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Answer :
Sure! Let's factor the expression [tex]\(20x^3 - 25x^2 + 4x - 5\)[/tex] by grouping.
1. Group the Terms:
We start by grouping the terms in pairs:
[tex]\[
(20x^3 - 25x^2) + (4x - 5)
\][/tex]
2. Factor Each Group:
- First Group: [tex]\(20x^3 - 25x^2\)[/tex]
- The greatest common factor (GCF) of [tex]\(20x^3\)[/tex] and [tex]\(25x^2\)[/tex] is [tex]\(5x^2\)[/tex].
- Factoring out [tex]\(5x^2\)[/tex], we get:
[tex]\[
5x^2(4x - 5)
\][/tex]
- Second Group: [tex]\(4x - 5\)[/tex]
- There is no common factor other than 1, so we factor out 1:
[tex]\[
1(4x - 5)
\][/tex]
3. Factor the Common Binomial:
- Both groups contain the common binomial factor [tex]\((4x - 5)\)[/tex].
- We can factor [tex]\((4x - 5)\)[/tex] out of the expression:
[tex]\[
(4x - 5)(5x^2 + 1)
\][/tex]
So, the factored form of the expression [tex]\(20x^3 - 25x^2 + 4x - 5\)[/tex] is [tex]\((4x - 5)(5x^2 + 1)\)[/tex].
1. Group the Terms:
We start by grouping the terms in pairs:
[tex]\[
(20x^3 - 25x^2) + (4x - 5)
\][/tex]
2. Factor Each Group:
- First Group: [tex]\(20x^3 - 25x^2\)[/tex]
- The greatest common factor (GCF) of [tex]\(20x^3\)[/tex] and [tex]\(25x^2\)[/tex] is [tex]\(5x^2\)[/tex].
- Factoring out [tex]\(5x^2\)[/tex], we get:
[tex]\[
5x^2(4x - 5)
\][/tex]
- Second Group: [tex]\(4x - 5\)[/tex]
- There is no common factor other than 1, so we factor out 1:
[tex]\[
1(4x - 5)
\][/tex]
3. Factor the Common Binomial:
- Both groups contain the common binomial factor [tex]\((4x - 5)\)[/tex].
- We can factor [tex]\((4x - 5)\)[/tex] out of the expression:
[tex]\[
(4x - 5)(5x^2 + 1)
\][/tex]
So, the factored form of the expression [tex]\(20x^3 - 25x^2 + 4x - 5\)[/tex] is [tex]\((4x - 5)(5x^2 + 1)\)[/tex].
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