Question

factor trinomials (a = 1)
score: 1/2 penalty: 1 off
question
factor.
x^2 - 6x - 7
answer attempt 1 out of 2
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Explanation:

Step1: Find two numbers

We need two numbers that multiply to - 7 (the constant term) and add up to - 6 (the coefficient of the x - term). The numbers are - 7 and 1 since (-7)×1=-7 and - 7 + 1=-6.

Step2: Rewrite the trinomial

Rewrite $x^{2}-6x - 7$ as $x^{2}-7x+x - 7$.

Step3: Group the terms

Group the terms: $(x^{2}-7x)+(x - 7)$.

Step4: Factor out the GCF from each group

Factor out the greatest - common factor (GCF) from each group. From $x^{2}-7x$, the GCF is x, so we get $x(x - 7)$. From $x - 7$, the GCF is 1. So, $(x^{2}-7x)+(x - 7)=x(x - 7)+1(x - 7)$.

Step5: Factor out the common binomial factor

Factor out the common binomial factor $(x - 7)$: $(x - 7)(x + 1)$.

Answer:

$(x - 7)(x + 1)$