4. Polynomial Functions

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = x³ + 3x² -x + 1; k = 1+i

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $(6x^3+7x^2+12x-5)÷(3x-1)$

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $(12x^2+x-4)÷(3x-2)$

Use synthetic division to perform each division. (x⁵ + 3x⁴ + 2x³ + 2x² + 3x+1) / x+2

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x² - 5x+1; k = 2+i

Use synthetic division to perform each division. x⁷+1 / x+1

Divide using long division. State the quotient, and the remainder, r(x). (x⁴+2x³−4x²−5x−6)/(x²+x−2)

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = x² - 2x + 2; k = 1-i

The remainder theorem indicates that when a polynomial ƒ(x) is divided by x-k, the remainder is equal to ƒ(k). Consider the polynomial function ƒ(x) = x³ - 2x² - x+2. Use the remainder theorem to find each of the following. Then determine the coordinates of the corresponding point on the graph of ƒ(x). ƒ (1)

Perform each division. See Examples 9 and 10. (4x³+9x²-10x-6)/(4x+1)

When 2x²−7x+9 is divided by a polynomial, the quotient is 2x-3 and the remainder is 3. Find the polynomial.

Use synthetic division to perform each division. (x⁴ + 4x³ + 2x² + 9x+4) / x+4

Divide using long division. $(4x^3-3x^2-2x+1)÷(x+1)$

Divide using long division. State the quotient, and the remainder, r(x).$\(\frac{2x^5 - 8x^4 + 2x^3 + x^2}{2x^3 + 1}\)$

Divide using synthetic division. (x⁴−256)/(x−4)