Q1.
Which of the following expressions are polynomials? Give reason.
(i)
(ii)
(iii)
Q2.
Write the coefficient of
(i)
(ii)
(iii)
Q3.
Give an example of
(i) a trinomial of degree
.
(ii) a monomial of degree
(iii) a binomial of degree
Q4.
.
.
Verify whether the following are the zeroes of the polynomial, indicated against
them.
(i)
(ii)
(iii)
Q5.
Evaluate:
Q6.
Find the remainder when
Q7.
Using the remainder theorem, find the remainder when
divided by
is divisible by
.
is
and verify the result by actual division.
Q8.
Using factor theorem, show that
Q9.
For what value of
Q10.
Show that
is a factor of
is the polynomial
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are the factors of
.
is divisible by
?
.
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Q11.
Factorise:
Q12.
Factorise:
Q13.
Split the middle term and factorise the following:
(i)
(ii)
Q14.
Factorise
Q15.
Also write the identity used.
Using suitable identity, evaluate
.
Q16.
Factorise:
Q17.
Find the product using a suitable identity, write the identity also.
Q18. Factorise:
Q19.
If
, by using an identity find the value of
Also write the identity used.
Q20.
Write the expansion of
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.
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Answers
A1.
An expression of the form
where
are real numbers and
polynomial. Therefore, (i)
(ii)
(i)
A3.
(i)
is a polynomial.
is not a polynomial since the exponents of
(iii)
A2.
is a non-negative integer is called a
is not a polynomial since the exponents of
(ii)
in
is not an integer.
in the term
.
(iii)
(ii)
(iii)
A4.
(i) Yes (ii) No (iii) Yes
A5.
A6.
A7.
A8.
Hint: By factor theorem,
will be a factor of
if
.
A9.
A10.
Hint: a will be a factor of
if
A11.
A12.
A13.
(i)
(ii)
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Page 3 of 4
A14.
Identify:
A15.
A16.
A17.
A18.
Identity: If
Identity: If
then
A19.
Identity:
A20.
Identity:
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