IBHM 086 107.pdf


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4 Polynomials

✗ 10 Find an expression for f(x) from its graph.
M
C

7

4

1

M–

M+

CE

%

8

9



5

6

÷

2

3

+

0

ON
X

=

y ⫽ f (x)

y

1
⫺3

1
2

0

4

x

⫺96

M
C
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%

8

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÷

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+

0

M
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ON
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M–

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%

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5

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÷

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7
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1

ON
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M

M–

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CE

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12 Solve x3 ⫺ 7x2 ⫺ 2x ⫹ 31 ⫽ 0, correct to 3 significant figures.

=

+

0

11 Solve 5x3 ⫺ 6x ⫹ 7 ⫽ 0, correct to 3 significant figures.

=

ON
X

13 Using algebraic long division, find

=

x3 ⫺ 5x2 ⫹ 6x ⫺ 4
.
2x ⫹ 1

✗ 14 Using algebraic long division, find 1x ⫺ 4x ⫹ 3x ⫺ 52 ⫼ 1x ⫹ 12.
✗ 15 The polynomial x ⫹ ax ⫺ 3x ⫹ b is divisible by 1x ⫺ 22 and has a remainder 6
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when divided by 1x ⫹ 12. Find the value of a and of b.

[IB May 03 P1 Q4]

✗ 16 The polynomial f1x2 ⫽ x

⫹ 3x2 ⫹ ax ⫹ b leaves the same remainder when divided

✗ 17 When the polynomial x

⫹ ax ⫹ 3 is divided by x ⫺ 1, the remainder is 8. Find

3

M
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M+

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%

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5

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2

3

7

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=

4

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%

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by x ⫺ 2 as when divided by x ⫹ 1. Find the value of a.

ON
X

=

the value of a.

✗ 18 Consider f1x2 ⫽ x
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[IB Nov 01 P1 Q3]

ON
X

3

[IB Nov 02 P1 Q1]

⫺ 2x2 ⫺ 5x ⫹ k. Find the value of k if x ⫹ 2 is a factor of f(x).

=

[IB Nov 04 P1 Q1]

107