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

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 + 3x + 4; k = 2+i

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) = 4x⁴ + x² + 17x + 3; k= -3/2

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) = x³ + 3x² -x + 1; 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 (-2)

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)

Determine whether each statement is true or false. If false, explain why. Because x-1 is a factor of ƒ(x)=x⁶-x⁴+2x²-2, we can also conclude that ƒ(1) = 0.

Determine whether each statement is true or false. If false, explain why. For ƒ(x)=(x+2)⁴(x-3), the number 2 is a zero of multiplicity 4.

Determine whether each statement is true or false. If false, explain why. A polynomial function having degree 6 and only real coefficients may have no real zeros.

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. x³-5x²+3x+1; x-1

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. 4x²+2x+54; x-4

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. x³+2x²+3; x-1

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. 2x³+x+2; x+1

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. $2x^4+5x^3-2x^2+5x+6;x+3$

Factor ƒ(x) into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=2x^3-3x^2-5x+6{;}^{}k=1$

Factor ƒ(x) into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=-6x^3-25x^2-3x+4;k=-4$

Factor $\text{ƒ}\left(x\right)$ into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=x^4+2x^3-7x^2-20x-12;k=-2$ (multiplicity $2$)

Factor $\text{ƒ}\left(x\right)$ into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=2x^4+x^3-9x^2-13x-5;k=-1$ (multiplicity $3$)

For each polynomial function, one zero is given. Find all other zeros. $\text{ƒ}\left(x\right)=x^3-x^2-4x-6;3$

For each polynomial function, one zero is given. Find all other zeros. $\text{ƒ}\left(x\right)=x^3+4x^2-5;1$

For each polynomial function, one zero is given. Find all other zeros. $\text{ƒ}\left(x\right)=4x^3+6x^2-2x-1;\frac{1}{2}$

For each polynomial function, one zero is given. Find all other zeros. $\text{ƒ}\left(x\right)=-x^4-5x^2-4;-i$

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=(x+1{)}^2(x-1{)}^3(x^2-10)$

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=3x(x-2)(x+3)(x^2-1)$

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=(x^2+x-2{)}^5(x-1+\sqrt{3}{)}^2$

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=(2x^2-7x+3{)}^3(x-2-\sqrt{5})$

Find a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. Zeros of -3, 1, and 4; ƒ(2)=30

Find a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. Zeros of -2, 1, and 0; ƒ(-1)=-1

Find a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. Zero of -3 having multiplicity 3; ƒ(3)=36

Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. 5+i and 5-i