Question

1. $x^2 + 2x - 24$
2. $m^2 - 5m - 50$
3. $u^2 - 10u - 56$
4. $v^2 - 11v - 42$
5. $a^2 + 9a - 70$
6. $x^2 - 2x - 8$
7. $v^2 - v - 12$
8. $k^2 - 6k - 72$
9. $x^2 + 5x - 6$
10. $n^2 + n - 72$
11. (partially obscured, likely a quadratic) - 24
12. $p^2 - p - 20$
13. $r^2 + 6r - 55$
14. $a^2 + 2a - 8$

Explanation:

All problems require factoring quadratic trinomials of the form $x^2+bx+c$, which means finding two numbers that multiply to $c$ and add to $b$, then writing the trinomial as $(x+m)(x+n)$ where $m$ and $n$ are those two numbers.

17) Factor $x^2+2x-24$

Step1: Find pair: sum=2, product=-24

Numbers are $6$ and $-4$ (since $6+(-4)=2$, $6\times(-4)=-24$)

Step2: Write factored form

$(x+6)(x-4)$

18) Factor $m^2-5m-50$

Step1: Find pair: sum=-5, product=-50

Numbers are $5$ and $-10$ (since $5+(-10)=-5$, $5\times(-10)=-50$)

Step2: Write factored form

$(m+5)(m-10)$

19) Factor $u^2-10u-56$

Step1: Find pair: sum=-10, product=-56

Numbers are $4$ and $-14$ (since $4+(-14)=-10$, $4\times(-14)=-56$)

Step2: Write factored form

$(u+4)(u-14)$

20) Factor $v^2-11v-42$

Step1: Find pair: sum=-11, product=-42

Numbers are $3$ and $-14$ (since $3+(-14)=-11$, $3\times(-14)=-42$)

Step2: Write factored form

$(v+3)(v-14)$

21) Factor $a^2+9a-70$

Step1: Find pair: sum=9, product=-70

Numbers are $14$ and $-5$ (since $14+(-5)=9$, $14\times(-5)=-70$)

Step2: Write factored form

$(a+14)(a-5)$

22) Factor $x^2-2x-8$

Step1: Find pair: sum=-2, product=-8

Numbers are $2$ and $-4$ (since $2+(-4)=-2$, $2\times(-4)=-8$)

Step2: Write factored form

$(x+2)(x-4)$

23) Factor $v^2-v-12$

Step1: Find pair: sum=-1, product=-12

Numbers are $3$ and $-4$ (since $3+(-4)=-1$, $3\times(-4)=-12$)

Step2: Write factored form

$(v+3)(v-4)$

24) Factor $k^2-6k-72$

Step1: Find pair: sum=-6, product=-72

Numbers are $6$ and $-12$ (since $6+(-12)=-6$, $6\times(-12)=-72$)

Step2: Write factored form

$(k+6)(k-12)$

25) Factor $x^2+5x-6$

Step1: Find pair: sum=5, product=-6

Numbers are $6$ and $-1$ (since $6+(-1)=5$, $6\times(-1)=-6$)

Step2: Write factored form

$(x+6)(x-1)$

26) Factor $n^2+n-72$

Step1: Find pair: sum=1, product=-72

Numbers are $9$ and $-8$ (since $9+(-8)=1$, $9\times(-8)=-72$)

Step2: Write factored form

$(n+9)(n-8)$

28) Factor $p^2-p-20$

Step1: Find pair: sum=-1, product=-20

Numbers are $4$ and $-5$ (since $4+(-5)=-1$, $4\times(-5)=-20$)

Step2: Write factored form

$(p+4)(p-5)$

29) Factor $r^2+6r-55$

Step1: Find pair: sum=6, product=-55

Numbers are $11$ and $-5$ (since $11+(-5)=6$, $11\times(-5)=-55$)

Step2: Write factored form

$(r+11)(r-5)$

30) Factor $a^2+2a-8$

Step1: Find pair: sum=2, product=-8

Numbers are $4$ and $-2$ (since $4+(-2)=2$, $4\times(-2)=-8$)

Step2: Write factored form

$(a+4)(a-2)$

Answer:

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