Answer:
(x-5)(x+12).
Explanation:
Given the polynomial:
[tex]7x-60+x^2[/tex]First, we write it in the standard form of a polynomial:
[tex]x^2+7x-60[/tex]Next, multiply the first and last term:
[tex]x^2\times-60=-60x^2[/tex]Pick factors of the product that add up to the middle term:
[tex]\begin{gathered} -60x^2=12x\text{ and -5x} \\ 12x-5x=7x \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} x^2+7x-60=x^2+12x-5x-60 \\ =x(x+12)-5(x+12) \\ =(x-5)(x+12) \end{gathered}[/tex]The factored form of the polynomial is (x-5)(x+12).
Note: A polynomial is prime if it cannot be factored. Since the example above can be factored, it is not prime.
