Factor Theorem

f(x) = x³ + 6x² – 9x -14

Find f(1)

• -3

• -16

• -21

• 0

f(x) = x³ + 6x² – 9x -14

---> f(1) = 16

Is (x-1) a factor of f(x)?

• No

• Yes

• Need more information to tell

f(x) = x³ + 6x² – 9x -14

Find f(2)

• -3

• 2

• -21

• 0

f(x) = x³ + 6x² – 9x -14

---> f(2) = 0

Is (x-2) a factor of f(x)?

• No

• Yes

• Need more information to tell

f(x) = x³ + 4x² -17x - 60

• A factor of f(x) is (x-5)

• A factor of f(x) is (x-4)

• A factor of f(x) is (x-3)

f(x) = x³ + 4x² -17x - 60

• f(x) = (x-3)(x+4)(x-5)

• f(x) = (x+3)(x-4)(x+5)

• f(x) = (x+3)(x+4)(x+5)

• f(x) = (x-3)(x-4)(x-5)

The factor theorem states that if f(a) = 0, then a factor of f(x) is

• (x - a)

• (x + a)

• -(a + x)

• (-x - a)

Which explanation correctly uses the factor theorem to show why (x+2) is not a factor of x³ - 2x² – 11x +12

• f(2) = -10, so (x+2) is not a factor

• f(-2) = 18, so (x+2) is not a factor

• The actual factorisation is (x-4)(x-1)(x+3)

Which explanation correctly uses the factor theorem to show why (x-4) is a factor of x³ - 2x² – 11x +12

• f(4) = 0, so (x-4) is a factor

• f(-4) = 0, so (x-4) is a factor