Question

factoring trinomials (a = 1)
date
factor each completely.

1. $b^2 + 8b + 7$
2. $n^2 - 11n + 10$
3. $m^2 + m - 90$
4. $n^2 + 4n - 12$
5. $n^2 - 10n + 9$
6. $b^2 + 16b + 64$
7. $m^2 + 2m - 24$
8. $x^2 - 4x + 24$
9. $k^2 - 13k + 40$
10. $a^2 + 11a + 18$
11. $n^2 - n - 56$
12. $n^2 - 5n + 6$

Explanation:

Step1: Find pair summing to 8, product 7

$b^2+8b+7=(b+1)(b+7)$

Step2: Find pair summing to -11, product 10

$n^2-11n+10=(n-1)(n-10)$

Step3: Find pair summing to 1, product -90

$m^2+m-90=(m+10)(m-9)$

Step4: Find pair summing to 4, product -12

$n^2+4n-12=(n+6)(n-2)$

Step5: Find pair summing to -10, product 9

$n^2-10n+9=(n-1)(n-9)$

Step6: Find pair summing to 16, product 64

$b^2+16b+64=(b+8)^2$

Step7: Find pair summing to 2, product -24

$m^2+2m-24=(m+6)(m-4)$

Step8: Check for real factor pair

No real integers sum to -4, product 24; $x^2-4x+24$ is prime.

Step9: Find pair summing to -13, product 40

$k^2-13k+40=(k-5)(k-8)$

Step10: Find pair summing to 11, product 18

$a^2+11a+18=(a+2)(a+9)$

Step11: Find pair summing to -1, product -56

$n^2-n-56=(n-8)(n+7)$

Step12: Find pair summing to -5, product 6

$n^2-5n+6=(n-2)(n-3)$

Answer:

1. $(b+1)(b+7)$
2. $(n-1)(n-10)$
3. $(m+10)(m-9)$
4. $(n+6)(n-2)$
5. $(n-1)(n-9)$
6. $(b+8)^2$
7. $(m+6)(m-4)$
8. Prime (cannot be factored over integers)
9. $(k-5)(k-8)$
10. $(a+2)(a+9)$
11. $(n-8)(n+7)$
12. $(n-2)(n-3)$