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[k^(2),1-k,-7]

$\left[k^{2}, 1-k,-7\right]$

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Factor by grouping

Full solution

Q.

\left[k^{2}, 1-k,-7\right]

Write Polynomial Correctly: First, let's write down the polynomial correctly, it should be $k^2 - k - 7$ .
Find Two Numbers: Now, we need to find two numbers that multiply to $-7$ (the constant term) and add up to $-1$ (the coefficient of the middle term $k$ ).
Identify Numbers: The numbers that work are $-7$ and $1$ because $-7 \times 1 = -7$ and $-7 + 1 = -1$ .
Write Polynomial Expression: So, we can write the polynomial as $k^2 + 1k - 7k - 7$ .
Factor by Grouping: Next, we factor by grouping. Group the first two terms together and the last two terms together: $k^2 + 1k$ + $-7k - 7$ .
Factor Out Common Factors: Factor out a $k$ from the first group and a $-7$ from the second group: $k(k + 1) - 7(k + 1)$ .
Final Factored Form: Since both groups contain the factor $(k + 1)$ , we can factor that out: $(k + 1)(k - 7)$ .

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