When the function f(x) = 2x^n + ax^2 - 6 is divided by (x - 1), the remainder is -7 and when divided by (x + 3), the remainder is 129. Calculate the value of "a" and "n" and hence write the polynomial function completely.

Step-by-step explanation:

Step-by-step explanation:

From the fact that the remainder is -7 after we divide by x -1 , then we know that f(1) = -7. But f(1) = 2 + a - 6.

So 2 + a - 6 = -7

a - 4 = -7

a = 4 - 7

a = -3.

Also we know that when divided by x + 3 the remainder is 129. Hence f( -3) = 129

129 = f(-3) = 2 (-3)^ n + (-3)(-3)^2 -6

129 = 2 (-3)^n -27 - 6

129 = 2 (-3)^n -33

129 + 33 = 2(-3)^n

162 = 2 (-3)^n

81 = (-3)^n

Hence n =4 and therefore f(x) = 2x^4 -3x^2 - 6.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.