If a polynomial f(x) is divided by x - 3 and the remainder is 7, what is f(3)?

F(3) = 7, as per the Remainder Theorem.

To determine if x - 4 is a factor of the polynomial f(x), what must be true about f(4)?

F(4) must equal 0 for x - 4 to be a factor of f(x).

Fill in the blank: The Remainder Theorem states that the remainder of a polynomial f(x) divided by x - a is equal to ___ .

F(a)

True or False: If f(2) = 0, then x - 2 is guaranteed to be a factor of f(x).

True.

What is the first step in using the Factor Theorem to factor a polynomial?

Find a value 'a' such that f(a) = 0.

Given f(x) = 2x³ - 3x² + 4, what is the remainder when f(x) is divided by x - 1?

The remainder is f(1) = 2(1)³ - 3(1)² + 4 = 2 - 3 + 4 = 3.

Fill in the blank: To factor the polynomial f(x), one must first divide f(x) by ___ to find the quotient.

X - a

If f(x) = x² - 5x + 6, which linear factors can be derived from this polynomial?

The factors are (x - 2)(x - 3).

True or False: The sum of the coefficients of a polynomial can be found by evaluating f(1).

True.

Using the Factor Theorem, if x + 3 is a factor of f(x), what must be true about f(-3)?

F(-3) must equal 0.

Calculate f(0) for the polynomial f(x) = 4x² + 2x - 5.

F(0) = 4(0)² + 2(0) - 5 = -5.

If f(x) = x³ - 6x² + 11x - 6, what are all the roots of f(x)?

The roots are x = 1, x = 2, and x = 3.

Fill in the blank: The value of k in the polynomial f(x) = x³ + 2x² - kx + 10 is found when f(2) = ___ .

0, since x - 2 is a factor.

What is the process to completely factor the polynomial f(x) = 2x³ + 3x² - 8x - 12?

First, find a root, then use synthetic division to factor it down.

Using the Remainder Theorem, if f(x) = 2x³ - 3x² + 4 and you divide by x - 2, what is the remainder?

The remainder is 8.

• Using f(2) to evaluate.

• Calculates the polynomial value.

• Remainder Theorem applies here.