Problem 104

Question

Use an example and explain how to factor out the greatest common factor of a polynomial.

Step-by-Step Solution

Verified

Answer

The factored form of the polynomial $12x^3 - 18x^2 + 6x$ after factoring out the GCF is $6x(2x^2 - 3x + 1)$.

1Step 1: Identify the polynomial

Let's look at the polynomial $12x^3 - 18x^2 + 6x$.

2Step 2: Find the greatest common factor

For $12x^3 - 18x^2 + 6x$, the numbers 12, 18, and 6 share a greatest common factor of 6. In terms of the variable $x$, the GCF is $x$, as it is common to all the terms.

3Step 3: Factoring out the greatest common factor

Divide each term of the polynomial by the GCF (which is $6x$). So, $12x^3$ divided by $6x$ gives $2x^2$, $-18x^2$ divided by $6x$ gives $-3x$, and $6x$ divided by $6x$ gives 1. This brings us to the factored form: $6x(2x^2 - 3x + 1)$.

Problem 104

Other exercises in this chapter

Problem 103

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm working with a polynomial that has a GCF other than \(1,

View solution

Problem 104

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$-10 a^{4} b^{2}+15 a^{3} b^{3}+25 a^{2} b^{4}$$

View solution

Problem 104

Factor completely. (Hint on Exercises $97-102$ : Factors contain rational numbers.) $$(x+2)^{2}-49$$

View solution

Problem 104

My graphing calculator showed the same graphs for $y_{1}=4 x^{2}-20 x+24 \quad$ and $\quad y_{2}=4\left(x^{2}-5 x+6\right), \quad$ so I can conclude that th

View solution