9th Class Math Chapter 6 Algebraic Manipulations Short Questions Answer
| Class: | 9th Class | Subject: | Math |
| Chapter: | Chapter 6 | Board: | All Boards |
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9th Class Math Chapter 6 Algebraic Manipulations Short Questions Answer
Find the H.C.F of the following by factorization. 8x⁴ – 128, 12x³ – 96
Solution:
8x⁴ – 128 = 8(x⁴ – 16) = 8(x⁴ – 4²)
= 8(x² – 2²)(x² + 2²)
H.C.F. = 2³(x – 2)(x + 2)(x² + 4)
12x³ – 96 = 12(x³ – 8) = 2² x 3(x³ – 2³)
= 2² x 3(x – 2)(x² + 2x² + 4)
H.C.F. = 2²(x – 2)
= 4(x – 2)
Find the H.C.F. of the following by division method. y³ + 3y² – 3x – 9, y³ + 3y² – 8y – 24
Find the L.C.M. of the following by factorization. 12x² – 75, 6x² – 13x – 5, 4x² – 20x + 25
Solution:
12x² – 75 = 3(4x² – 25) = 3[(2x)² – 5²]
= 3(2x – 5) (2x + 5)
6x² – 13x – 5 = 6x² – 15x + 2x – 5
= 3x (2x – 5) (3x + 1)
= (2x – 5) (3x + 1)
4x² – 20x + 25 = (2x)² – 2(2x)(5) + 25
= 3x (2x – 5) (3x + 1)
= (2x – 5)²
So, L.C.M. = 3(2x + 5) (3x + 1) (2x – 5)²
If H.C.F. of x⁴ + 3x³ + 5x² + 26x + 56 and x⁴ + 2x³ – 4x² – x + 28 is x² + 5x + 7. Find their L.C.M.
Solution:
Let p(x) = x⁴ + 3x³ + 5x² + 26x + 56
Q(x) = x⁴ + 2x³ – 4x² – x + 28
H.C.F. = x² + 5x + 7
L.C.M. = p(x) x Q(x)/H.C.F.
= (x⁴ + 3x³ + 5x² + 26x + 56)( x⁴ + 2x³ – 4x² – x + 28)/x² + 5x + 7
Now dividing
So, L.C.M.
= (x² + 5x + 7)(x² + 2x + 8)(x⁴ + 2x³ – 4x62 – x + 28)/x²+5x +7
= (x² + 2x + 8)(x⁴ + 2x³ – 4x62 – x + 28)
Simplify
Find square root by using factorization. (x² + 1/x²) + 10 (x + 1/x) + 27 (x ≠ 0)
Ans: Solution:
= x² + 1/x² + 2 + 10 (x + 1/x) + 27 – 2
= (x + 1/x)² + 10 (x + 1/x) + 25
= (x + 1/x)² + 2 (x + 1/x) + 5 + 5²
= [(x + 1/x) + 5]²
Required square root is ± [(x + 1/x) + 5]
Find square root using division method. 4x²/y² + 20x/y + 13 – 30y/x + 9y²/x² (x ≠ 0)(y ≠ 0)
Solution:
How to Write Perfect Short Answers?
In Board Exams, the examiner looks for specific keywords and presentation. Here is how to attempt Chapter 6 questions:
- Ideal Length: Write 3 to 5 lines for each short question. Too short gets fewer marks, too long wastes time.
- Highlighting: Use a Blue Marker to highlight key dates, names, or scientific terms in your answer.
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