Test: Factorisation- 1 - Class 8 MCQ

We have 4y² - 12y+9. comparing the equation with (a-b)²=a²-2ab+b²,gives us a²=(2y)²,2ab=2*3*2y and b²=(3)².Hence the answer is (2y-3)².

10x² − 18x³ + 14x⁴ = 2x(5x− 9x² + 7x³) = 2x²(5− 9x + 7x²)

8 (x³y²z² + x²y³z² + x²y²z³) ÷ 4x²y²z² 

= 

To factorise the expression x² + xy + 8x + 8y:

1. Group the terms into pairs that have common factors:

   x² + xy + 8x + 8y = (x² + xy) + (8x + 8y)

2. Factor out the common terms from each pair:
   • From x² + xy, factor out x:

     x(x + y)

   • From 8x + 8y, factor out 8:

     8(x + y)

3. Now, the expression becomes:

   x(x + y) + 8(x + y)

4. Notice that both terms have a common factor of (x + y). Factor this out:

   (x + y)(x + 8)

Thus, the factorised form is (x + 8)(x + y).

7x²y²z²÷14xyz
=(7/14)(x²/x)(y²/y)(z²/z)
=1/2(x)(y)(z)
=1/2xyz.

26xy(x + 5) (y - 4) / 13x(y - 4)
Cancelling 13x(y-4)
=2y(x+5)

(x³+2x²+3x)/2x
=x(x²+2x+3)/2x
=(x²+2x+3)/2

To factorise the expression 12x + 36, follow these steps:

• Identify the greatest common divisor (GCD) of the coefficients 12 and 36, which is 12.
• Factor out the GCD from each term: 12x + 36 = 12(x) + 12(3).
• Combine the terms inside the parentheses: 12(x + 3).

Thus, the factorised form of 12x + 36 is 12(x + 3).

To find the common factors of 2y and 22xy, we break down each term into its numerical and variable components:

• The numerical coefficients are 2 and 22. Their greatest common factor (GCF) is 2.
• The variables in both terms include y; there's no common x since it's only present in the second term.

Combining these, the greatest common factor is 2y.

Therefore, the correct answer is A.