The factor theorem (AQA GCSE Further Maths): Quizzes

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The factor theorem
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If (x−3)(x - 3) is a factor of f(x)f(x), what is the value of f(3)f(3)?

f(3)=0f(3) = 0

If f(−2)=0f(-2) = 0, which expression is a factor of f(x)f(x)?

(x+2)(x + 2)

What is the degree of the polynomial 2x4+3x2−5x+12x^4 + 3x^2 - 5x + 1?

4

For f(x)=x3−2x2−5x+6f(x) = x^3 - 2x^2 - 5x + 6, what is f(1)f(1)?

00

For f(x)=x3+4x2−3x−18f(x) = x^3 + 4x^2 - 3x - 18, which values should you test first?

±1,±2,±3,±6,±9,±18±1, ±2, ±3, ±6, ±9, ±18

A polynomial of degree 5 has at most how many linear factors?

5

If f(2/3)=0f(2/3) = 0 for polynomial f(x)f(x), which is a factor?

(3x−2)(3x - 2)

For f(x)=x3+2x2−x−2f(x) = x^3 + 2x^2 - x - 2, which value makes f(x)=0f(x) = 0?

x=1x = 1

When testing for factors systematically, in what order should you test values?

Increasing absolute value

What common mistake do students make when finding factors?

Forgetting to test negative values

To show (x−5)(x - 5) is a factor of f(x)f(x), what should you do?

Substitute x=5x = 5 and show f(5)=0f(5) = 0

After finding one factor of a cubic, what method finds the remaining factors?

Polynomial long division

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