Answer:
C. [tex](-7x+60)(x+4)[/tex]
Step-by-step explanation:
Consider the expression [tex]-7x^2+32x+240.[/tex]
First, note that
[tex]a=-7\\ \\b=32\\ \\c=240[/tex]
Find the discriminant
[tex]D=b^2-4ac=32^2-4\cdot (-7)\cdot 240=1,024+6,720=7,744\\ \\\sqrt{D}=\sqrt{7,744}=88[/tex]
Now,
[tex]x_1=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-32+88}{2\cdot (-7)}=-4\\ \\x_2=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-32-88}{2\cdot (-7)}=\dfrac{60}{7}[/tex]
Write the factored form:
[tex]-7x^2+32x+240=-7(x-(-4))\left(x-\dfrac{60}{7}\right)=(x+4)(-7x+60)[/tex]
