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Answer :
Sure! Let's factor the expression [tex]\(10x^3 - 25x^2 - 2x + 5\)[/tex] by grouping.
1. Group the terms:
Start by grouping the terms into two pairs:
[tex]\[
(10x^3 - 25x^2) + (-2x + 5)
\][/tex]
2. Factor out the greatest common factor (GCF) in each group:
- For the first group [tex]\(10x^3 - 25x^2\)[/tex], the GCF is [tex]\(5x^2\)[/tex]. Factor it out:
[tex]\[
5x^2(2x - 5)
\][/tex]
- For the second group [tex]\(-2x + 5\)[/tex], the GCF is [tex]\(-1\)[/tex]. Factor it out:
[tex]\[
-1(2x - 5)
\][/tex]
3. Rewrite the expression with factored groups:
After factoring, we have:
[tex]\[
5x^2(2x - 5) - 1(2x - 5)
\][/tex]
4. Factor by grouping common terms:
Notice that [tex]\((2x - 5)\)[/tex] is a common factor in both groups. Factor it out:
[tex]\[
(2x - 5)(5x^2 - 1)
\][/tex]
So, the factored form of the expression [tex]\(10x^3 - 25x^2 - 2x + 5\)[/tex] is:
[tex]\[
(2x - 5)(5x^2 - 1)
\][/tex]
That's the result! If you have any more questions, feel free to ask!
1. Group the terms:
Start by grouping the terms into two pairs:
[tex]\[
(10x^3 - 25x^2) + (-2x + 5)
\][/tex]
2. Factor out the greatest common factor (GCF) in each group:
- For the first group [tex]\(10x^3 - 25x^2\)[/tex], the GCF is [tex]\(5x^2\)[/tex]. Factor it out:
[tex]\[
5x^2(2x - 5)
\][/tex]
- For the second group [tex]\(-2x + 5\)[/tex], the GCF is [tex]\(-1\)[/tex]. Factor it out:
[tex]\[
-1(2x - 5)
\][/tex]
3. Rewrite the expression with factored groups:
After factoring, we have:
[tex]\[
5x^2(2x - 5) - 1(2x - 5)
\][/tex]
4. Factor by grouping common terms:
Notice that [tex]\((2x - 5)\)[/tex] is a common factor in both groups. Factor it out:
[tex]\[
(2x - 5)(5x^2 - 1)
\][/tex]
So, the factored form of the expression [tex]\(10x^3 - 25x^2 - 2x + 5\)[/tex] is:
[tex]\[
(2x - 5)(5x^2 - 1)
\][/tex]
That's the result! If you have any more questions, feel free to ask!
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