Factorisation Test

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Factorisation Test - 5

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Weekly Quiz Competition

Question 1
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The factorisation of is

A

B

C

D

Solution
Question 2
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If (x + 5)²- 2(5x) = a² + b², find the values of a and b.

A
a = x, b = 10

B
a = 10, b = x

C
a = x, b = 5

D
a = b = 5x

Solution

(x + 5)²- 2(5x) = a² + b²

Comparing both left hand side and right hand side, we get

a = x and b = 5
Question 3
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The factors of are

A

B

C

D

Solution

We know that

So,
Question 4
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The factors of 5x² + 2x - 3 are

A
(5x + 3), (x + 1)

B
(2x - 3), (x + 1)

C
(5x - 3), (x + 1)

D
(x - 3), (x + 1)

Solution

5x² + 2x - 3
= 5x²+ 5x - 3x - 3
= 5x (x + 1) - 3 (x + 1)
= (5x - 3) (x + 1)
Question 5
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The factors of are

A

B

C

D

Solution

We know that
So,
Question 6
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The factors of are

A

B

C

D

Solution
Question 7
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The factors of are

A
(2p² + 9 - 14p), (14p - 63)

B
(2p² + 49 - 49p), (14p - 343)

C
(14p - 49), (2p² - 14p + 49)

D
(14p - 49), (2p²+ 7 - 14p)

Solution

We know that So,
Question 8
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The factorisation of (a + b)² - 4ab - 9 is

A
(a - b) (a - b)

B
(a - b + 9) (a - b - 9)

C
(a - b + 3) (a - b - 3)

D
(a + b + 3) (a + b + 3)

Solution

We know that

So,
Question 9
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Find the factors of a⁴ + 2a²b³ + b⁶.

A
(a² + b²), (a² + b²)

B
(a³ + b³), (a² + b³)

C
(a² + b³), (a² + b³)

D
(a² + b²), (a² + b³)

Solution

a⁴ + 2a²b³ + b⁶
= (a²)² + 2a²b³ + (b³)²
= (a² + b³)²
= (a² + b³)(a² + b³)
Question 10
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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 11
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Divide .

A

B

C

D

Solution
Question 12
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One of the factors of (x - 2)(x² + 16) - 8x(x - 2) is

A
(x - 4)

B
(x + 2)

C
(x + 6)

D
(x - 6)

Solution

(x - 2)(x² + 16) - 8x(x - 2)
Question 13
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Factorise:

A

B

C

D

Solution
Question 14
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Simplify:

A

B

C

D

Solution
Question 15
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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 16
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Fill in the blanks:

(i) is equal to P .

(ii) is equal to Q .

(iii) When we divide by , the resultant is kbc - a. So, k is equal to R .

A
(P) = , (Q) = 15a + 1, (R) = 2

B
(P) = , (Q) = 15a + 1, (R) = 2

C
(P) = , (Q) = 15a + 1, (R) = 1

D
(P) = , (Q) = 5a + 1, (R) = 2

Solution

(i)

(ii)

(iii)

So, k = 2
Question 17
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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.

Question 18

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Match the expressions given in Column I with one of their factors given in Column II.

Column I	Column II
(P)	(A) (x + 7)
(Q)	(B) (3x + 1)
(R)	(C) (5x - 12)
(S)	(D) (x + 1)

(P)-(D), (Q)-(A), (R)-(B), (S)-(C)

(P)-(D), (Q)-(B), (R)-(A), (S)-(C)

(P)-(D), (Q)-(C), (R)-(B), (S)-(A)

(P)-(D), (Q)-(A), (R)-(C), (S)-(B)

Solution

(P)

(Q)

(R)
-12x² - x + 1
= -(12x² + x - 1)
=(-1)(12x² + 4x - 3x - 1)
=
=

(S)

Question 19
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Do as directed.
(P) Factorise:
(Q) Find the greatest common factor of 6x²y³, 18x³y² and 30x⁴y⁵z.
(R) Divide x² - 5x - 14 by x² - 4x - 21.

A

B

C

D

Solution

(i)

(ii) The greatest common factor of 6x²y³, 18x³y² and 30x⁴y⁵z is 6x²y².

(iii) Dividing x²- 5x - 14 by x² - 4x - 21: