Factor of a Polynomial

Q.

4s2 -4s+1

Split the middle term and factorise the given expression

Q.

The graph y= p(x) is shown below. How many zeroes does the polynomial p(x) have?

1. 1

2. 2

3. 3

4. 4

Q. If one of the zero of the quadratic polynomial (k-1)x+kx+1 is -3. Find the value of k.

Q.

Use the Factor Theorem to determine whether $\text{g(x)}$ is a factor of $\text{p(x)}$ in the following case: ${\text{p(x) = x}}^3-4x^2+x+6,g\left(x\right)=x–3$

Q.

Which of the following is a factor of
$(x+y{)}^3-(x^3+y^3)$?

1. $x{y}^2$

2. $x^2-2xy+y^2$

3. $3xy$

4. $x^2+xy+y^2$

Q. Write the family of quadratic polynomials having $-\frac{1}{4}$ and 1 as its zeros.

Q. The graph of a polynomial y = f(x), shown in Fig. 2.18. Find the number of real zeros of f(x).

Q. Which among the following is a factor of $x^2+\frac{x}{6}-\frac{1}{6}?$

1. $3x+1$
2. $2x+1$
3. $x-\frac{1}{2}$
4. $x-\frac{1}{5}$

Q. The graph of a polynomial f(x) is as shown in Fig. 2.21. Write the number of real zeros of f(x).

Q.

If c, d are zeroes of x2-10x-11b and a , b are zeroes of x2-10cx-11d then value of a+b+c+d= ?

A) 1210

B)-1

C)2530

D)-11

Q. In Fig. 2.17, the graph of a polynomial p(x) is given. Find the zeros of the polynomial.

Q.

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2+x-2, find the value of 1\alpha-1\beta

Q.

Observe the following figure.

The polynomial drawn in above graph has how many zeros?

1. 4

2. 3

3. 1

4. 2

Q.

Number of zeroes of the “zero polynomial” is equal to ?

1. $0$

2. $1$

3. $2$

4. Infinite

Q.

If ‘a’ and ‘b’ are the roots of the equation $x^2$ – 8x + 15 = 0, then find the value of ‘a’ and ‘b’.

Q.

What is the value of the polynomial
$x^2-3x+5$ at $x=3?$

1. 5

2. -5

3. 23

4. 13

Q. Question 17
Which of the following is a factor of $(x+y{)}^3–(x^3+y^3)$?

A) $x^2+y^2+2xy$
B) $x^2+y^2–xy$
C) $x{y}^2$
​​​​​​​D) $3xy$

Q.

abx^2 + (b^2 - ac)x - bc=0. Solve using quadratic formula.

Q.

State true or false:

A polynomial cannot have more than one zero.

1. True
2. False

Q. In Fig. 1, the graph of a polynomial p (x) is shown. The number of zeroes of p (x) is

(a) 4

(b) 1

(c) 2

(d) 3

Q.

If one zero of 3x²-8x+2k+1 is 7 times the other, find the value of k.

Q.

Factorise the following expression: $q^2-10q+21$

Q. find the value of k for which the quadratic polynomial kx^2+x+k has equal zeros as 1/2.

Q.

If α, β, γ are the zeros of the polynomial 2x³ + x² - 13x + 6, then the value of αβγ is

1. -3

2. -1/2

3. -13/2

4. 3

Q. Solve the quadratic equation by factorization :
16x-10÷x=27

Q. If $(x-a)$ is the HCF of
$x^2-x-6and{x}^2+3x-18$ ,
then find the value of a.

1. -2
2. -6
3. -3
4. 3

Q.

The factors of the polynomial equation P(x) = $4x^3+x^2+5x+8$ is

1. (x + 1), (4x² – 3x + 8)

2. (x + 2), (x² – 3x + 8)

3. (x + 3), (x² + 8x – 3)

4. (x + 4), (4x² + 3x – 8)

Q.

If one zero of 2x² - 3x + k is reciprocal to the other, then the value of k is :

1. -3

2. -2/3

3. -3/2

4. 2

Q. Question 19
If $\frac{x}{y}+\frac{y}{x}=-1$ (where $x,y\ne 0$ ), then the value $x^3-y^3$ is

A) 1
B) -1
C) 0
D) $\frac{1}{2}$

Q.

How many first-degree polynomials as factors a quadratic polynomial can have ?

1. 5

2. 2

3. 3

4. 4