Question

lesson check
do you know how?

1. what is a simpler form of $6x(2x^3 + 7x)$?
2. what is the gcf of the terms in $4a^4 + 6a^2$?

factor each polynomial.

1. $6m^2 - 15m$
2. $4x^3 + 8x^2 + 12x$

Explanation:

Question 9

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\), here \(a = 6x\), \(b=2x^{3}\) and \(c = 7x\). So we have \(6x\times2x^{3}+6x\times7x\)

Step2: Multiply the coefficients and add the exponents of like bases

For the first term: \(6\times2 = 12\) and \(x\times x^{3}=x^{1 + 3}=x^{4}\), so the first term is \(12x^{4}\). For the second term: \(6\times7=42\) and \(x\times x=x^{1+1}=x^{2}\), so the second term is \(42x^{2}\)

Step1: Find GCF of coefficients

The coefficients are \(4\) and \(6\). The factors of \(4\) are \(1,2,4\) and factors of \(6\) are \(1,2,3,6\). The greatest common factor of \(4\) and \(6\) is \(2\)

Step2: Find GCF of variables

The variables are \(a^{4}\) and \(a^{2}\). The lowest power of \(a\) is \(a^{2}\)

Step3: Combine the GCF of coefficients and variables

The GCF is the product of GCF of coefficients and GCF of variables, so \(2\times a^{2}=2a^{2}\)

Step1: Find GCF of coefficients

Coefficients are \(6\) and \(15\). Factors of \(6\): \(1,2,3,6\); factors of \(15\): \(1,3,5,15\). GCF of \(6\) and \(15\) is \(3\)

Step2: Find GCF of variables

The variable terms are \(m^{2}\) and \(m\). The lowest power of \(m\) is \(m\)

Step3: Factor out the GCF

We factor out \(3m\) from \(6m^{2}-15m\). \(6m^{2}\div3m = 2m\) and \(- 15m\div3m=- 5\)

Answer:

\(12x^{4}+42x^{2}\)

Question 10