Polynomials Thursday, 31 October 2019.

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Presentation transcript:

Polynomials Thursday, 31 October 2019

Long Division Example Work out each of the following a) 4095  12 b) 5595  15

Example Divide by

Example Divide by

Factor theorem Example What is the remainder when is divided by

Example What is the remainder when is divided by Example What is the remainder when is divided by

That is the remainder is P(a) Let P(x) be a polynomial in x to be divided by the linear function x – a Where Q(x) = Quotient R = Remainder Putting x = a That is the remainder is P(a) If R = 0 when P(x) is divided by (x – a) i.e. If P(a) = 0 then (x – a) is a factor of P(x)

Example Show that (x + 1) is a factor of the cubic and hence factorise completely

Example Show that (x – 2) is a factor of x3 – 4x2 + x + 6 Hence factorise completely x3 – 4x2 + x + 6 Solve the equation x3 – 4x2 + x + 6 = 0

Example Solve the equation

Past A – Level paper question a) When ax3 – 12x2 – 6x + 5 is divided by x + 1, the remainder is –3. Find the value of the constant a. b) Factorise 8x3 – 14x2 – 7x +6