How do you factor: \( k^2 - 13k + 40 \)?

The factored form of the expression k² - 13k + 40 is (k - 5)(k - 8).
We have,
To factor the quadratic expression k² - 13k + 40, you can look for two numbers that multiply to give the constant term (40) and add up to the coefficient of the linear term (-13).
In this case, the two numbers are -5 and -8.
Now, rewrite the middle term (-13k) using these two numbers:
k² - 5k - 8k + 40
Next, group the terms and factors by grouping:
(k² - 5k) + (-8k + 40)
Take out the common factors from each group:
k(k - 5) - 8(k - 5)
Now, you can see that there is a common binomial factor, (k - 5), in both terms.
Factor it out:
(k - 5)(k - 8)
Therefore,
The factored form of k² - 13k + 40 is (k - 5)(k - 8).
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Answered by swapnalimalwadeVT | 2024-06-17

k 2 − 13 k + 40 = k 2 − 5 k − 8 k + 40 = k ( k − 5 ) − 8 ( k − 5 ) = = ( k − 5 ) ( k − 8 )

Answered by kate200468 | 2024-06-24

The quadratic expression k 2 − 13 k + 40 can be factored as ( k − 8 ) ( k − 5 ) by identifying two numbers that multiply to 40 and add up to -13. These numbers are -8 and -5. By regrouping and factoring, we arrive at the solution.
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Answered by kate200468 | 2024-12-26