If (x+1) is a factor of x³ + 2x² - 5x - 6, find the other factors us

1.	If (x+1) is a factor of x³ + 2x² - 5x - 6, find the other factors using long division.
Answer» ANSWER: Let F(x)=x 3 −2x 2 −5x+6 ⇒f(1)=1 3 −21 2 −5×1+6=1−2−5+6=0 Using synthetic DIVISION, we have x 2 −x−6=0 is the other FACTOR (x−1)(x 2 −x−6)=0 =(x−1)(x 2 −3x+2x−6)=0 =(x−1)(x(x−3)+2(x−3))=0 =(x−1)(x+2)(x−3) are the factors of f(x)

If (x+1) is a factor of x³ + 2x² - 5x - 6, find the other factors using long division.

Answer»

Let F(x)=x

−2x

−5x+6

⇒f(1)=1

−21

−5×1+6=1−2−5+6=0

Using synthetic DIVISION, we have

−x−6=0 is the other FACTOR

(x−1)(x

−x−6)=0

=(x−1)(x

−3x+2x−6)=0

=(x−1)(x(x−3)+2(x−3))=0

=(x−1)(x+2)(x−3) are the factors of f(x)