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## Ask AI on The Internet

Question: factor k²-13k+40

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To factor the quadratic expression $$k^2 - 13k + 40$$, you want to find two numbers that multiply to 40 and add up to -13. Here's how you can do that step-by-step: 1. **Write down the quadratic expression:** $$k^2 - 13k + 40$$ 2. **Identify a, b, and c:** In this quadratic expression, $$a = 1$$, $$b = -13$$, and $$c = 40$$. 3. **Find two numbers that multiply to ac and add to b:** We are looking for two numbers that multiply to $$40 \times 1 = 40$$ and add up to $$-13$$. After examining pairs of factors, we find that the pair $$-8$$ and $$-5$$ fits: $(-8) \cdot (-5) = 40$ $(-8) + (-5) = -13$ 4. **Rewrite the middle term using these numbers:** Rewrite $$-13k$$ as $$-8k - 5k$$: $k^2 - 8k - 5k + 40$ 5. **Factor by grouping:** Group the terms to factor by grouping: $(k^2 - 8k) + (-5k + 40)$ Factor out the greatest common factor (GCF) from each group: $k(k - 8) - 5(k - 8)$ 6. **Factor out the common binomial factor:** $(k - 8)(k - 5)$ So, the factored form of $$k^2 - 13k + 40$$ is: $(k - 8)(k - 5)$

May 24, 2024, 6:03 a.m.

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