Question

(x+5)(x+4)(x-2)-(x^2+11x-9)(x+1)+5x^2

Can someone help me to prove that the value of the following expression does not depend on the value of variable x

Answer 1

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

STEP

2

:

Equation at the end of step 2

(((x+5)•(x+4)•(x-2))•(x2+11x-9))•(x+26)

STEP

3

:

Equation at the end of step 3

((x+5)•(x+4)•(x-2)•(x2+11x-9))•(x+26)

STEP

4

:

Trying to factor by splitting the middle term

4.1 Factoring x2+11x-9

The first term is, x2 its coefficient is 1 .

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

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

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

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 11 .

-9 + 1 = -8

-3 + 3 = 0

-1 + 9 = 8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

4

:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)

Explanation:

Answer 2

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)
STEP
2
:
Equation at the end of step 2

(((x+5)•(x+4)•(x-2))•(x2+11x-9))•(x+26)
STEP
3
:
Equation at the end of step 3

((x+5)•(x+4)•(x-2)•(x2+11x-9))•(x+26)
STEP
4
:
Trying to factor by splitting the middle term

4.1 Factoring x2+11x-9

The first term is, x2 its coefficient is 1 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is -9

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

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 11 .

-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step
4
:

(x+5)•(x+4)•(x-2)•(x2+11x-9)•(x+26)