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:

We can solve this question by following the steps given below:

Step 1: Arrange the divisor as well as dividend individually in decreasing order of their degree of terms.

Step 2: By performing the division, we seek to find the quotient. To find the very first term of the quotient, divide the first term of the dividend by the highest degree term in the divisor. Now write the quotient.

Step 3: Multiply the divisor by the quotient obtained. Put the product underneath the dividend. Subtract the product obtained as done in the case of a division operation.

Step 4: Write the result obtained after drawing another bar to separate it from prior operations performed. Bring down the remaining terms of the dividend.

Step 5: Again, divide the dividend by the highest degree term of the remaining divisor. Repeat the previous steps to get the quotient until the degree of divisor is smaller than or equal to the degree of dividend.

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

Quotient = x - 3, Remainder = 7x - 9

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

Quotient = x² + x - 3, Remainder = 8

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

Quotient = - x² - 2, Remainder = - 5x + 10

☛ Check: Class 10 Maths NCERT Solutions Chapter 2

Video Solution:

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

NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.3 Question 1

Summary:

By dividing the polynomial p(x) by the polynomial g(x) 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 are i) x - 3, 7x - 9 ii) x² + x - 3, 8 iii) - x² - 2, - 5x + 10 respectively.

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