Question

Determine the product, h(x), of the linear and quadratic factors.

f(x) = x2 - 4x = 1, g(x) = x +4

Answer 1

`h(x)=x^3-17x-4`

Explanation:

Given
`f(x)=x^2 - 4x -1\ and\ g(x)=x+4\\`

`h(x)=f(x)* g(x)`

`(x^2-4x-1)(x+4)\ \ \\Distribute\ parenthesis\\=x^2x+x^2* \:4+\left(-4x\right)x+\left(-4x\right)* \:4+\left(-1\right)x+\left(-1\right)* \:4`

Apply minus-plus rules

`+(-a)=-a`

`=x^2x+4x^2-4x(x)-4*\:4x-1*\:x-1*\:4`

`\\Simplify\\=x^3+4x^2-4x^2-16x-x-4\\=x^3-16x-x-4\\=x^3-17x-4`

`h(x)=x^3-17x-4`