6 3 Add,Sub,Mult Polynomials
Transcript of 6 3 Add,Sub,Mult Polynomials
ADDING, SUBTRACTING, & MULTIPLYING POLYNOMIALS
JOURNAL ENTRY ERROR ANALYSIS
A student simplified 6a³ -a³ and got a 6 as a result. Write an explanation of the student’s error using the words coefficient and like terms.
CHALLANGE
A 35-centimeter stick is cut into three pieces so that the two end pieces are each equal in length to one-third of the middle piece. How long is each piece?
MULTIPLYING POLYNOMIALS
3a(6b + 7) (3a)(6b) + (3a)(7) 18ab + 21a
2x(3x² + x – 4) (2x)(3x²) + (2x)(x) + (2x)(-4) 6x³ + 2x² + -8x
YOUR TURN
-4a²(-2a² + 3ab – 2b + 5)
MULTIPLYING BINOMIALS
(x + 2)(x + 3) x(x+ 3) + 2(x + 3) (x)( x)+ (x)(3) + 2(x) + 2(3) x² + 3x + 2x + 6 x² + 5x + 6
FOIL METHOD
(x + 3)(x + 2) + + +
x² + 2x + 3x + 6 x² + 5x+ 6
first2)
outer(xinside
last
First
x·xOuter
x ·2
Inside
3 · x
Last
3 · 2
YOUR TURN – USE FOIL METHOD
1. (x + 4)(x - 3) 2. (2x + 2)(x + 6)
3. (3ab² + b)(-2ab² - b) 4. (4xy + 3)(2x²y + 1)
FOIL
1. (x + 4)(x – 4) 2. (x + 3)(x – 3)
3. (3y – 1)(3y + 1) 4. (2x² + 3)(2x² - 3)
5. (2x +y) (2x -y) 6. (x²y - 2)(x²y + 3)
FOIL
1.(y + 1)(y + 1) 2. (x + 2)²
3. (2x - 3)² 4. .(y² + 1)²
5.(2x – y)² 6. .(2y² - 2x)²
SOME BINOMIAL PRODUCTS APPEAR SO MUCH WE NEED TO RECOGNIZE THE PATTERNS!
Sum & Difference (S&D): (a + b)(a – b) = a2 – b2 Example: (x + 3)(x – 3) = x2 – 9
Square of Binomial: (a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
MULTIPLYING POLYNOMIALS: VERTICALLY (-x2 + 2x + 4)(x – 3)= -x2 + 2x + 4
* x – 3 3x2 – 6x – 12 -x3 + 2x2 + 4x
-x3 + 5x2 – 2x – 12
MULTIPLYING POLYNOMIALS : HORIZONTALLY
(x – 3)(3x2 – 2x – 4)= (x – 3)(3x2) + (x – 3)(-2x) + (x – 3)(-
4) = (3x3 – 9x2) + (-2x2 + 6x) + (-4x + 12) = 3x3 – 9x2 – 2x2 + 6x – 4x +12 = 3x3 – 11x2 + 2x + 12
MULTIPLYING 3 BINOMIALS :
(x – 1)(x + 4)(x + 3) = FOIL the first two: (x2 – x +4x – 4)(x + 3) = (x2 + 3x – 4)(x + 3) = Then multiply the trinomial by the binomial (x2 + 3x – 4)(x) + (x2 + 3x – 4)(3) = (x3 + 3x2 – 4x) + (3x2 + 9x – 12) = x3 + 6x2 + 5x - 12
SOME BINOMIAL PRODUCTS APPEAR SO MUCH WE NEED TO RECOGNIZE THE PATTERNS!
Sum & Difference (S&D): (a + b)(a – b) = a2 – b2 Example: (x + 3)(x – 3) = x2 – 9
Square of Binomial: (a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
LAST PATTERNLAST PATTERN
Cube of a Binomial (a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 - 3a2b + 3ab2 – b3
EXAMPLE:EXAMPLE:
(x + 5)3 =a = x and b = 5x3 + 3(x)2(5) + 3(x)(5)2 + (5)3 =
x3 + 15x2 + 75x + 125