Question
Factor the polynomial. \[ 24 c y-12 c x-12 a y+6 a x \]
Ask by Huff Norton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The factored form of the polynomial is \(6(2c - a)(2y - x)\).
Solution
To factor the polynomial \( 24c y - 12c x - 12a y + 6a x \), follow these steps:
1. **Factor by Grouping:**
Group the terms in pairs:
\[
(24c y - 12c x) + (-12a y + 6a x)
\]
2. **Factor Out the Greatest Common Factor (GCF) from Each Group:**
- From the first group \(24c y - 12c x\), factor out \(12c\):
\[
12c(2y - x)
\]
- From the second group \(-12a y + 6a x\), factor out \(6a\):
\[
6a(-2y + x) = -6a(2y - x)
\]
3. **Combine the Factored Groups:**
\[
12c(2y - x) - 6a(2y - x)
\]
4. **Factor Out the Common Binomial Factor \((2y - x)\):**
\[
(2y - x)(12c - 6a)
\]
5. **Factor Out the Numerical GCF from the Remaining Terms:**
\[
(2y - x) \cdot 6(2c - a) = 6(2c - a)(2y - x)
\]
**Final Factored Form:**
\[
6(2c - a)(2y - x)
\]
Answer: After factoring, the expression is 6 ( 2 c – a ) multiplied by (2 y – x). Thus,
6(2c−a)(2y−x)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To factor the polynomial \( 24 c y - 12 c x - 12 a y + 6 a x \), we start by grouping the terms: \[ (24 cy - 12 cx) + (-12 ay + 6 ax). \] Now, we can factor out the common factors from each group: 1. From the first group \( 24 cy - 12 cx \), we can factor out \( 12c \): \[ 12c(2y - x). \] 2. From the second group \( -12 ay + 6 ax \), we can factor out \( -6a \): \[ -6a(2y - x). \] Now, we can rewrite the polynomial as: \[ 12c(2y - x) - 6a(2y - x). \] Since both terms contain the common factor \( (2y - x) \), we can factor that out: \[ (2y - x)(12c - 6a). \] Thus, the factored form of the polynomial is: \[ (2y - x)(12c - 6a). \]
