Question

Two polynomial functions are given. f(x)={((1)/(2)x^(3)-5x^(2)+10x-3)} h(x)=(12+(3)/(4)x-2x^(3)+3x^(2)) Find f(x)-h(x)

Answer 1

To find f(x)-h(x), subtract the two polynomial functions term by term. The result is (5/2)x^3 - 8x^2 + (37/4)x - 15.

Step-by-step explanation:

To find f(x)-h(x), we subtract the two polynomial functions term by term.

Step 1:

Subtract the coefficients of x^3:

f(x) - h(x) = (1/2)x^3 - (-2)x^3 = (1/2 + 2)x^3 = 5/2x^3

Step 2:

Subtract the coefficients of x^2:

f(x) - h(x) = -5x^2 - 3x^2 = -8x^2

Step 3:

Subtract the coefficients of x:

f(x) - h(x) = 10x - (3/4)x = (10 - 3/4)x = (40/4 - 3/4)x = 37/4x

Step 4:

Subtract the constant terms:

f(x) - h(x) = -3 - 12 = -15

Putting it all together, f(x) - h(x) = (5/2)x^3 - 8x^2 + (37/4)x - 15.