Page 33 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

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6. When the polynomial x + ax + b is divided by (x – 1) and (x + 2), its remainder is 4 and 5 respectively.
Find the values of a and b.
1 7. When x + px + qx + 1 is divided by (x – 2), its remainder is 9; when it is divided by (x + 3), its remainder
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is 19. Find the values of p and q.
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8. The expression 2x + ax + b can be divided exactly by (x + 1), and its remainder is 16 when divided by
(x – 3). Find the values of a and b.
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9. The expression ax – 8x + bx + 6 can be divided exactly by x – 2x – 3. Find the values of a and b.
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10. When the polynomials x + 4x – 2x + 1 and x + 3x – x + 7 are divided by (x – p), the remainders are
equal. Find the possible values of p.
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11. The expressions x – 4x + x + 6 and x – 3x + 2x + k have a common factor. Find the possible values
of k.
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12. If (x – a) is a factor of the expression ax – 3x – 5ax – 9, find the possible values of a. Factorise the
expression for each of the values of a.
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13. Given that f(x) ≡ x + kx – 2x + 1 has a remainder k when it is divided by (x – k), find the possible
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values of k.
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14. Find the value of k if (x + 1) is a factor of 2x + 7x + kx – 3. Using this value of k, solve the equation
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2x + 7x + kx – 3 = 0.
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15. Find the values of a and b if f(x) ≡ ax + bx + 12 can be divided exactly by both (x + 1) and (x – 2)
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respectively. With these values of a and b, solve the equation f(x) = 0.
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16. The expression x + ax + bx – 8 is divisible by (x + 1). When it is divided by (x – 2), its remainder is
42. Find the values of a and b and the value of the expression when x = 1.
Polynomial and rational inequalities
The relations such as x . 0, 2x – 1 < 0 and 3x + 2x . 1 are known as inequalities.
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The basic rules governing inequalities involving real numbers are as follows:
For any a, b  R with a . b,
(a) a + c . b + c, c  R,
(b) ac . bc, c  R, c . 0,
(c) ac , bc, c  R, c , 0.

Inequalities involving algebraic polynomials also obey the basic rules of inequalities for real numbers. The set
of numbers which satisfy an inequality is called the solution set. For example, if 2x – 3 < 4x + 9, then the

solution set is {x : x  –6}.
An inequality may be solved according to the type of function given, using the analytical method or graphical
method, or by drawing the real number line.

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