Question

x²-x-56=0 find the zeros by splitting the middle term
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Answer 1

Answer:

1.1 Factoring x2-x-56

The first term is, x2 its coefficient is 1 .

The middle term is, -x its coefficient is -1 .

The last term, "the constant", is -56

Step-1 : Multiply the coefficient of the first term by the constant 1 • -56 = -56

Step-2 : Find two factors of -56 whose sum equals the coefficient of the middle term, which is -1 .

-56 + 1 = -55

-28 + 2 = -26

-14 + 4 = -10

-8 + 7 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 7

x2 - 8x + 7x - 56

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

x • (x-8)

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

7 • (x-8)

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

(x+7) • (x-8)

Which is the desired factorization

zero of polynomial are -7 and 8

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Answer 2

${x}^{2} - x - 56 = 0 \\ {x}^{2} - 8x + 7x - 56= 0 \\ x(x - 8) + 7(x - 8) = 0 \\ (x + 7)(x - 8) = 0 \\ x + 7 = 0 \: \: \: \: x - 8 = 0 \\ x = - 7 \: \: \: \: x = 8$