#### Algebra Book Back Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k= ?

(a)

-6

(b)

-7

(c)

-8

(d)

11

2. The type of the polynomial 4–3x3 is

(a)

constant polynomial

(b)

linear polynomial

(c)

(d)

cubic polynomial.

3. The sum of the polynomials p(x) = x3 – x2 – 2, q(x) = x2–3x+ 1

(a)

x3 – 3x – 1

(b)

x3 + 2x2 – 1

(c)

x3 – 2x2 – 3x

(d)

x3 – 2x2 + 3x –1

4. The remainder when p(x) = x3 – ax2 + 6x – a is divided by (x – a) is

(a)

–5a

(b)

$\frac {1}{5}$

(c)

5

(d)

5a

5. Degree of the polynomial (y3–2)(y3 + 1) is

(a)

9

(b)

2

(c)

3

(d)

6

6. 3 x 2 = 6
7. Which of the following expressions are polynomials. If not give reason: ${ m }^{ 2 }-\sqrt [ 3 ]{ m } +7m-10$

8. Find the Zeros of the following polynomials. f(x) = 2x + 1

9. If p(x) = x2– 2$\sqrt { 2 }$x +1, find p(2$\sqrt { 2 }$) .

10. 3 x 3 = 9
11. Let p(x) =4x2-3x+2x3+5 and q(x)=x2+2x+4 find p(x)+q(x)

12. Rewrite the following polynomial in standard form.
$\sqrt { 2 } x^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5{ x }^{ 3 }$

13. What should be added to 2x3+6x2-5x+8 to get 3x3 -2x2+6x+15?

14. 2 x 5 = 10
15. Classify the following polynomials based on number of terms.

16. If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.