Question

homework 7: factoring trinomials ($x^{2}+bx + c$)directions: factor each polynomial. check your answers by foil..1. $x^{2}+5x + 6$2. $a^{2}+11a + 30$3. $m^{2}+18m + 56$4. $w^{2}+4w + 4$5. $y^{2}+9y + 8$6. $k^{2}+17k + 66$7. $y^{2}-6y + 8$8. $x^{2}-11x + 28$9. $n^{2}-n - 90$10. $p^{2}-14p + 40$11. $x^{2}+3x - 70$12. $w^{2}-12w + 36$13. $m^{2}+5m - 6$14. $b^{2}-15b + 56$15. $x^{2}-10x - 39$16. $a^{2}+11a + 18$17. $x^{2}-14x - 51$18. $m^{2}-8m + 7$directions: factor each polynomial. look for a gcf first.19. $2k^{2}-8k - 90$20. $x^{3}+2x^{2}-48x$21. $4w^{2}-52w - 120$22. $2x^{2}+10x + 8$23. $3y^{2}+24y + 48$24. $5m^{3}+30m^{2}-35m$

Explanation:

Step1: Find pair summing to 5, product 6

Factors of 6: 2 and 3 (2+3=5)
$x^2+5x+6=(x+2)(x+3)$

Step2: Find pair summing to 11, product 30

Factors of 30: 5 and 6 (5+6=11)
$a^2+11a+30=(a+5)(a+6)$

Step3: Find pair summing to 18, product 56

Factors of 56: 7 and 8 (7+8=15? No, 14 and 4: 14+4=18, 14×4=56)
$m^2+18m+56=(m+4)(m+14)$

Step4: Find pair summing to 4, product 4

Factors of 4: 2 and 2 (2+2=4)
$w^2+4w+4=(w+2)^2$

Step5: Find pair summing to 9, product 8

Factors of 8: 1 and 8 (1+8=9)
$y^2+9y+8=(y+1)(y+8)$

Step6: Find pair summing to 17, product 66

Factors of 66: 6 and 11 (6+11=17)
$k^2+17k+66=(k+6)(k+11)$

Step7: Find pair summing to -6, product 8

Factors of 8: -2 and -4 (-2+-4=-6)
$y^2-6y+8=(y-2)(y-4)$

Step8: Find pair summing to -11, product 28

Factors of 28: -4 and -7 (-4+-7=-11)
$x^2-11x+28=(x-4)(x-7)$

Step9: Find pair summing to -1, product -90

Factors of -90: 9 and -10 (9+-10=-1)
$n^2-n-90=(n+9)(n-10)$

Step10: Find pair summing to -14, product 40

Factors of 40: -4 and -10 (-4+-10=-14)
$p^2-14p+40=(p-4)(p-10)$

Step11: Find pair summing to 3, product -70

Factors of -70: 10 and -7 (10+-7=3)
$x^2+3x-70=(x+10)(x-7)$

Step12: Find pair summing to -12, product 36

Factors of 36: -6 and -6 (-6+-6=-12)
$w^2-12w+36=(w-6)^2$

Step13: Find pair summing to 5, product -6

Factors of -6: 6 and -1 (6+-1=5)
$m^2+5m-6=(m+6)(m-1)$

Step14: Find pair summing to -15, product 56

Factors of 56: -7 and -8 (-7+-8=-15)
$b^2-15b+56=(b-7)(b-8)$

Step15: Find pair summing to -10, product -39

Factors of -39: 3 and -13 (3+-13=-10)
$x^2-10x-39=(x+3)(x-13)$

Step16: Find pair summing to 11, product 18

Factors of 18: 2 and 9 (2+9=11)
$a^2+11a+18=(a+2)(a+9)$

Step17: Find pair summing to -14, product -51

Factors of -51: 3 and -17 (3+-17=-14)
$x^2-14x-51=(x+3)(x-17)$

Step18: Find pair summing to -8, product 7

Factors of 7: -1 and -7 (-1+-7=-8)
$m^2-8m+7=(m-1)(m-7)$

Step19: Factor out GCF 2 first

$2k^2-8k-90=2(k^2-4k-45)$
Find pair summing to -4, product -45: 5 and -9
$2(k+5)(k-9)$

Step20: Factor out GCF $x$ first

$x^3+2x^2-48x=x(x^2+2x-48)$
Find pair summing to 2, product -48: 8 and -6
$x(x+8)(x-6)$

Step21: Factor out GCF 4 first

$4w^2-52w-120=4(w^2-13w-30)$
Find pair summing to -13, product -30: 2 and -15
$4(w+2)(w-15)$

Step22: Factor out GCF 2 first

$2x^2+10x+8=2(x^2+5x+4)$
Find pair summing to 5, product 4: 1 and 4
$2(x+1)(x+4)$

Step23: Factor out GCF 3 first

$3y^2+24y+48=3(y^2+8y+16)$
Find pair summing to 8, product 16: 4 and 4
$3(y+4)^2$

Step24: Factor out GCF $5m$ first

$5m^3+30m^2-35m=5m(m^2+6m-7)$
Find pair summing to 6, product -7: 7 and -1
$5m(m+7)(m-1)$

Answer:

1. $(x+2)(x+3)$
2. $(a+5)(a+6)$
3. $(m+4)(m+14)$
4. $(w+2)^2$
5. $(y+1)(y+8)$
6. $(k+6)(k+11)$
7. $(y-2)(y-4)$
8. $(x-4)(x-7)$
9. $(n+9)(n-10)$
10. $(p-4)(p-10)$
11. $(x+10)(x-7)$
12. $(w-6)^2$
13. $(m+6)(m-1)$
14. $(b-7)(b-8)$
15. $(x+3)(x-13)$
16. $(a+2)(a+9)$
17. $(x+3)(x-17)$
18. $(m-1)(m-7)$
19. $2(k+5)(k-9)$
20. $x(x+8)(x-6)$
21. $4(w+2)(w-15)$
22. $2(x+1)(x+4)$
23. $3(y+4)^2$
24. $5m(m+7)(m-1)$