Question

Show that X + 1 X - 2 and X + 3 are the factors of the polynomial p x = 2 x cube + 2 x square - 5 x minus 6

Answer 1

Step-by-step explanation:

Given, (x−2) , (x+3) and (x−4) are factors of polynomial x3−3x2−10x+24.

Then, f(x)=x3−3x2−10x+24.

If (x−2) is a factor, then  x−2=0⟹x=2.

Replace x by 2, we get,

f(2)=(2)3−3(2)2−10(2)+24

f(2)=8−12−20+24

f(2)=0.

The value of f(2) is zero.

Then (x−2) is the factor of  the polynomial x3−3x2−10x+24.

If (x+3) is factor, then x+3=0⟹x=−3.

Replace x by −3, we get,

f(−3)=(−3)3−3(−3)2−10(−3)+24

f(−3)=−27−27+30+24

f(−3)=0.

The value of f(−3) is zero.

Then (x+3) is the factor of the polynomial x3−