Question

Using factor theorem, factorize each of the following polynomial:
y³-2y²-29y-42

Answer 1

The factorised given polynomial is $y^3-2y^2-29y-42=(y+2)(y+3)(y-7)$

Step-by-step explanation:

Given that the polynomial $y^3-2y^2-29y-42$

To factorise the given polynomial  :

Let f(y) be the given polynomial

$f(y)=y^3-2y^2-29y-42$

By using the Factor theorem here

• Put y=-2 in the polynomial f(y) we get

$f(-2)=(-2)^3-2(-2)^2-29(-2)-42$

$=-8-8+58-42$

$=58-58$

$=0$

$f(-2)=0$

Therefore y+2 is a factor and it satisfies the given polynomial.( by factor theorem )                                  

• Put y=-3 in f(y)  

$f(-3)=(-3)^3-2(-3)^2-29(-3)-42$

$=-27-18+87-42$

$=87-87$

$=0$

$f(-3)=0$

Therefore y+3 is a factor and it satisfies the given polynomial.( by factor theorem )

• Put y=7 in f(y)

$f(7)=(7)^3-2(7)^2-29(7)-42$

$=343-98-203-42$

$=343-343$

$=0$

$f(7)=0$

Therefore y-7 is a factor and it satisfies the given polynomial.( by factor theorem )

Therefore the factors are y+2,y+3,y-7

The factorised given polynomial is $y^3-2y^2-29y-42=(y+2)(y+3)(y-7)$