

22x

21

242x

17x3x14x

3x

14x

2x

x

7

3

2 3 7x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

3x2 – 16x + 16

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

23x

16

248x

16x4x12x

4x

12x

3x

x

4

4

3 4 4x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

6x2 + 17x + 5

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

26x

5

230x

17x2x15x

2x

15x

3x

2x

5

1

3 1 2 5x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

9x2 – 15x + 4

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

29x

4

236x

15x3x12x

3x

12x

3x

3x

4

1

3 1 3 4x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

3n2 + 11n – 4

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

23n

4

212n

11n

n12n

n

12n

3n

n

4

1

3 1 4n n

Holt Algebra 1

8-4 Factoring ax2 + bx + c

2x2 + 9x – 18

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

22x

18

236x

9x3x12x

3x

12x

2x

x

6

3

2 3 6x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

4x2 – 15x – 4

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

24x

4

216x

15xx16x

x

16x

4x

x

4

1

4 1 4x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

6x2 + 7x – 3

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

26x

3

218x

7x2x9x

2x

9x

3x2x

3

1

3 1 2 3x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

–2x2 – 5x – 3

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

22x

3

26x

5x2x3x

2x

3x

x2x

3

1

1 2 3x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

–6x2 – 17x – 12

Place the quadratic and constant terms in

opposite corners of a 2 x 2 square.

Place the product of these terms in the

upper quadrant of a 2 x 2 diamond. Place the

linear

Step 1:

Step 2

term of

:

the trinomial in the lower quadrant

of your 2 x 2 diamond.

Fill in the left and right quadrants of

your diamond with linear terms whose product is

the upper quadrant of the diamond and whose

sum

Step

is t

3:

he lower quadrant of the diamond.

Use the left and right quadrants of your

diamond to fill in the remaining cells of your square.

Determine the factors of each cell of

your 2

Step 4:

Step 5:

x 2 square.

Ste The sum of these factors make up the

binomial factors of your trino

p 6:

mial.

26x

12

272x

17x8x9x

8x

9x

3x2x

3

4

3 4 2 3x x

Holt Algebra 1

8-4 Factoring ax2 + bx + c

HW pp.552-554/25-69 odd,75-81,83,90-96