Question

What is the factored form of 5x2 − 18x − 8?

Answer 1

5*-8=-40

What multiplies to -40 and adds to -18? -20 and +2

(5x+2)(x-4)

Answer 2

`5x^2-18x-8=5x^2-20x+2x-8=5x(x-4)+2(x-4)\\\\=\boxed{(x-4)(5x+2)}\\--------------------------\\5x^2-18x-8=0\\a=5;\ b=-18;\ c=-8\\\\\Delta=b^2-4ac\\\Delta=(-18)^2-4\cdot5\cdot(-8)=324+160=484 \ \textgreater \ 0\\\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(484)=22\\\\x_1=(18-22)/(2\cdot5)=(-4)/(10)=-(2)/(5)\\\\x_2=(18+22)/(2\cdot5)=(40)/(10)=4\\\\5x^2-18x-8=5\left(x+(2)/(5)\right)(x-4)=(5x+2)(x-4)`