Remainder Factor Theorem

• True

• False

Complete the synthetic division and use the remainder to determine a true statement concerning p(x) and its solutions.

• -2 is a solution of p(x) since the remainder is equal to 0.

• -2 is not a solution of p(x) since the remainder is equal to 1.

• -2 is not a solution of p(x) since the remainder is equal to 33.

• 2 is not a solution of p(x) since the remainder is equal to -1.

Complete the rest of this synthetic division problem.

Determine the remainder.

• The remainder is 18.

• The remainder is 0.

• The remainder is 108.

• The remainder is 28.

Based on the remainder you found, which statement is true?

Assume that a polynomial has a solution at the x-value 4. Which of the following must be a factor of that same polynomial?

• 4x

• x-4

• x+4

Assume that x-2 is a factor of a polynomial. Which x-value must be a solution of that same polynomial?

• The x-value -2

• The x-value 2

• The x-value 0

Finish dividing p(x)=5x^3+34x^2+26x+C by x+6. Determine what value C must equal if x+6 is a factor of p(x).

• C would need to be equal to 0.

• C would need to be equal to 12.

• C would need to be equal to -12.

• C would need to be equal to 300.

What is a way to show that (x-5) is a factor of the polynomial 2x⁴ - 3x³ - 35x² - 9x + 45?

• You can use synthetic division and show that the remainder is 10

• You can use synthetic division and show that the remainder is zero

• Multiply (x - 5) five times by itself.

• There is no way to show that (x-5) is a factor of 2x⁴ - 3x³ - 35x² - 9x + 45.

Which statement is true?

• (x-3) is a factor of (x³ - 3x² + 2x + 2)

• (x-3) is not a factor of (x³ - 3x² + 2x + 2)

• The remainder when (x³ - 3x² + 2x + 2) is divided by (x-3) is zero.

• The remainder when (x³ - 3x² + 2x + 2) is divided by (x-3) is not zero. The remainder is 17.

• w is a zero of the polynomial function

• the graph touches or crosses at w