Question

simplify =:(5x2-7x)+(9-2x- 15x2)​

Answer 1

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

((5 • (x2)) - 7x) + ((9 - 2x) - (3•5x2))

STEP

2

:

Equation at the end of step

2

:

(5x2 - 7x) + (-15x2 - 2x + 9)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

-10x2 - 9x + 9 = -1 • (10x2 + 9x - 9)

Trying to factor by splitting the middle term

4.2 Factoring 10x2 + 9x - 9

The first term is, 10x2 its coefficient is 10 .

The middle term is, +9x its coefficient is 9 .

The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 10 • -9 = -90

Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is 9 .

-90 + 1 = -89

-45 + 2 = -43

-30 + 3 = -27

-18 + 5 = -13

-15 + 6 = -9

-10 + 9 = -1

-9 + 10 = 1

-6 + 15 = 9 That's it

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

10x2 - 6x + 15x - 9

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

2x • (5x-3)

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

3 • (5x-3)

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

(2x+3) • (5x-3)

Which is the desired factorization

Final result :

(3 - 5x) • (2x + 3)