Question

Find x²-11x+42 as difference of two squares
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Answer 1

Factoring x2-11x-42

The first term is, x2 its coefficient is 1 .

The middle term is, -11x its coefficient is -11 .

The last term, "the constant", is -42

Step-1 : Multiply the coefficient of the first term by the constant 1 • -42 = -42

Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -11 .

-42 + 1 = -41

-21 + 2 = -19

-14 + 3 = -11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 3

x2 - 14x + 3x - 42

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

x • (x-14)

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

3 • (x-14)

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

(x+3) • (x-14)

Which is the desired factorization

Equation at the end of step

1

:

(x + 3) • (x - 14) = 0