Completely factor the polynomial y=2x^{3}+3x^{2}+50x+75 given that x=\frac{-3}{2} is a

Josh Sizemore

Josh Sizemore

Answered question

2021-12-09

Completely factor the polynomial y=2x3+3x2+50x+75 given that x=32 is a zero.

Answer & Explanation

Karen Robbins

Karen Robbins

Beginner2021-12-10Added 49 answers

Step 1
Factorization is the process of splitting the expression into most simplest form. Most commonly, the term having least power is taken common from the whole expression and the simplification is done.
For example if the expression 5x2+5x is to be simplified, then the term having least power is 5x is taken common, thus the simplest form of the expression becomes 5x(x+1)
Step 2
The given polynomial is y=2x3+3x2+50x+75
Rearrange the term as below
y=2x3+3x2+50x+75
=2x3+50x+3x2+75...(i)
Step 3
Now take 2x common from (2x2+50x) term and 3 from 3x2+75
y=2x(x2+25)+3(x2+25)
=(2x+3)(x2+25)
The polynomial y=2x3+3x2+50x+75 is written in factor form as (2x+3)(x2+25) having 32 is zero.

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