Polynomial Equations and Their Solutions

What is the first step in solving a polynomial equation like x^2 + 5x - 24 = 0?

• Finding the derivative

• Factoring the polynomial

• Using the quadratic formula

• Completing the square

Which pair of numbers are the factors of 12 that add up to 7 in the polynomial x^2 + 7x + 12?

• 5 and 2

• 3 and 4

• 2 and 6

• 1 and 12

What is the result of evaluating f(x) = x^2 + 2x - 7 for x = 3 using substitution?

• 10

• 12

• 8

• 5

According to the remainder theorem, what is the remainder when a polynomial p(x) is divided by x - a?

• x

• 0

• a

• p(a)

What are the zeros of the polynomial x^2 - 3x - 10?

• x = 5 and x = -2

• x = -5 and x = 2

• x = -5 and x = -2

• x = 5 and x = 2

What is the factorization of x^2 - 3x - 10?

• (x + 5)(x + 2)

• (x - 5)(x - 2)

• (x + 5)(x - 2)

• (x - 5)(x + 2)

When x^2 + 5x - 24 = 0 and one solution is x = 3, what is the other solution?

• x = 8

• x = -8

• x = -5

• x = 5

What is the first step in solving x^3 + 4x^2 - 15x - 18 = 0 when one solution is x = 3?

• Use synthetic division

• Perform long division by x - 3

• Use the quadratic formula

• Complete the square

What are the factors of the polynomial x^3 + 4x^2 - 15x - 18?

• (x - 3)(x + 6)(x + 1)

• (x + 3)(x - 6)(x - 1)

• (x - 3)(x - 6)(x - 1)

• (x + 3)(x + 6)(x + 1)

What are the zeros of the polynomial x^3 + 4x^2 - 15x - 18?

• x = -3, x = 6, x = 1

• x = 3, x = -6, x = -1

• x = -3, x = -6, x = 1

• x = 3, x = 6, x = 1