Algebra 2 - Theorems About Roots of Polynomials

Use the Complex Conjugate Root Theorem to state another complex solution, given that -2-5i is a root.

• -2-5i

• 2+5i

• -2+5i

• 5i

Write the simplest polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x)=(x+2)(x-1)(x-4)

• f(x)=x³+8

• f(x)=x³−3x²−6x+8

• f(x)=x³−3x²+8

Using the following roots, write the polynomial in factored form.

-6, √6, 3

• (x+6)(x+√6)(x-3)(x+√6)

• (x+6)(x-√6)(x+3)(x+√6)

• (x-6)(x-√6)(x+3)(x+√6)

• (x+6)(x-√6)(x-3)(x+√6)

If these two roots are known, what are other roots for this 4th degree polynomial? -7i, 3√2, _____, ______

• -7i, 3√2

• -7i, -3√2

• 7i, -3√2

• 7i, 3√2

Name the Theorem

If P(x) is a polynomial with rational coefficients, then the irrational roots of P(x) = 0 occur in conjugate pairs.

• Binomial Theorem

• Conjugate Root Theorem

• Rational Root Theorem

• Factor Theorem

What is the degree of the following polynomial that has 4 real roots and 2 complex roots?

• 6

• 4

• 2

• 8

Which of the following is a COMPLETE list of all possible Rational Zeros?

f(x) = x³ + 2x² - 6x + 8

• ±1, ±8

• ±1, ±2, ±4, ±8

• ±1, ±2, ±4

• 1, 2, 4, 8

Solve by using Rational Root Theorem:

2x³ - 11x² + 12x + 9 = 0

• -1, 1, 3

• -1, 3/2, 3

• -1/2, 3, 3

• -1/2, 1, 3

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is not a factor. There is a remainder.

Solve by using Rational Root Theorem:

x³ + 3x² - 6x - 8 = 0

• -4, -1, 2

• -4, -1, ±√2

• 1, 2, 4

• 4,-1,√2