4. Polynomial Functions

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (12x^2+x−4)÷(3x−2)

Use synthetic division to perform each division. (x^4 + 4x^3 + 2x^2 + 9x+4) / x+4

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (x^4−81)/(x−3)

Use synthetic division to find ƒ(2). ƒ(x)=5x^4-12x^2+2x-8

In Exercises 17–32, divide using synthetic division. (2x^2+x−10)÷(x−2)

Use synthetic division to perform each division. x^3 - 1 / x-1

In Exercises 17–32, divide using synthetic division. (x^5+4x^4−3x^2+2x+3)÷(x−3)

In Exercises 17–32, divide using synthetic division. (x^4−256)/(x−4)

For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x^2 + 5x+6; k = -2

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x^3−11x^2+7x−5;f(4)

For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x^2 - 5x+1; k = 2+i

Solve the equation 2x3−3x2−11x+6=0 given that -2 is a zero of f(x)=2x^3−3x^2−11x+6.

Solve the equation 12x^3+16x^2−5x−3=0 given that -3/2 is a root.

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = 2x^3 - 6x^2 -9x + 4; k=1

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = 5x^4 + 2x^3 -x+3; k=2/5