To factor [tex]\(20x^2 + 25x - 12x - 15\)[/tex] by grouping, follow these steps:
### Step 1: Group terms with common factors
First, we can rewrite the polynomial by grouping terms with common factors:
[tex]\[
(20x^2 - 12x) + (25x - 15)
\][/tex]
### Step 2: Factor the Greatest Common Factor (GCF) from each group
Next, we factor out the GCF from each group separately.
- For the first group [tex]\((20x^2 - 12x)\)[/tex]:
- The coefficients are 20 and -12. The GCF of 20 and -12 is 4.
- Factor out the GCF and we get: [tex]\(4x(5x - 3)\)[/tex]
- For the second group [tex]\((25x - 15)\)[/tex]:
- The coefficients are 25 and -15. The GCF of 25 and -15 is 5.
- Factor out the GCF and we get: [tex]\(5(5x - 3)\)[/tex]
So, the expression now looks like:
[tex]\[
4x(5x - 3) + 5(5x - 3)
\][/tex]
### Step 3: Factor out the common binomial
Observe that [tex]\((5x - 3)\)[/tex] is a common factor in both terms, so we can factor out [tex]\((5x - 3)\)[/tex]:
[tex]\[
(5x - 3)(4x + 5)
\][/tex]
Thus, the polynomial [tex]\(20x^2 + 25x - 12x - 15\)[/tex] can be factored as:
[tex]\[
(5x - 3)(4x + 5)
\][/tex]
