Question

complete the sum to product x
a) -7, 4 \t\t\t\tb) 7, -4
c) -7, -4 \t\t\t\td) 2, -14

1. factor

$3v^2 - 4v - 7$
a) $(3v - 7)(v + 1)$ \t\t\t\tb) $3(v - 7)(v - 1)$
c) $(3v + 1)(v - 9)$ \t\t\t\td) $(3v + 1)(v - 10)$

1. factor:

$4h^2 - 17h + 4$
a) $(2h - 2)^2$ \t\t\t\tb) $4(h + 4)(h + 1)$
c) $(2h - 2)(2h + 2)$ \t\t\t\td) $(h - 4)(4h - 1)$

1. factor:

$2x^2 + 13x + 15$
a) $(2x + 1)(x + 15)$ \t\t\t\tb) $(x + 3)(x + 5)$
c) $(2x - 3)(x - 5)$ \t\t\t\td) $(2x + 3)(x + 5)$

Explanation:

Step1: Verify sum-product pair

Check which pair multiplies to $-28$ and adds to $-3$.
For option b: $7 \times (-4) = -28$, $7 + (-4) = -3$

Step2: Factor $3v^2-4v-7$

Find two terms: $3v^2+3v-7v-7$, group: $3v(v+1)-7(v+1)=(3v-7)(v+1)$

Step3: Factor $4h^2-17h+4$

Find two terms: $4h^2-16h-h+4$, group: $4h(h-4)-1(h-4)=(h-4)(4h-1)$

Step4: Factor $2x^2+13x+15$

Find two terms: $2x^2+10x+3x+15$, group: $2x(x+5)+3(x+5)=(2x+3)(x+5)$

Answer:

1. b) 7, -4
2. a) $(3v-7)(v+1)$
3. d) $(h - 4)(4h - 1)$
4. d) $(2x + 3)(x + 5)$