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CHAPTER 6 : POLYNOMIALS

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1. Find the values of a and b if ( )f x  ax  bx  12 is divisible by x  and x   2
.
By using these values of a and b, solve the equation ( )f x  0.

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2. Find the value of r for which x   2 is a factor of   3p x  x  4x  rx  8.
Hence, factorize ( )p x completely.

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3. Given that ( )Q x  px   p   2 x 3p 2 has a remainder of 5 when divided by x   2 .

(a) Find the values of p .
(b) By using the positive value of p from part (a), find all the zeroes of ( )Q x .

4. Given a polynomial ( ) 2P x  x  7x  10x 24.
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3
(a) Show that x   2 is a factor of ( )P x .

(b) Factorize ( )P x completely.

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(c) Express as a partial fractions.
P ( )
x


2
3
5. The polynomial ( )P x is defined by ( ) 2P x  x  ax  4x b
.
(a) If x  2 is a factor of ( )P x , and 4 is the remainder when ( )P x is divided by x  1 ,
find the values of a and b.
(b) Find all the factors of ( )P x .

x  1
(c) Express as partial fractions.
P   x

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6. Determine the integers p and q such that x  x  4x   x  p x q  . Hence, express
4
5x 2
in the form of partial fractions.
x  x  4x 4
3
2


2
3
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7. Given x  1 is a factor of the polynomial   2P x  x  ax  2x b When ( )P x is divided
by x  2 , the remainder is – 6. Find the values of a and b. Hence, factorise ( )P x completely.