To factor the expression \( 50k^3 – 40k^2 + 75k – 60 \), we need to look for common factors and patterns. Here is how we can approach it:
1. **Group the terms**: Group the expression in pairs of terms to simplify it.
\[ 50k^3 – 40k^2 + 75k – 60 = (50k^3 – 40k^2) + (75k – 60) \]
2. **Factor each group**:
- For the first group, \( 50k^3 – 40k^2 \):
\[ 50k^3 – 40k^2 = 10k^2(5k – 4) \]
- For the second group, \( 75k – 60 \):
\[ 75k – 60 = 15(5k – 4) \]
3. **Rewrite the expression using these factorizations**:
\[ 50k^3 – 40k^2 + 75k – 60 = 10k^2(5k – 4) + 15(5k – 4) \]
4. **Factor out the common factor \((5k – 4)\)**:
\[ 50k^3 – 40k^2 + 75k – 60 = (10k^2 + 15)(5k – 4) \]
Now, we look for our possible answers:
- \((2k^2 + 15)(5k – 20)\)
- \(5(2k^2 + 3)(5k – 4)\)
- \(5(2k^2 – 3)(5k + 4)\)
- \((10k^2 – 3)(25k + 4)\)
The correct factorization, based on our work, is \((10k^2 + 15)(5k – 4)\). Although this exact form is not listed among the options, by factoring \(10\) out of each term in the factor \(10k^2 + 15\), we get:
\[ 10(k^2 + 1.5)(5k - 4) = 10( k^2 + 1.5)(5k - 4) \]
The closest option to our result initially taking common factor 5 from our factors \(10k^2 + 15\) indicate the solution is not directly matching our answer. But pattern from detailed factor's 10 is shown. We see \( 5(2k^2 + 3)(5k - 4) \) contains similar setup.
Thus correct likely answer rechecking:
\[ 5 (2k^2 + 3)(5k - 4) \]
By examining more calibrated,
upon reviewing correction demonstrates: \(10k^2+15\) translates directly to clarify relatable near option \( 10 considering corrections, regardless exact pair discrepancy solve analysis proven it's \( 5 (2k^2 + 3)(5k -4)\) On scope review.
Thus stated likely \( 5 (2k^2 + 3)(5k - 4)) \ math confirming .
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Feel corrections reviewed-choose comprehend method always cross-verify requisite pattern numeric breakdown facet assumptions thus correct provided terms \(5(2k^2+3)(5k-4)\),
3.
Factor the expression.
50k3 – 40k2 + 75k – 60
(2k2 + 15)(5k – 20)
5(2k2 + 3)(5k – 4)
5(2k2 – 3)(5k + 4)
(10k2 – 3)(25k + 4)
1 answer