Question

factor completely.
$5x^{2}-7x + 2$
answer
attempt 1 out of 2

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $x^{2}$ (which is 5) and the constant term (which is 2). So, $5\times2 = 10$.

Step2: Find two - numbers

Find two numbers that multiply to 10 and add up to - 7. The numbers are - 5 and - 2 since $(-5)\times(-2)=10$ and $-5+( - 2)=-7$.

Step3: Rewrite the middle term

Rewrite the middle term $-7x$ as $-5x-2x$. So, $5x^{2}-7x + 2=5x^{2}-5x-2x + 2$.

Step4: Group the terms

Group the terms: $(5x^{2}-5x)+(-2x + 2)$.

Step5: Factor out the GCF from each group

Factor out the greatest - common factor (GCF) from each group. From the first group $5x^{2}-5x$, the GCF is $5x$, so $5x^{2}-5x = 5x(x - 1)$. From the second group $-2x + 2$, the GCF is - 2, so $-2x + 2=-2(x - 1)$.

Step6: Factor out the common binomial factor

We now have $5x(x - 1)-2(x - 1)$. Factor out the common binomial factor $(x - 1)$: $(x - 1)(5x-2)$.

Answer:

$(x - 1)(5x - 2)$