पाण्याचे उपयोग लिहा.
Answers
Answer:
x2 + 8x + 15 = x2 + 5x + 3x + 15 = (x + 3) (x + 5)
x2 + 3x – 10 = x2 + 5x – 2x – 10 = (x – 2) (x + 5)
Clearly, the common factor is x + 5.
Polynomials Class 9 Extra Questions Short Answer Type 1
Question 1.
Expand :
(i) (y – √3)2
(ii) (x – 2y – 3z)2
Solution: (i)
(y – √3)2 = y2 -2 × y × √3 + (√3)2 = y2 – 2√3 y + 3 (x – 2y – 3z)2
= x2 + 1 – 2y)2 + (-3z)2 + 2 × x × (-2y) + 2 × (-2y) × (-3z) + 2 × (-3z) × x
= x2 + 4y2 + 9z2 – 4xy + 12yz – 6zx
Question 2.
If x + = 1x = 7, then find the value of x3 + 1x3
Solution:
We have x + 1x = 7
Cubing both sides, we have
Polynomials Class 9 Extra Questions Maths Chapter 2 with Solutions Answers 2
Question 3.
Show that p – 1 is a factor of p10 + p8 + p6 – p4 – p2 – 1.
Solution:
Let f(p) = p10 + p8 + p6 – p4 – p2 – 1
Put p = 1, we obtain
f(1) = 110 + 18 + 16 – 14 – 12 – 1
= 1 + 1 + 1 – 1 – 1 – 1 = 0
Hence, p – 1 is a factor of p10 + p8 + p6 – p4 – p2 – 1.
Question 4.
If 3x + 2y = 12 and xy = 6, find the value of 27x3 + 8y3
Solution