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CBSE - Class 9 Mathematics Polynomials Worksheet

Classify the following as linear, quadratic and cubic polynomials:
(i) $x^2 + x$

Verify whether the following are zeroes of the polynomial, indicated against them.
(vii) $p(x) = 3x^2 – 1, x = –\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}$

Factorise:
(i) $4x^2 + 9y^2 + 16z^2 + 12xy – 24yz – 16xz$

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(ii) Area : $35y^2 + 13y –12$

Find the value of the polynomial $5x – 4x^2 + 3$ at
(iii) $x = 2$

Use suitable identities to find the following products:
(ii) $(x + 8) (x – 10)$

Factorise:
(ii) $2x^2 + y^2 + 8z^2 – 2\sqrt{2}xy + 4\sqrt{2}yz – 8xz$

Write the following cubes in expanded form:
(iv) $(x - \frac{2}{3}y)^3$

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i) Volume : $3x^2 – 12x$

10.

Determine which of the following polynomials has $(x + 1)$ a factor :
(ii) $x^4 + x^3 + x^2 + x + 1$

11.

Use suitable identities to find the following products:
(iii) $(3x + 4) (3x – 5)$

12.

Evaluate the following products without multiplying directly:
(ii) $95 \times 96$

13.

Find $p(0)$, $p(1)$ and $p(2)$ for each of the following polynomials:
(i) $p(y) = y^2 – y + 1$

14.

Verify whether the following are zeroes of the polynomial, indicated against them.
(i) $p(x) = 3x + 1, x = –\frac{1}{3}$

15.

Factorise :
(iii) $x^3 + 13x^2 + 32x + 20$

16.

Write the coefficients of $x^2$ in each of the following:
(iv) $\sqrt{2}x - 1$

17.

Verify whether the following are zeroes of the polynomial, indicated against them.
(iv) $p(x) = (x + 1) (x – 2), x = – 1, 2$

18.

Write the following cubes in expanded form:
(iii) $(\frac{3}{2}x + 1)^3$

19.

Classify the following as linear, quadratic and cubic polynomials:
(iv) $1 + x$

20.

Factorise each of the following:
(iii) $27 – 125a^3 – 135a + 225a^2$

Worksheet Answers

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