Question

1. factor the expression: $10v^2 + 11v - 8$

a) $(5v + 8)(2v + 1)$
b) $(v + 8)(v - 1)$
c) $(5v + 8)(2v - 1)$
d) $(10v - 8)(v + 1)$

1. based on the method we learned in class, which of these puzzles can be used to find the values that split the middle term?

a) image of a cross puzzle with c at top and a + b at bottom
b) image of a cross puzzle with c at top and a·b at bottom
c) image of a cross puzzle with a·c at left and b at right
d) image of a cross puzzle with a·c at top and b at bottom

1. factor completely: $3x^2 + 18x + 15$

hint: factor gcf first.
a) $3(x^2 + 6x + 5)$
b) $(x + 5)(x + 1)$
c) $3(x + 5)(x + 1)$
d) prime

1. factor the expression: $21z^2 - 70z + 49$

a) $7(3z - 7)(z - 1)$
b) $7(3z + 7)(z + 1)$
c) $7(3z - 7)(z + 1)$
d) $7(3z + 7)(z - 1)$

1. factor the expression: $-2h^2 + 4h + 70$

a) $-2(h + 7)(h + 5)$
b) $-2(h - 7)(h - 5)$
c) $-2(h + 7)(h - 5)$
d) $-2(h - 7)(h + 5)$

Explanation:

Step1: Factor $10v^2+11v-8$

Use AC method: $10\times(-8)=-80$, find pair $16,-5$ (sum=11). Split term: $10v^2+16v-5v-8$. Factor groups: $2v(5v+8)-1(5v+8)=(5v+8)(2v-1)$

Step2: Identify split middle term puzzle

The X-puzzle for splitting the middle term of $ax^2+bx+c$ has product $a\cdot c$ at top, sum $b$ at bottom.

Step3: Factor $3x^2+18x+15$

Factor GCF 3 first: $3(x^2+6x+5)$. Factor quadratic: $x^2+6x+5=(x+5)(x+1)$, so full factor: $3(x+5)(x+1)$

Step4: Factor $21z^2-70z+49$

Factor GCF 7 first: $7(3z^2-10z+7)$. Factor quadratic: $3z^2-10z+7=(3z-7)(z-1)$, so full factor: $7(3z-7)(z-1)$

Step5: Factor $-2h^2+4h+70$

Factor GCF $-2$ first: $-2(h^2-2h-35)$. Factor quadratic: $h^2-2h-35=(h-7)(h+5)$, so full factor: $-2(h-7)(h+5)$

Answer:

1. c) $(5v + 8)(2v - 1)$
2. d)

      a·c
       ×
        b

1. c) $3(x + 5)(x + 1)$
2. a) $7(3z - 7)(z - 1)$
3. d) $-2(h - 7)(h + 5)$