factor the quadratic expression completely.\n-3x^2 + 17x - 20 =

Answer:

$-(3x - 5)(x - 4)$

Explanation:

Step1: Factor out -1

$-1(3x^{2}-17x + 20)$

Step2: Multiply coefficients

For $3x^{2}-17x + 20$, $a = 3$, $c=20$, $ac=3\times20 = 60$.

Step3: Find two numbers

Find two numbers that multiply to 60 and add up to -17. The numbers are -12 and -5 since $(-12)\times(-5)=60$ and $-12+( - 5)=-17$.

Step4: Rewrite middle term

$3x^{2}-12x-5x + 20$

Step5: Group terms

$(3x^{2}-12x)+(-5x + 20)$

Step6: Factor each group

$3x(x - 4)-5(x - 4)$

Step7: Factor out common factor

$(3x - 5)(x - 4)$

Step8: Combine with -1

$-1(3x - 5)(x - 4)=-(3x - 5)(x - 4)$