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Answer :
To factor the trinomial [tex]\(2x^5 + 28x^4 + 66x^3\)[/tex], we start by finding the greatest common factor (GCF) of all the terms.
1. Identify the GCF of the coefficients:
- The coefficients of the terms are 2, 28, and 66.
- The GCF of 2, 28, and 66 is 2, as it is the largest number that divides all three coefficients.
2. Identify the smallest power of [tex]\(x\)[/tex]:
- The powers of [tex]\(x\)[/tex] in the terms are 5, 4, and 3.
- The smallest power is [tex]\(x^3\)[/tex].
3. Factor out the GCF and the smallest power of [tex]\(x\)[/tex]:
- The GCF of the entire expression is [tex]\(2x^3\)[/tex].
- We factor [tex]\(2x^3\)[/tex] out of each term:
[tex]\[
2x^5 + 28x^4 + 66x^3 = 2x^3(x^2) + 2x^3(14x) + 2x^3(33)
\][/tex]
4. Write the factored expression:
[tex]\[
2x^5 + 28x^4 + 66x^3 = 2x^3(x^2 + 14x + 33)
\][/tex]
So, the factored expression is [tex]\(2x^3(x^2 + 14x + 33)\)[/tex].
1. Identify the GCF of the coefficients:
- The coefficients of the terms are 2, 28, and 66.
- The GCF of 2, 28, and 66 is 2, as it is the largest number that divides all three coefficients.
2. Identify the smallest power of [tex]\(x\)[/tex]:
- The powers of [tex]\(x\)[/tex] in the terms are 5, 4, and 3.
- The smallest power is [tex]\(x^3\)[/tex].
3. Factor out the GCF and the smallest power of [tex]\(x\)[/tex]:
- The GCF of the entire expression is [tex]\(2x^3\)[/tex].
- We factor [tex]\(2x^3\)[/tex] out of each term:
[tex]\[
2x^5 + 28x^4 + 66x^3 = 2x^3(x^2) + 2x^3(14x) + 2x^3(33)
\][/tex]
4. Write the factored expression:
[tex]\[
2x^5 + 28x^4 + 66x^3 = 2x^3(x^2 + 14x + 33)
\][/tex]
So, the factored expression is [tex]\(2x^3(x^2 + 14x + 33)\)[/tex].
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