question\nfactor completely.\n5x² - 22x + 21

Explanation:

Step1: Multiply coefficient of $x^{2}$ and constant

Multiply 5 and 21: $5\times21 = 105$.

Step2: Find two numbers for -22

We need two numbers that multiply to 105 and add up to -22. The numbers are -15 and -7 since $(-15)\times(-7)=105$ and $-15+( - 7)=-22$.

Step3: Rewrite the middle - term

Rewrite $-22x$ as $-15x-7x$: $5x^{2}-15x - 7x+21$.

Step4: Group the terms

Group the terms: $(5x^{2}-15x)+(-7x + 21)$.

Step5: Factor out the GCF from each group

Factor out 5x from the first group and -7 from the second group: $5x(x - 3)-7(x - 3)$.

Step6: Factor out the common binomial factor

Factor out $(x - 3)$: $(x - 3)(5x-7)$.

Answer:

$(x - 3)(5x-7)$