exercise 2.3 class 10 maths

exercise 2.3 class 10 maths involve complete answers for each question in the exercise 2.3. The solutions provide students a strategic methods to prepare for their exam. exercise 2.3 class 10 maths questions and answers helps students to perform better in exam and it will clear doubts definitely. Students will find it extremely easy to understand the questions and learn solving the problems.exercise 2.3 class 10 maths prepared by www.mathematicsandinformationtechnology.com team in very delicate, easy and creative way.

 

Question 1:

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

(i) p(x)=x³- 3x² + 5x - 3, g( x )= x² -2  

 (ii)p(x)=x⁴- 3x²+ 4x +5,g( x )= x² +1-x  

 (iii) p(x)=x⁴- 5x +6, g( x )= 2-x²     

Solution 1:

p(x)=x³- 3x² + 5x - 3, g( x )= x² -2 

        

Answer: Quotient:  x-3 ; Remainder = 7x-9.

(ii) p(x)=x⁴- 3x²+ 4x +5,g( x )= x² +1-x

          

Answer: Quotient: x²+x-3   ; Remainder = +8 .

(iii) p(x)=x⁴- 5x +6, g( x )= 2-x²     

                            
Answer: Quotient: -x²-2   ; Remainder =-5x+10.

Question 2.

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

(i) t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12

(ii) x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

(iii) x² – 3x + 1, x⁵ – 4x³ + x² + 3x + 1 

Answer 2:

(i) t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12

t² – 3= t² + 0.t – 3

Since the remainder is  0 ,

Hence, t² – 3 is a factor of   2t⁴ + 3t³ – 2t² – 9t – 12

(ii) x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Since the remainder is 0,

Hence, x² + 3x + 1 is a factor of  3x⁴ + 5x³ – 7x² + 2x + 2

(iii) x² – 3x + 1, x⁵ – 4x³ + x² + 3x + 1 

Since the remainder is not equal to 0,

Hence, x² – 3x + 1 is not a factor of   x⁵ – 4x³ + x² + 3x + 1 

Question 3.

Question 4.

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).

Solution 4:

p(x)=x³ – 3x² + x + 2 (Dividend)

g(x) = ?     (Divisor)

Quotient = (x − 2)

Remainder = (− 2x + 4)

Dividend = Divisor × Quotient + Remainder

x³ – 3x² + x + 2=g(x) . (x-2) + (-2x+4)

x³ – 3x² + x + 2 + 2x - 4=g(x) . (x-2)

x³ – 3x² + 3x -2=g(x) . (x-2) 

g(x)  is the quotient when we divide x³ – 3x² + x + 2 by (x-2)

therefore g(x)=x²-x+1