Question

One of the factors of the polynomial x3 + 5x2 + 6x is (x2 + 3x). What is the other factor? x − 2 x + 2 x + 1 x − 1

Answer 1

to find the other factor you are going to need to divide the polynomial by the factor it gave

`( {x}^(3) + 5 {x}^(2) + 6x) / ( {x}^(2) + 3x)`

I do not have a pen and paper nearby to explain how to divide polynomials but if you leave a comment saying you don't know how I will explain it to you.
after dividing you get the answer x+2

Answer 2

Option B ( x+2)

Explanation:

The given polynomial is ( x³ + 5x² + 6x )

Now we will factorize the polynomial.

( x³ + 5x² + 6x ) = x³ + 3x² + 2x² + 6x

= x ( x² + 3x ) + 2 ( x² + 3x )

= ( x² + 3x ) ( x + 2 )

As one factor is already given as ( x² + 3x )

Therefore, other factor will be ( x+ 2)

Option B ( x+2) is the answer.