Question

Can the polynomial in the numerator of the expression x^2-5x+7/x-9 be factored to derive (x-9) as a factor? Looking at the middle term in the numerator, what number must you add to -9 to get the coefficient -5

Answer 1

From remainder theorem, we can get that (x-9) is not a factor.

`\begin{gathered} x^2-5x+7 \\ 9^2-5(9)+7=43 \end{gathered}`

Given as below,

`ax^2+bx+c`

For a quadratic expression to be factorizable, then two factors of c have to add up to b

We must add 4 to -9 to get -5.

However, 4 and -9 will give us -36 when multiplied.