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Answer :
To factor the expression [tex]\(5x^3 + 25x^2\)[/tex] by the greatest common factor (GCF), we can follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Look at the terms in the expression: [tex]\(5x^3\)[/tex] and [tex]\(25x^2\)[/tex].
- The coefficients are 5 and 25. The GCF of 5 and 25 is 5.
- The variable parts are [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex]. The GCF of [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] is [tex]\(x^2\)[/tex], since [tex]\(x^2\)[/tex] is the highest power of [tex]\(x\)[/tex] that divides both [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- The GCF of the expression is [tex]\(5x^2\)[/tex].
- Factor [tex]\(5x^2\)[/tex] out of each term:
- From the first term: [tex]\(5x^3 ÷ 5x^2 = x\)[/tex].
- From the second term: [tex]\(25x^2 ÷ 5x^2 = 5\)[/tex].
3. Write the factored expression:
- After factoring out the GCF, the expression becomes:
[tex]\[5x^2(x + 5)\][/tex]
So, the expression [tex]\(5x^3 + 25x^2\)[/tex] factors to [tex]\(5x^2(x + 5)\)[/tex].
1. Identify the Greatest Common Factor (GCF):
- Look at the terms in the expression: [tex]\(5x^3\)[/tex] and [tex]\(25x^2\)[/tex].
- The coefficients are 5 and 25. The GCF of 5 and 25 is 5.
- The variable parts are [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex]. The GCF of [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] is [tex]\(x^2\)[/tex], since [tex]\(x^2\)[/tex] is the highest power of [tex]\(x\)[/tex] that divides both [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Factor out the GCF:
- The GCF of the expression is [tex]\(5x^2\)[/tex].
- Factor [tex]\(5x^2\)[/tex] out of each term:
- From the first term: [tex]\(5x^3 ÷ 5x^2 = x\)[/tex].
- From the second term: [tex]\(25x^2 ÷ 5x^2 = 5\)[/tex].
3. Write the factored expression:
- After factoring out the GCF, the expression becomes:
[tex]\[5x^2(x + 5)\][/tex]
So, the expression [tex]\(5x^3 + 25x^2\)[/tex] factors to [tex]\(5x^2(x + 5)\)[/tex].
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