Can x - 1 be the remainder on division of a polynomial p (x) by 2x + 3? Justify your answer

Solution:

Given, polynomial p(x) divided by (2x + 3).

We have to check whether the remainder is x - 1.

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

Here, g(x) = 2x + 3

r(x) = x - 1.

Degree of r(x) = 1

Degree of g(x) = 1

Degree of r(x) = degree of g(x)

r(x) is not equal to zero

Degree of r(x) is not less than the degree of g(x)

Therefore, x - 1 cannot be the remainder of p(x).

✦ Try This: Can x - 1 be the remainder on division of a polynomial p(x) by x + 2? Justify your answer

Given, polynomial p(x) divided by (x + 2).

We have to check whether the remainder is x - 1.

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

Here, g(x) = x + 2

r(x) = x - 1.

Degree of r(x) = 1

Degree of g(x) = 1

Degree of r(x) = degree of g(x)

r(x) is not equal to zero

Degree of r(x) is not less than the degree of g(x)

Therefore, x - 1 cannot be the remainder of p(x)

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.2 Solved Problem 1

Summary:

x - 1 cannot be the remainder on division of a polynomial p (x) by 2x + 3

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