Question

When the function f(x) is divided by x+8, the quotient is 3x² −32x+1 and the remainder is -3. Find the function f(x) and write the result in standard form.

a) f(x)=3x³ −83x² +8x+1
b) f(x)=3x³ −56x²−24x−24
c) f(x)=3x³ −68x² −24x−3
d) f(x)=3x ³−56x² +8x−3

Answer 1

To find the function f(x) when divided by x+8, we can use the division algorithm to obtain the quotient and remainder. The given quotient is 3x²-32x+1 and the remainder is -3. By dividing the quotient further, we can determine the quadratic term, linear term, and constant term. Finally, we can write the function f(x) in the standard form.

Step-by-step explanation:

To find the function f(x) when divided by x+8, we need to use the division algorithm. The quotient is given as 3x²-32x+1 and the remainder is -3.

First, we divide the given quotient by x+8 to obtain the constant term. 1 divided by (x+8) is 0 and the remainder is 1.

Next, we divide the given quotient by x+8 to obtain the linear term. -32x divided by (x+8) is -4 and the remainder is -32.

Finally, we divide the linear term by x+8 to obtain the quadratic term. -4 divided by (x+8) is -0.5 and the remainder is -4.

Therefore, the function f(x) when divided by x+8 is 3x²-4x-0.5 and the remainder is -4.