Factorisation Test

Result

Factorisation Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

One of the factors of 3(a + b)(2x + 2y) + 6(a + b)(3x - 5y) is

A
(x + y)

B
(x - y)

C
(8x + y)

D
(x + 8y)

Solution

3(a + b)(2x + 2y) + 6(a + b)(3x - 5y)
= 3(a + b)[(2x + 2y) + 2(3x - 5y)]
= 3(a + b)[(2x + 2y + 6x - 10y)]
= 3(a + b)(8x - 8y)
= 3(a + b)8(x - y)
= 24(a + b)(x - y)
Question 2
1 / -0

Which of the following is/are the factor(s) of (6y² - 9y + 3)(x² + x - 12)?

(i) (x - 3)(x + 4)
(ii) (6y - 3)
(iii) (y - 2)

A
Only (ii)

B
Only (i)

C
Only (iii)

D
Both (i) and (ii)

Solution

(6y² - 9y + 3)(x² + x - 12)
= (6y² - 6y - 3y + 3)(x² + 4x - 3x - 12)
= [6y(y - 1) - 3(y - 1)][x(x + 4) - 3(x + 4)]
= [(6y - 3)(y - 1)][(x - 3)(x + 4)]
= (6y - 3)(y - 1)(x - 3)(x + 4)
Question 3
1 / -0

Which of the following statements is CORRECT?

A
There are two ways to divide a polynomial by a monomial, either by dividing each term of the polynomial by the monomial or by the common factor method.

B
The only way to divide a polynomial by a polynomial is to divide each term in the dividend polynomial by the divisor polynomial.

C
"Division is the inverse of multiplication." This idea is applicable only in the case of numbers but not in the case of division of algebraic expressions.

D
Any regrouping (or rearrangement) of the given expression may lead to factorisation.

Solution

Statement (1) is correct, whereas statements (2), (3) and (4) are incorrect.

In the case of division of a polynomial by a polynomial, we cannot proceed by dividing each term in the dividend polynomial by the divisor polynomial. Instead, we factorise both the polynomials and cancel their common factors.

Also, in the case of numbers, division is the inverse of multiplication. This idea is also applicable to the division of algebraic expressions.

And in factorisation by regrouping, we should remember that any regrouping (i.e. rearrangement) of the terms in the given expression may not lead to factorisation.
We must observe the expression and come out with the desired regrouping by trial and error.