Question

factorization of quadratic polynomials​

Answer 1

Step-by-step explanation:

Factoring x^2-21x+90

The first term is, x2 its coefficient is 1 .

The middle term is, -21x its coefficient is -21 .

The last term, "the constant", is +90

Step-1 : Multiply the coefficient of the first term by the constant 1 • 90 = 90

Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -21 .

-90 + -1 = -91

-45 + -2 = -47

-30 + -3 = -33

-18 + -5 = -23

-15 + -6 = -21 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -6

x2 - 15x - 6x - 90

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-15)

Add up the last 2 terms, pulling out common factors :

6 • (x-15)

Step-5 : Add up the four terms of step 4 :

(x-6) • (x-15)

Which is the desired factorization

Equation at the end of step 1 :

(x - 6) • (x - 15) = 0

so,X= 6

X= 15

Answer 2

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