Algebra 2: Roots and Factors of Polynomials

What does the factor theorem help us determine about a polynomial?

• The roots of the polynomial

• The symmetry of the polynomial

• The degree of the polynomial

• The coefficients of the polynomial

If a polynomial has a root of 3 + 2i, what other root must it also have?

• -3 + 2i

• -3 - 2i

• 3 - 2i

• 3 + 2i

What is the degree of a polynomial if it has four roots?

• 5

• 2

• 3

• 4

How do you find the factor of a polynomial given a root of 3 plus or minus 2i?

• By multiplying both sides by 2

• By subtracting 3 from both sides

• By squaring both sides

• By adding 3 to both sides

What is the result of squaring the expression (x - 3) when finding factors?

• x^2 + 6x + 9

• x^2 + 9

• x^2 - 9

• x^2 - 6x + 9

What is the factor of a polynomial if x is plus or minus the square root of 10?

• x^2 - 5

• x^2 + 5

• x^2 - 10

• x^2 + 10

When multiplying polynomials, what is the first step after finding all factors?

• Divide each term by the constant

• Add all factors together

• Multiply each term by the constant

• Multiply each term by every other term

What method is used to find remaining factors after dividing a polynomial?

• Completing the square

• Partial fraction decomposition

• Long division

• Synthetic division

What is the process of breaking down a polynomial into its factors called?

• Integration

• Simplification

• Differentiation

• Factoring

If a polynomial is divided by x^2 + 6x + 13, what is the next step?

• Multiply the quotient by the divisor

• Add the remainder to the quotient

• Check for further factorization

• Subtract the remainder from the dividend