Question

1. $b^2 - 6b + 8$
2. $n^2 + 6n + 8$
3. $2n^2 + 6n - 108$
4. $5n^2 + 10n + 20$
5. $2k^2 + 22k + 60$
6. $a^2 - a - 90$
7. $p^2 + 11p + 10$
8. $5v^2 - 30v + 40$
9. $2p^2 + 2p - 4$
10. $4v^2 - 4v - 8$
11. $x^2 - 15x + 50$
12. $v^2 - 7v + 10$
13. $p^2 + 3p - 18$
14. $6v^2 + 66v + 60$

Explanation:

13) Factor $b^2 - 6b + 8$

Step1: Find pair summing to -6, product 8

Pairs: $-2, -4$ (since $-2 + (-4) = -6$, $(-2)(-4)=8$)

Step2: Write factored form

$(b-2)(b-4)$

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14) Factor $n^2 + 6n + 8$

Step1: Find pair summing to 6, product 8

Pairs: $2, 4$ (since $2+4=6$, $2\times4=8$)

Step2: Write factored form

$(n+2)(n+4)$

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15) Factor $2n^2 + 6n - 108$

Step1: Factor out GCF 2

$2(n^2 + 3n - 54)$

Step2: Factor quadratic inside

Find pair: $9, -6$ ($9+(-6)=3$, $9\times(-6)=-54$)
$2(n+9)(n-6)$

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16) Factor $5n^2 + 10n + 20$

Step1: Factor out GCF 5

$5(n^2 + 2n + 4)$

Step2: Check quadratic (no real factors)

Quadratic $n^2+2n+4$ has discriminant $2^2-4(1)(4)=-12<0$, so no real factorization.

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17) Factor $2k^2 + 22k + 60$

Step1: Factor out GCF 2

$2(k^2 + 11k + 30)$

Step2: Factor quadratic inside

Find pair: $5, 6$ ($5+6=11$, $5\times6=30$)
$2(k+5)(k+6)$

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18) Factor $a^2 - a - 90$

Step1: Find pair summing to -1, product -90

Pairs: $9, -10$ ($9+(-10)=-1$, $9\times(-10)=-90$)

Step2: Write factored form

$(a+9)(a-10)$

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19) Factor $p^2 + 11p + 10$

Step1: Find pair summing to 11, product 10

Pairs: $1, 10$ ($1+10=11$, $1\times10=10$)

Step2: Write factored form

$(p+1)(p+10)$

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20) Factor $5v^2 - 30v + 40$

Step1: Factor out GCF 5

$5(v^2 - 6v + 8)$

Step2: Factor quadratic inside

Find pair: $-2, -4$ ($-2+(-4)=-6$, $(-2)(-4)=8$)
$5(v-2)(v-4)$

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21) Factor $2p^2 + 2p - 4$

Step1: Factor out GCF 2

$2(p^2 + p - 2)$

Step2: Factor quadratic inside

Find pair: $2, -1$ ($2+(-1)=1$, $2\times(-1)=-2$)
$2(p+2)(p-1)$

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22) Factor $4v^2 - 4v - 8$

Step1: Factor out GCF 4

$4(v^2 - v - 2)$

Step2: Factor quadratic inside

Find pair: $1, -2$ ($1+(-2)=-1$, $1\times(-2)=-2$)
$4(v+1)(v-2)$

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23) Factor $x^2 - 15x + 50$

Step1: Find pair summing to -15, product 50

Pairs: $-5, -10$ ($-5+(-10)=-15$, $(-5)(-10)=50$)

Step2: Write factored form

$(x-5)(x-10)$

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24) Factor $v^2 - 7v + 10$

Step1: Find pair summing to -7, product 10

Pairs: $-2, -5$ ($-2+(-5)=-7$, $(-2)(-5)=10$)

Step2: Write factored form

$(v-2)(v-5)$

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25) Factor $p^2 + 3p - 18$

Step1: Find pair summing to 3, product -18

Pairs: $6, -3$ ($6+(-3)=3$, $6\times(-3)=-18$)

Step2: Write factored form

$(p+6)(p-3)$

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26) Factor $6v^2 + 66v + 60$

Step1: Factor out GCF 6

$6(v^2 + 11v + 10)$

Step2: Factor quadratic inside

Find pair: $1, 10$ ($1+10=11$, $1\times10=10$)
$6(v+1)(v+10)$

Answer:

1. $(b-2)(b-4)$
2. $(n+2)(n+4)$
3. $2(n+9)(n-6)$
4. $5(n^2 + 2n + 4)$
5. $2(k+5)(k+6)$
6. $(a+9)(a-10)$
7. $(p+1)(p+10)$
8. $5(v-2)(v-4)$
9. $2(p+2)(p-1)$
10. $4(v+1)(v-2)$
11. $(x-5)(x-10)$
12. $(v-2)(v-5)$
13. $(p+6)(p-3)$
14. $6(v+1)(v+10)$