Factorisation Using Factor Theorem

Q.

Factorise $x^2+3x+2$ by using the Factor Theorem.

1. $(x+5)(x+2)$

2. $(x+4)(x+2)$

3. $(x+1)(x+6)$

4. $(x+1)(x+2)$

Q. Factorise $x^2–5x+6$ by using the Factor Theorem.

Q.

Factorise $x^2-3x+2$ by using the Factor Theorem.

1. $(x-1)(x-4)$

2. $(x-1)(x-5)$

3. $(x-1)(x-2)$

4. $(x-1)(x-6)$

Q.

Factorise $x^2+5x+6$ by using the Factor Theorem.

1. $(x+2)(x+3)$

2. $(x+2)(x+6)$

3. $(x+5)(x+3)$

4. $(x+2)(x+4)$

Q.

Factorise $x^2–5x+6$ by using the Factor Theorem.

1. $(x–2)(x–10)$

2. $(x–7)(x–3)$

3. $(x–2)(x–3)$

4. $(x–2)(x–4)$

Q.

If $x^g$+$\frac{1}{x^a}$ is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial?

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Q. Factorise $\frac{x^3+5}{x+2}$ using synthetic division.

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

Q. State whether True or False.
The H.C.F. and L.C.M. of:

Q. The value of $(2x-3y{)}^3+(x+3y{)}^3+3(2x-3y{)}^2(x+3y)+3(2x-3y\left)\right(x+3y{)}^2=$

1. $27x^3$
2. $(2x-3y{)}^3+(x+3y{)}^3$
3. $0$
4. $29x^3+(x+3y{)}^3$

Q. $(2x-3y{)}^3+(x+3y{)}^3+3(2x-3y{)}^2(x+3y)+3(2x-3y\left)\right(x+3y{)}^2=$

1. 
2. 
3. 
4. 

Q. State whether the following expression are polynomials or not? Justify your answer.
$\frac{1}{2x}$

Q.

If $(x^2+y^2+z^2)=(xy+yz+zx)$, $\text{what is the value of}{x}^3+y^3+z^3$?

1. 3xyz

2. -3xyz

3. 2xyz

4. -2xyz

Q.

If $x^g$+$\frac{1}{x^a}$ is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial?

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