factor the following trinomial. 4x^2 - 13x + 10 (4x - ?)(x - )

Answer

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply 4 (leading coefficient of $4x^{2}$) and 10 (constant term), $4\times10 = 40$.

Step2: Find two numbers

Find two numbers that multiply to 40 and add up to 13 (coefficient of the middle - term with sign considered). The numbers are 8 and 5 since $8\times5=40$ and $8 + 5=13$.

Step3: Rewrite the middle - term

Rewrite $-13x$ as $-8x-5x$. So, $4x^{2}-13x + 10=4x^{2}-8x-5x + 10$.

Step4: Group the terms

Group the terms: $(4x^{2}-8x)+(-5x + 10)$.

Step5: Factor out the GCF from each group

From the first group $4x^{2}-8x$, the GCF is $4x$, so $4x^{2}-8x=4x(x - 2)$. From the second group $-5x + 10$, the GCF is $-5$, so $-5x + 10=-5(x - 2)$.

Step6: Factor out the common binomial factor

We have $4x(x - 2)-5(x - 2)=(4x - 5)(x - 2)$.

Answer:

$(4x - 5)(x - 2)$