Question

Factor each expression 1)4a^2-16ab^3+8ab^2c 2) n^2+8n+15 3) g^2-9g+20 4) z^2-7z-30 5) 4y^3-36y

Answer 1

Hello,

1)
$4a^2-16ab^3+8ab^2c=4a(a-4b^3+2b^2c)$

2)
$n^2+8n+15\\ =n^2+5n+3n+15\\ =n(n+5)+3(n+5)\\ =(n+5)(n+3)$

3)
$g^2-9g+20\\ =g^2-5g-4g+20\\ =g(g-5)-4(g-5)\\ =(g-5)(g-4)$

4)
$z^2-7z-30\\ =z^2-10z+3z-30\\ =z(z-10)+3(z-10)\\ =(z-10)(z+3)$

5)
$4y^3-36y\\ =4y(y^2-9)\\ =4y(y-3)(y+3)$