Factorisation of Quadratic Polynomials

Q.

Factorise:$49x^2-36$.

Q. Question 1 (ii)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.

iii) $-2\sqrt{3},-9$

Q.

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by $\frac{1}{15}$. Find the fraction.

Q. Solve the following quadratic equations by factorization method: [2 MARKS]

(i) $x^2-8x+16=0$

(ii) $x^2+14x–32=0$

Q. If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $4x^2+4x+1$, then form a quadratic polynomial whose zeroes are $2\alpha$ and $2\beta$.

1. $x^2+x+1$
2. $x^2-2x+1$
3. $x^2+2x+1$
4. $x^2+12x+1$

Q. What are the factors of $x^2+5x-24$?

1. $(x+3)(x+8)$
2. $(x-3)(x-8)$
3. $(x-3)(x+8)$
4. $(x+3)(x-8)$

Q. The zeroes of the following quadratic polynomial $6x^2+x-5$ are .

1. $\frac{1}{2}$ & 1
2. $\frac{5}{6}$ & -1
3. -1 & 2

Q.

Determine which of the following polynomials has $(x+1)$ a factor :

$x^3+x^2+x+1$

Q.

Determine which of the following polynomials has $(x+1)$ a factor :

(ii) $x^4+x^3+x^2+x+1$

Q. The zeroes of the following quadratic polynomial $6x^2+x-5$ are .

1. $\frac{1}{2}$ & 1
2. $\frac{5}{6}$ & -1
3. -1 & 2

Q. If $\alpha$ and $\beta$ are the zeroes of polynomial $P\left(x\right)=x^2-3x+2k$, and $\alpha +\beta =\alpha .\beta$, then the value of k is ...............

1. 3
2. 1
3. 3/2
4. -3

Q. Question 1 (iv)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
iv) $=\frac{-3}{2\sqrt{5}},-\frac{1}{2}$

Q.

Which of the following is the factor of the polynomial
$x^3-3x^2-10x+12$ ?

1. $x-0$

2. $x-1$

3. $x-2$

4. $x+1$

Q. are the factors of the polynomial $x^2+2x-8$.

1. $(x-4)\&(x-2)$
2. $(x+4)\&(x-2)$
3. $(x-4)\&(x+2)$

Q. Factorise the polynomial $2y^3+y^3-2y-1$

1. $(y-1)(y-1)(2y+1)$
2. $(y+1)(y+1)(2y+1)$
3. $(y-1)(y+1)(2y+1)$
4. $(y-1)(y-1)(2y-1)$

Q. Question 1(i)
Find the roots of the following quadratic equations by factorisation:
(i) $x^2-3x-10=0$

Q. If one of the zeroes of a quadratic polynomial $(k-1)x^2+kx+1$ is -3, then the value of k is .

1. $\frac{4}{3}$
2. $-\frac{4}{3}$
3. $\frac{2}{3}$

Q.

1. $81$
2. $36$
3. $64$
4. $49$

Q.

Which of the following is a factor of $(49x^2-1)+(1+7x{)}^2$?

1. $1-7x$

2. $1+7x$

3. $49x$

4. $x+1$

Q. If one of the zeroes of a quadratic polynomial $(k-1)x^2+kx+1$ is -3, then the value of k is .

1. $\frac{4}{3}$
2. $-\frac{4}{3}$
3. $\frac{2}{3}$

Q.

Select the option that contains the factor of $4x^3+4x^2-x-1$

1. $(x+\frac{1}{2})$

2. $(2x-1)$

3. $(x-3)$

4. $(2x-2)$

Q. are the factors of the polynomial $x^2+2x-8$.

1. $(x-4)\&(x-2)$
2. $(x+4)\&(x-2)$
3. $(x-4)\&(x+2)$

Q. Explain why $3.\overline{1416}$ is a rational number.
[1 mark]
[ <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> RS Aggarwal]
[Rational Numbers and Their Decimal Expansions]

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

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

Q. $4a^2-12ab+9b^2+4a-6b$

1. $(2a-3b)(2a-3b+2)$
2. $(2a+3b)(2a-3b+2)$
3. $(2a-3b)(2a+3b-2)$
4. $(2a+3b)(2a-3b-2)$

Q.

Find the zeroes of the following quadratic polynomial $6x^2+x-5$.

1. $\frac{1}{2},1$

2. 6, 5

3. $\frac{5}{6},-1$

4. 2, 1

Q. Solve the given quadratic equation by factorization method
$\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$

Q. are the factors of the polynomial $x^2+2x-8$.

1. $(x-4)\&(x-2)$
2. $(x+4)\&(x-2)$
3. $(x-4)\&(x+2)$

Q. are the factors of the polynomial $x^2+2x-8$.

1. $(x-4)\&(x-2)$
2. $(x+4)\&(x-2)$
3. $(x-4)\&(x+2)$

Q. The zeroes of the following quadratic polynomial $6x^2+x-5$ are .

1. $\frac{1}{2}$ & 1
2. $\frac{5}{6}$ & -1
3. -1 & 2