Answer :
Sure, let's factor the expression [tex]\(2 x^6 + 32 x^4\)[/tex] step-by-step.
Step 1: Identify the greatest common factor (GCF) of the terms in the expression.
- The terms in the expression are [tex]\(2 x^6\)[/tex] and [tex]\(32 x^4\)[/tex].
- The GCF of the coefficients [tex]\(2\)[/tex] and [tex]\(32\)[/tex] is [tex]\(2\)[/tex].
- The GCF of the variables [tex]\(x^6\)[/tex] and [tex]\(x^4\)[/tex] is [tex]\(x^4\)[/tex].
So, we can factor out [tex]\(2 x^4\)[/tex] from the expression.
Step 2: Factor out the GCF from each term in the expression.
- When we factor [tex]\(2 x^4\)[/tex] out of [tex]\(2 x^6\)[/tex], we get [tex]\(2 x^4 \cdot x^2\)[/tex].
- When we factor [tex]\(2 x^4\)[/tex] out of [tex]\(32 x^4\)[/tex], we get [tex]\(2 x^4 \cdot 16\)[/tex].
Therefore, factoring out [tex]\(2 x^4\)[/tex], we get:
[tex]\[2 x^6 + 32 x^4 = 2 x^4 (x^2 + 16)\][/tex]
So, the factored form of the expression [tex]\(2 x^6 + 32 x^4\)[/tex] is:
[tex]\[2 x^4 (x^2 + 16)\][/tex]
Step 1: Identify the greatest common factor (GCF) of the terms in the expression.
- The terms in the expression are [tex]\(2 x^6\)[/tex] and [tex]\(32 x^4\)[/tex].
- The GCF of the coefficients [tex]\(2\)[/tex] and [tex]\(32\)[/tex] is [tex]\(2\)[/tex].
- The GCF of the variables [tex]\(x^6\)[/tex] and [tex]\(x^4\)[/tex] is [tex]\(x^4\)[/tex].
So, we can factor out [tex]\(2 x^4\)[/tex] from the expression.
Step 2: Factor out the GCF from each term in the expression.
- When we factor [tex]\(2 x^4\)[/tex] out of [tex]\(2 x^6\)[/tex], we get [tex]\(2 x^4 \cdot x^2\)[/tex].
- When we factor [tex]\(2 x^4\)[/tex] out of [tex]\(32 x^4\)[/tex], we get [tex]\(2 x^4 \cdot 16\)[/tex].
Therefore, factoring out [tex]\(2 x^4\)[/tex], we get:
[tex]\[2 x^6 + 32 x^4 = 2 x^4 (x^2 + 16)\][/tex]
So, the factored form of the expression [tex]\(2 x^6 + 32 x^4\)[/tex] is:
[tex]\[2 x^4 (x^2 + 16)\][/tex]
