Assertion (A): (x − 1) is a factor of x³ − 1. Reason (R): p(1) = 0 for p(x) = x³ − 1. Which is correct?

Both A and R are true, and R correctly explains A.. p(1) = 1 − 1 = 0, so by the Factor Theorem (x − 1) is a factor. R is true and is exactly the reason A holds.

Assertion (A): $(x - 1)$ is a factor of $x^{3} - 1$ . Reason (R): $p (1) = 0$ for $p (x) = x^{3} - 1$ . Which is correct?

Class 9PolynomialsPolynomials

ABoth A and R are true, and R correctly explains A.
BBoth A and R are true, but R does not explain A.
CA is true but R is false.
DA is false but R is true.

Step-by-Step Solution

p (1) = 1 - 1 = 0

, so by the Factor Theorem

(x - 1)

is a factor. R is true and is exactly the reason A holds.

Answer: A) Both A and R are true, and R correctly explains A.

Key idea: Factor Theorem

(x - a)

is a factor of

p (x)

if and only if

p (a) = 0

.**

It's a special case of the remainder theorem (with remainder 0).

Use it to test factors:
Is

(x + 3)

a factor of

p (x) = x^{2} + 5 x + 6

?
Substitute

x = - 3

(note:

x + 3 = 0

→

x = - 3) . p (- 3) = 9 - 15 + 6 = 0

. ✓ Yes,

(x + 3)

is a factor.

This is the standard way to factor cubics — guess and test small zeros.

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If a + b + c = 0, then a³ + b³ + c³ equals which of the following?Factorise the cubic x³ − 3x² − x + 3 completely.Which of the following statements is correct?The sum of the zeros of x² − 7x + 12 is ______.Without dividing, find the remainder when p(x) = x³ + 1 is divided by (x + 1).

Assertion (A): (x−1) is a factor of x3−1. Reason (R): p(1)=0 for p(x)=x3−1. Which is correct?

Step-by-Step Solution

Key idea: Factor Theorem

Master this chapter in 30 minutes a day.

More Class 9 Polynomials practice

Assertion (A): $(x - 1)$ is a factor of $x^{3} - 1$ . Reason (R): $p (1) = 0$ for $p (x) = x^{3} - 1$ . Which is correct?