The Factor Theorem (Leaving Cert Mathematics): Quizzes

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The Factor Theorem
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How many roots does a quadratic equation have?

Two roots

How many roots does a cubic equation have?

Three roots

If P(c)=0P(c) = 0 for some number cc, what is a factor of P(x)P(x)?

(x−c)(x - c)

If x=−3x = -3 is a root, what is the corresponding factor?

(x+3)(x + 3)

Given f(x)=2x3+5x2−4x−3f(x) = 2x^3 + 5x^2 - 4x - 3, what is f(−3)f(-3)?

00

What does it mean if a factor divides evenly into a polynomial?

The remainder is 0

In polynomial division, what is the first step?

Divide 1st dividend term by 1st divisor term

When dividing 2x32x^3 by xx in polynomial division, what is the result?

2x22x^2

In polynomial division, what happens to terms after multiplying?

Switch the signs

What always happens to the first column in polynomial division?

It always cancels

What does a remainder of 0 indicate in polynomial division?

The divisor is a factor

From quotient 2x2−x−1=02x^2 - x - 1 = 0, what are the remaining roots?

x=1x = 1 and x=−12x = -\frac{1}{2}

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