Solving Polynomials in Factored Form Review

Solve the equation:

(x + 9)(x - 3) = 0

• x = -9 or x = -3

• x = -9 or x = 3

• x = 9 or x = -3

• x = 9 or x = 3

Answer explanation

To solve (x + 9)(x - 3) = 0, set each factor to zero: x + 9 = 0 gives x = -9, and x - 3 = 0 gives x = 3. Thus, the solutions are x = -9 or x = 3.

Tags

CCSS.HSA-REI.B.4B

Solve the equation:

(x + 4)(x - 6) = 0

• x = 4 or x = 6

• x = -4 or x = -6

• x = 4 or x = -6

• x = -4 or x = 6

Answer explanation

To solve (x + 4)(x - 6) = 0, set each factor to zero: x + 4 = 0 gives x = -4, and x - 6 = 0 gives x = 6. Thus, the solutions are x = -4 or x = 6.

Tags

CCSS.HSA-REI.B.4B

There is only one root in the problem (3x - 6)² = 0. The answer is 2.

• True

• False

Answer explanation

The equation (3x - 6)² = 0 has only one solution, which is found by setting 3x - 6 = 0. Solving this gives x = 2. Therefore, the statement is true.

Tags

CCSS.HSA-REI.B.4B

Which of the following is NOT a root of the polynomial equation listed below?

(2x + 1) (x - 4) (x + 3) = 0

• x = 4

• x = -3

Answer explanation

The roots of the polynomial (2x + 1)(x - 4)(x + 3) = 0 are found by setting each factor to zero: 2x + 1 = 0 (x = -1/2), x - 4 = 0 (x = 4), and x + 3 = 0 (x = -3). Thus, x = 1/2 is NOT a root.

Tags

CCSS.HSF-IF.C.7C

Which TWO values are solutions to the equation below?

30x - 6x² = 0

• x = 0

• x = 5

• x = 6

Answer explanation

To solve 30x - 6x^2 = 0, factor out 6x: 6x(5 - x) = 0. This gives solutions x = 0 and x = 5. Thus, the correct answers are x = 0 and x = 5.

What is the GCF of 36x² and 16x?

• 4

• 4x

• 4x²

• 144x²

Answer explanation

To find the GCF of 36x² and 16x, we look for the highest common factor of the coefficients (36 and 16), which is 4, and the lowest power of x, which is x. Thus, the GCF is 4x.

What are the x-intercepts of the graph of the polynomial equation below?

y = (x + 2) (3x - 6)

Tags

CCSS.HSA.APR.B.3

What are the x-intercepts of the graph of the polynomial equation below?

y = (4x - 12) (x + 1)

Tags

CCSS.HSA.APR.B.3

What are the roots of the graph shown?

• x = -5, -2

• x = -5, 2

• x = 5, 2

• x = 5, -2

Answer explanation

The roots of the graph are the x-values where it intersects the x-axis. The correct roots are x = 5 and x = -2, as these values satisfy the equation represented by the graph.