Question

Part A: Factor 3x2y2 − xy2 − 2y2. Show your work. (4 points)

Part B: Factor x2 + 6x + 9. Show your work. (3 points)

Part C: Factor x2 − 25. Show your work. (3 points)

Answer 1

A.

$3x^2y^2-xy^2-2y^2=y^2(3x^2-x-2)=y^2(3x^2+2x-3x-2)\\\\=y^2[x(3x+2)-1(3x+2)]=y^2(3x+2)(x-1)$

B.

$x^2+6x+9=x^2+2\cdot x\cdot3+3^2=(x+3)^2=(x+3)(x+3)\\\\\text{Used}\ (a+b)^2=a^2+2ab+b^2$

C.

$x^2-25=x^2-5^2=(x-5)(x+5)\\\\\text{Used}\ a^2-b^2=(a-b)(a+b)$