Page 95 - Maths Skills - 8

Factorisation 93

3. If 2(a + b ) = (a + b) , then Answer the following questions on the basis of the
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(i) a + b = 0 (ii) a = b above data.
(iii) 2a = b (iv) ab = 0 1. If the height corresponding to side PQ is 2x + 3,
4. The value of (525) – (475) is then find the length of side RS.
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(i) 100 (ii) 1000 2. She fenced the garden with wire which cost a
total of rupees x. Find the rate of wire per unit
(iii) 100000 (iv) 50,000 length.
5. Which of the following is the complete 3. Find the area of parallelogram shaped garden
factorisation of 12x – 92x? for x = 4 unit.
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(i) 4x (3x – 23) (ii) 4x (3x – 23x)
(iii) x (12x – 92) (iv) 4 (3x – 23x) E. Assertion-Reason Based Questions
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6. A rectangle has area of x + 13x + 40 square fact. Directions for Questions 1 to 3: In each of the
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questions given below, there are two statements
The width is (x + 5) fact. What is the length? marked as Assertion (A) and Reason (R). Mark your
(i) (x + 2) (ii) (x + 4) answer as per the codes provided below:
(iii) (x + 8) (iv) (x + 10) (a) Both A and R are true and R is the correct
explanation of A.
B. Fill in the blanks
(b) Both A and R are true but R is not the correct
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1. 8x 6x 12x __________ explanation of A.
2x (c) A is true but R is false.
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2. a b 2 ab __________ (d) A is false but R is true.
Q. 1. Assertion (A): x – 16 can be factorised as
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( ab )
(x + 4) (x – 4).
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3. 18x 9x 6x 2 __________ Reason (R): a – b can be factorised as
3x 2 (a + b) (a –b), where a and b are any integers.
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C. Write ‘T’ for true and ‘F’ for false statements Q. 2. Assertion (A): x + 4x + 4 = (x + 2) (x – 2)
Reason (R): a + 2ab + b = (a + b) (a + b)
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1. x + (a + b)x + ab is the same as (x + a + b) .
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Q. 3. Assertion (A): The factors of 4x – 2x is 2x (2x – 1)
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2. The factorisation of x – 10 x + 21 is Reason (R): a × b – ab can be written as
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(x – 7) (x –3). ab (ab – 1)
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3. The factorisation of p + 6p – 16 is SUBJECTIVE TYPE QUESTIONS
(p – 8) (p – 2).
F. Solve the following word problems
4. 12d – 25 is the same as (11d – 5) . 1. Using division, show that (2x + 3) is a factor of
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8x + 36x + 54x + 27.
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5. The product of (a – 7) (a + 2) will be 2. If y + 3 is a factor of 2y – 14y + k, then find the
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a – 5a – 14. value of k.
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3. If a + a + 8a + a + p is divisible by (a + 1),
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D. Case Study Based Questions then find the value of p.
Renu wants to make a garden in her house in the 4. What must be subtracted from
shape of a parallelogram PQRS, the area of which is x – 6x + 12x – 17x + 5, so that the resulting
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4x – 9 and its side QR is of length 3 m. polynomial is exactly divisible by x – 2x + 3?
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