Question

3(x-5)² +14(x-5)-24

Answer 1

Answer:

3x^{2} -16x-19

Step-by-step explanation:

If we are going to be simplying this problem, then we need to take it step by step.

Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.

Answer 2

Answer:

(3x - 19) • (x + 1)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((3•((x-5)2))+14•(x-5))-24

STEP

2

:

Equation at the end of step 2

(3 • (x - 5)2 + 14 • (x - 5)) - 24

STEP

3

:

Trying to factor by splitting the middle term

Factoring 3x2-16x-19

The first term is, 3x2 its coefficient is 3 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is -19

Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57

Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .

-57 + 1 = -56

-19 + 3 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3

3x2 - 19x + 3x - 19

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

x • (3x-19)

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

1 • (3x-19)

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

(x+1) • (3x-19)

Which is the desired factorization