Question

Two polynomials x³⁶ − 3x³⁵ and x − 3.

Assertion (A): If x − 3 is factor of x³⁶ − 3x³⁵; the remainder is zero.

Reason (R): The polynomial x - a is factor of polynomial p(x) = x³⁶ = ax³⁵; if p(a) = 0)

पर्याय

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

By factor theorem,

(x - a) is a factor of the polynomial f(x), if the remainder i.e. f(a) = 0.

Let f(x) = x³⁶ - 3x³⁵

When, x − 3 is a factor of f(x), then f(3) = 0, by factor theorem.

∴ Assertion (A) is true.

When, p(x) = x³⁶ - ax³⁵ is divided by x − a, we get:

Remainder, p(a) = a³⁶ − a.a³⁵

= a³⁶ − a³⁶

= 0.

Since, p(a) = 0, thus (x − a) is factor of p(x).

∴ Reason (R) is true.