x^2-8x+15
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2x^2-7x-15
So far I've got for the numerator:
(x-3)(x-5)
What goes below, and how did you do it? Thank you.
$\displaystyle \displaystyle \begin{align*} 2x^2 - 7x - 15 \end{align*}$
Multiply the a and c values to get -30. You need to look for two numbers that multiply to give -30 and add to give -7. They are -10 and 3. So break up the middle value and factorise by grouping.
$\displaystyle \displaystyle \begin{align*} 2x^2 - 7x - 15 &= 2x^2 - 10x + 3x - 15 \\ &= 2x(x - 5) + 3(x - 5) \\ &= (x - 5)(2x + 3) \end{align*}$
The most reliable way to factor a quadratic polynomial $\displaystyle ax^2+bx+c$ is by finding its roots using the quadratic formula. If the roots are $\displaystyle x_1$ and $\displaystyle x_2$, then $\displaystyle ax^2+bx+c=a(x-x_1)(x-x_2)$.