Page 94 - Maths Skills - 8

92 Maths

Example 3: Using division, show that (4x – 3) is a factor of 12x – x – 26x + 15.
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Solution: On dividing, we get

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4– 3x 12x – x –26x +15 3x 2 + 2– 5x Fact-o-meter
3 2
12x –9x When remainder is zero,
– +
then divisor is the factor
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8x – 26x
of the dividend.
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8x – 6x
– +
– 20x +15
– 20x +15
+ –
×

Since, remainder = 0, it indicates (4x – 3) completely divides (12x – x – 26x + 15).
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So, (4x – 3) is a factor of (12x – x – 26x + 15).
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Exercise 6.4

1. Divide.
(i) 64xy z by 64x yz (ii) 125x y z by 25xy z (iii) –54 (x + y + z ) by (x + y + z )
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3 2
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3 2
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2. Divide.
2xy
(i) p – p + 5p by p 2 (ii) x y + 8x y + 6xy by 2xy (iii) 6x y – 4x y + 2xy by
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3 2
3 2
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3. Divide.
(i) 3x – 3x + 5x + x – 2 by 3x – 1 (ii) x + 6x + 12x + 8 by x + 2
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(iii) 3x – x + 4x + 4 by 3x + 2 (iv) a + a – a – 1 by a + a + 1
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(v) x + x + x + x + x + 1 by x + 1 (vi) x – 1 by x – 1
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4. Using division, show that (a – 1) is a factor of a – 1.
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ASSESSMENT TIME
2. Factorisation of x + 1 is
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COMPETENCY BASED QUESTIONS
(i) (x + 1)(x – x + 1)
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A. Multiple-Choice Questions
(ii) (x + 1)(x + 1)
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1. Zero of the polynomial p(x) = a x, a ≠ 0 is (iii) (x + 1) (x + x + 1)
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(i) x = 0 (ii) x = 1 (iv) (x – 1) (x – x – 1)
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(iii) x = –1 (iv) a = 0