Noahlumadue31idn
Answered

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Assignment: Factor [tex]$20x^2 + 25x - 12x - 15$[/tex] by grouping.

1. Group terms with common factors.
2. Factor the GCF from each group.

[tex]
\begin{array}{l}
\left(20x^2 - 12x\right) + \left(25x - 15\right) \\
4x(5x - 3) + 5(5x - 3) \\
(5x - 3)(4x + 5)
\end{array}
[/tex]

3. Write the polynomial as a product of binomials.

Sagot :

GinnyAnsweridn
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]
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