Answer :
To factor the expression [tex]\(63x^3 - 45x^2 + 28x - 20\)[/tex] by grouping, follow these steps:
1. Group the terms:
Divide the expression into two groups:
[tex]\((63x^3 - 45x^2)\)[/tex] and [tex]\((28x - 20)\)[/tex].
2. Factor out the greatest common factor (GCF) from each group:
- In the first group [tex]\(63x^3 - 45x^2\)[/tex], the GCF is [tex]\(9x^2\)[/tex]. Factoring it out gives:
[tex]\[
9x^2(7x - 5)
\][/tex]
- In the second group [tex]\(28x - 20\)[/tex], the GCF is 4. Factoring it out gives:
[tex]\[
4(7x - 5)
\][/tex]
3. Factor out the common binomial factor:
- Now, notice that each group contains the common factor [tex]\((7x - 5)\)[/tex]. Factoring [tex]\((7x - 5)\)[/tex] out of the entire expression gives:
[tex]\[
(7x - 5)(9x^2 + 4)
\][/tex]
So the expression [tex]\(63x^3 - 45x^2 + 28x - 20\)[/tex] factors to [tex]\((7x - 5)(9x^2 + 4)\)[/tex].
1. Group the terms:
Divide the expression into two groups:
[tex]\((63x^3 - 45x^2)\)[/tex] and [tex]\((28x - 20)\)[/tex].
2. Factor out the greatest common factor (GCF) from each group:
- In the first group [tex]\(63x^3 - 45x^2\)[/tex], the GCF is [tex]\(9x^2\)[/tex]. Factoring it out gives:
[tex]\[
9x^2(7x - 5)
\][/tex]
- In the second group [tex]\(28x - 20\)[/tex], the GCF is 4. Factoring it out gives:
[tex]\[
4(7x - 5)
\][/tex]
3. Factor out the common binomial factor:
- Now, notice that each group contains the common factor [tex]\((7x - 5)\)[/tex]. Factoring [tex]\((7x - 5)\)[/tex] out of the entire expression gives:
[tex]\[
(7x - 5)(9x^2 + 4)
\][/tex]
So the expression [tex]\(63x^3 - 45x^2 + 28x - 20\)[/tex] factors to [tex]\((7x - 5)(9x^2 + 4)\)[/tex].
