Question

PLSSSS ANSWER ASAP........factor r^2 +4r - 32

Answer 1

`\huge\boxed{r^2+4r-32=(r+8)(r-4)}`

Explanation:

METHOD 1.

`r^2+4r-32\\\\\left\begin{array}{ccc}a\cdot b=-32\\a+b=4\end{array}\right\}a=8;\ b=-4\\\\r^2+8r-4r-32\qquad|\text{distribute}\\\\=r(r+8)-4(r+8)\\\\=(r+8)(r-4)`

METHOD 2.

Use the quadratic formula.

`ax^2+bx+c=a(x-x_1)(x-x_2)\\\\x_1=(-b-√(b^2-4ac))/(2a);\ x_2=(-b+√(b^2-4ac))/(2a)`

`r^2+4r-32\\\\a=1;\ b=4;\ c=-32\\\\b^2-4ac=4^2-4\cdot1\cdot(-32)=16+128=144\\\\√(b^2-4ac)=√(144)=12\\\\x_1=(-4-12)/(2\cdot1)=(-16)/(2)=-8\\\\x_2=(-4+12)/(2\cdot1)=(8)/(2)=4\\\\r^2+4r-32=(r-(-8))(r-4)=(r+8)(r-4)`