Test: Factorisation- 2 - Class 8 MCQ

The correct answer is Option A - 3ab (4a + 5b)

Find the greatest common factor of the numeric coefficients: the numbers 12 and 15 have common factor 3.

Find the common factor in the literal parts: between a² and a the common power is a, and between b and b² the common power is b; so the common literal factor is ab.

Combining numeric and literal parts gives the common factor 3ab.

Divide the coefficients by the common numeric factor: 12 ÷ 3 = 4 and 15 ÷ 3 = 5. The remaining literal parts after removing ab are a and b, so the terms become 4a and 5b.

Therefore, after factoring out 3ab the expression becomes 3ab(4a + 5b), which matches the chosen option.

C ) (x² +8x +16)
= (x² + 4x + 4x + 16)
= ( x² + 4x ) + (4x + 16 )
= x(x + 4 ) +4(x + 4 )
=(x + 4)(x + 4)
=(x + 4)² 

Solution:

When we factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions. 

To factorise the expression 6xy - 4y + 6 - 9x, we can follow these steps:

Thus, the fully factored form of the expression is (3x - 2)(2y - 3).

x² + 8x + 12 
two no whose product is 12 and sum is 8
ie. 2 and 6 so;
x²+2x+6x+12
x(x+2)+6(x+2)
(x+2)(x+6)

To find the quotient of -18xyz² divided by -3xz, follow these steps:

Therefore, the final quotient is 6yz.

First cancel the common factor (2x+1):

So, option (c) is the correct answer.

We have  p4 - 81 = (p²)² - (9)² 

Now using a² - b² = (a + b)(a - b), we have

         (p²)² - (9)² = (p² + 9)(p² -9)

We can factorise p² - 9  further as

              p² - 9 = (p)² - (3)²

                       = (p + 3)(p - 3)

∴           p⁴ - 81 = (p + 3)(p - 3)(p² + 9)