Question

# Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although 20x^{3} appears in both 20x^{3} + 8x^{2} and 20x^{3} + 10x, I’ll need to factor 20x^{3} in different ways to obtain each polynomial’s factorization?

Polynomial factorization
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $$20x^{3}$$ appears in both $$20x^{3} + 8x^{2} and 20x^{3} + 10x$$, I’ll need to factor $$20x^{3}$$ in different ways to obtain each polynomial’s factorization?

2020-12-25
Step 1
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $$20x^{3}$$ appears in both $$20x^{3} + 8x^{2}$$ and $$20x^{3} + 10x$$, I’ll need to factor $$20x^{3}$$ in different ways to obtain each polynomial’s factorization?
Step 2
We are given two expressions:
$$20x^{3} + 8x^{2}$$
and $$20x^{3} + 10x$$
if we factorize them,
$$20x^{3} + 8x^{2} =4x^{2}(5x+2)$$
and $$20x^{3} + 10x = 10x(2x^{2}+1)$$
We see that factorization depends on each term of the expression, so although both expressions contain one common term, because of the other term both have different ways.