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1.2.10 Manipulating polynomials

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Question 29

The polynomial $f\,$ is defined by $f(x)=x^3+ax^2+bx+6$ , where $a\,$ and $b\,$ are constants. When $f (x)$ is divided by $(x - 1)$ the remainder is 12, and $(x + 2)$ is a factor of $f (x)$ .

Find $a\,$ and $b$ , and hence express $f (x)$ as a product of a linear factor and an irreducible quadratic factor.

[6]

Markscheme

1.2.10 Manipulating polynomials Questions

A Level
Maths
1.2.10 Manipulating polynomials

72 exam-style questions on OCR A Level Maths 1.2.10 Manipulating polynomials. Each one has a worked solution and a mark scheme showing where the marks go.

1.2.10 Manipulating polynomials

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1.2.10 Manipulating polynomials

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

Question 29

The polynomial $f\,$ is defined by $f(x)=x^3+ax^2+bx+6$ , where $a\,$ and $b\,$ are constants. When $f (x)$ is divided by $(x - 1)$ the remainder is 12, and $(x + 2)$ is a factor of $f (x)$ .

Find $a\,$ and $b$ , and hence express $f (x)$ as a product of a linear factor and an irreducible quadratic factor.

[6]

Markscheme

1.2.10 Manipulating polynomials Questions

A Level
Maths
1.2.10 Manipulating polynomials

72 exam-style questions on OCR A Level Maths 1.2.10 Manipulating polynomials. Each one has a worked solution and a mark scheme showing where the marks go.