Factorisation by Regrouping Terms

Q.

Factorise: 5√5 x^2 + 30x + 8√5 by splitting the middle term

Q. Factorise the expression $x^3-6x^2+11x-6$.

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

Q.

If a + b = 1 and a - b = 7 ; Find

(i) $(a^2+b^2)$ (ii) ab

1. (i) 25 (ii) -12

2. (i) 51 (ii) 12

3. (i) 26 (ii) -13

4. (i) -25 (ii) 12

Q.

Factorise by grouping method:

$ab(x^2+1)+x(a^2+b^2)$

Q.

Factorise by grouping method:

$a^2+b-ab-a$

Q.

Factorise by grouping method:

$a^3+a-3a^2-3$

Q. Question 3
Check whether 7 + 3x is a factor of $3x^3+7x$.

Q.

Factorise by grouping method:

$ab-2b+a^2-2a$

Q.

Factorise by grouping method:

$16(a+b{)}^2-4a-4b$

Q.

Factorise by grouping method:

$(2a-b{)}^2-10a+5b$

Q.

Factorise by grouping method:

$a^2+4b^2-3a+6b-4ab$

Q.

Factorise by grouping method:

$y^2-(a+b)y+ab$

Q.

Factorise by grouping method:

$a^4-2a^3-4a+8$

Q.

Factorise by grouping method:

$x^2+y^2+x+y+2xy$

Q. Question 3
Check whether 7 + 3x is a factor of $3x^3+7x$.

Q. Check whether 7 + 3x is a factor of $3x^3+7x$.

Q.

What are the common factors of ​$3x^{3}y,5x{y}^{2}and15xy?$

1. 

2. 

3. 

4. 

Q. 82.If (x-1), (x+2)and (x-2)are factors of x3+ax2+bx+c, then the value of a+b+c is

Q.

Factorise by grouping method:

$m(x-3y{)}^2+n(3y-x)+5x-15y$

Q.

Factorise by grouping method:

$x(6x-5y)-4(6x-5y{)}^2$

Q.

The highest common factor of ​$3x^{3}y,5x{y}^2,15xy$ is ____.

1. 

2. 

3. 

4. 

Q.

Factorise by grouping method:

$a(a-4)-a+4$

Q.

The product of two numbers is $x^2+x-2$. If one of the numbers is $x-1$, Then the other number is

1. $x-2$

2. $x+2$

3. $x+1$

4. $x-1$

Q. Which of the following are the factors of $x^2-5x+6?$

1. $(x+2)(x+3)$
2. $(x+6)(x-1)$
3. $(x-2)(x-3)$
4. $(x-6)(x+1)$

Q. $11+5x-6x^2$

1. $(x+1)(11-6x)$
2. $(x-1)(11-6x)$
3. $(x+1)(11+6x)$
4. None of these

Q. $p^3{q}^3-pq-p^2{q}^2+p^4{q}^4$ can be regrouped and simplified as _______.

1. $\left(pq\right)(1+pq)(1-pq{)}^2$
2. $(-pq)(1-pq)(1+pq{)}^2$
3. $\left(pq\right)(1+pq)(1+pq{)}^2$
4. $(-pq)(1-pq)(1+pq{)}^2$

Q. Question 17
Determine which of the following polynomial has x – 2 a factor:
(i) $3x^2+6x-24$
(ii) $4x^2+x–2$

Q.

Factorize $(a^2-b^2)(c^2-d^2)-4abcd$

1. $(ac-bc-ad+bd)(ac-bc+ad-bd)$

2. $(ac-bc+ad+bd)(ac+bc-ad-bd)$

3. $(ac+bc-ad+bd)(ac+bc-ad-bd)$

4. $(ac-bc+ad+bd)(ac-bc-ad-bd)$

Q.

Q. Find the factors of the polynomials given below.
(i) 2x² + x – 1

(ii) 2m² + 5m – 3

(iii) 12x² + 61x + 77

(iv) 3y² – 2y – 1

(v) $\sqrt{3}{x}^2+4x+\sqrt{3}$

(vi) $\frac{1}{2}{x}^2-3x+4$