Factoring

Factoring

Page 80: Factoring GCF3x2 + 18x + 9

4k4 + 18k3 6k2

3X2 + 6X + 3=3(x2 + 6x + 3)=2k2(2k2 + 9k 3)=3(X2 + 2X + 1)

Mistake on the homework page 80#14) answer is P the problem is messed upPage 97: Factor by GroupingX2 + 3X + XK + 3K

M2 + MN 3M 3N

=X(X + 3) + K(X + 3)=(X + K) (X + 3) or (X + 3) (X + K) =M(M + N) 3(M + N)=(M 3) (M + N) or (M + N) (M 3)

Page 84 top left: Multiply (a + 5) (a 5)

(a2 6) (a2 + 6) = a2 5a + 5a 25 = a2 25 = a4 + 6a2 6a2 36 = a4 36

Page 84: Factoring Difference of Squares36x2 121y2

4a16 225

What about x2 + 25? Does it factor? = (6x 11y) (6x + 11y)= (2a8 15) (2a8 + 15)Try (x + 5) (x + 5) or (x + 5) (x 5) or (x 5) (x 5) Conclusion: Sum of Squares is NOT factorable. We call it prime.

Page 90: Quick FactorN2 + 6N + 5

N2 + 2N 15

A2 29AB + 100B2

A2 14AB 32B2

Factors of +5 Sum of +6= (N + 5) (N + 1) Factors of -15 Diff of +21*15 3*5= (N 3) (N + 5) Factors of +100 Sum of -291*100 2*50 4*25 10*10= (A 4B) (A 25B) Factors of -32 Diff of -141*32 2*16 4*8= (A + 2B) (A 16B)

Factoring: Sum & Difference of CubesA3 B3 = (A B)(A2 + AB + B2)A3 + B3 = (A + B)(A2 AB + B2)

1000X3 + 27

64X3 1

= (10X + 3) (100X2 30X + 9)= (4X 1) (16X2 + 4X + 1)

Page 91: Long Factor3x2 + 7x + 2

8u2 9u + 1

7n2 13n 2 Factors of +6 Sum of +71*6 2*3Factors of +8 Sum of -91*8 2*4Factors of -14 Diff of -131*14 2*7= 3x2 + 1x + 6x + 2=x(3x + 1) + 2(3x + 1)= 8u2 1u 8u + 1=u(8u 1) 1(8u 1)= 7n2 + 1n 14n 2 =n(7n + 1) 2(7n + 1)= (x + 2)(3x + 1) = (u 1)(8u 1) = (n 2)(7n + 1)

Page 93: Factoring, All Mixed UpBinomials:Take out GCF Check for Diff of Squares, Diff/Sum of Cubes

Trinomials: Take out GCF Check for Quick Factor (coef in front = 1)Check for Long Factor (coef in front 1)

Page 94: All Mixed Up with GCF3x2 15x + 18

60m3 + 54m2 6m = 3(x2 5x + 6) Factors of +6Sum of -51*6 2*3= 3(x 2) (x 3) = 6m(10m2 9m 1) Factors of -10Diff of -91*10 2*5= 6m(10m2 + 1m 10m 1) = 6m[ m(10m + 1) 1(10m + 1) ] = 6m (m 1) (10m + 1)

Page 93: Factoring, All Mixed UpBinomials:Take out GCF Check for Diff of Squares & Diff/Sum of CubesA2 B2 = (A B)(A +B)A3 B3 = (A B)(A2 + AB + B2)A3 + B3 = (A + B)(A2 AB + B2)

Trinomials: Take out GCF Check for Quick Factor (coef in front = 1)Check for Long Factor (coef in front 1)