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kirill115 [55]
3 years ago
11

X^3 + 5x^2 - 8x^2 - 40x + 7x + 35

Mathematics
1 answer:
Temka [501]3 years ago
3 0

Remark

x - 1 is a root.

Proof

x - 1 = 0

x =  1

(1)^3 + 5(1)^2 - 8(1)^2 - 40(1) + 7(1) + 35

1 + 5 - 8 - 40 + 7 + 35

6 + 7 + 35 - 48 = 0

Solution

Divide x - 1 into the original equation.

x^3 + 5x^2 - 8x^2 - 33x + 35

x - 1 || x^3 - 3x^2  - 33x + 35  || x^2 - 2x  - 35

         <u>x^3 -  x^2</u>

                  -2x^2 - 33x

                   <u>-2x^2 + 2x</u>

                             - 35x + 35

                             <u>-35x + 35</u>

                                       0

x^2 - 2x - 35 factors into (x - 7)(x + 5)

Complete factorization

(x - 1)(x - 7)(x + 5)    

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