RD Sharma Solutions for Class 9 Mathematics Chapter 6 Exercise VSAQs Factorization of Polynomials are provided here. In this exercise, students will learn how to perform factorization of a polynomial using different methods. RD Sharma Solutions for Class 9 help students to have a better understanding of the factorization of polynomials.
RD Sharma Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise VSAQs
Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 6 Factorization of Polynomials Exercise VSAQs Page Number 6.33
Exercise VSAQs Page No: 6.33
Question 1: Define zero or root of a polynomial.
Solution:
zero or root, is a solution to the polynomial equation, f(y) = 0.
It is that value of y that makes the polynomial equal to zero.
Question 2: If x = 1/2 is a zero of the polynomial f(x) = 8x3 + ax2 – 4x + 2, find the value of a.
Solution:
If x = 1/2 is a zero of the polynomial f(x), then f(1/2) = 0
8(1/2)3 + a(1/2)2 – 4(1/2) + 2 = 0
8 x 1/8 + a/4 – 2 + 2 = 0
1 + a/4 = 0
a = -4
Question 3: Write the remainder when the polynomial f(x) = x3 + x2 – 3x + 2 is divided by x + 1.
Solution:
Using factor theorem,
Put x + 1 = 0 or x = -1
f(-1) is the remainder.
Now,
f(-1) = (-1)3 + (-1)2 – 3(-1) + 2
= -1 + 1 + 3 + 2
= 5
Therefore 5 is the remainder.
Question 4: Find the remainder when x3 + 4x2 + 4x-3 if divided by x.
Solution:
Using factor theorem,
Put x = 0
f(0) is the remainder.
Now,
f(0) = 03 + 4(0)2 + 4×0 -3 = -3
Therefore -3 is the remainder.
Question 5: If x+1 is a factor of x3 + a, then write the value of a.
Solution:
Let f(x) = x3 + a
If x+1 is a factor of x3 + a then f(-1) = 0
(-1)3 + a = 0
-1 + a = 0
or a = 1
Question 6: If f(x) = x^4 – 2x3 + 3x2 – ax – b when divided by x – 1, the remainder is 6, then find the value of a+b.
Solution:
From the statement, we have f(1) = 6
(1)4 – 2(1)3 + 3(1)2 – a(1) – b = 6
1 – 2 + 3 – a – b = 6
2 – a – b = 6
a + b = -4
RD Sharma Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise VSAQs
RD Sharma Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise VSAQs are based on the remainder theorem, factor theorem and factorization of polynomials by using the factor theorem. Exercise VSAQs will help students to understand the important steps involved in factorization using different methods.
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