Answer to Question #243129 in Algebra for enKay

Question #243129

A)

The polynomial g(X)=3x^3-2x^2-12x+8


(I) using the factor theorem, show that (X+2) is a factor of g(X)


(II) factorize g(X) completely


1
Expert's answer
2021-09-28T14:42:22-0400

(i)


x+2=0=>x=2x+2=0=>x=-2

g(2)=3(2)32(2)212(2)+8g(-2)=3(-2)^3-2(-2)^2-12(-2)+8

=248+24+8=0=-24-8+24+8=0

Since g(2)=0,g(-2)=0, then by thefactor theorem (x+2)(x+2) is a factor of g(x).g(x).


(ii)


g(x)=3x32x212x+8g(x)=3x^3-2x^2-12x+8

=3x2(x+2)8x(x+2)+4(x+2)=3x^2(x+2)-8x(x+2)+4(x+2)

=(x+2)(3x28x+4)=(x+2)(3x^2-8x+4)

=(x+2)(3x(x2)2(x2))=(x+2)(3x(x-2)-2(x-2))

=(x+2)(x2)(3x2)=(x+2)(x-2)(3x-2)


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment