factor the quadratic expression completely.\n$2x^{2}-13x + 20=$

Answer

Explanation:

Step1: Multiply leading - coefficient and constant

For the quadratic $2x^{2}-13x + 20$, the leading - coefficient $a = 2$ and the constant $c = 20$. So $ac=2\times20 = 40$.

Step2: Find two numbers that multiply to $ac$ and add to the middle coefficient

We need two numbers that multiply to $40$ and add to $- 13$. The numbers are $-8$ and $-5$ since $(-8)\times(-5)=40$ and $-8+( - 5)=-13$.

Step3: Rewrite the middle term

Rewrite $-13x$ as $-8x-5x$. So $2x^{2}-13x + 20=2x^{2}-8x-5x + 20$.

Step4: Group the terms

Group the terms: $(2x^{2}-8x)+(-5x + 20)$.

Step5: Factor out the greatest common factor from each group

From the first group $2x^{2}-8x$, the GCF is $2x$, so $2x^{2}-8x=2x(x - 4)$. From the second group $-5x + 20$, the GCF is $-5$, so $-5x + 20=-5(x - 4)$.

Step6: Factor out the common binomial factor

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

Answer:

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