Home
Class 9
MATHS
Fill in the blanks. (i) When P (x) is ...

Fill in the blanks.
(i) When P (x) is divided by _____P_____ the remainder is P (a).
(ii)If P (a) = 0, then ____Q___ is a factor of P (x).
(iii) If p (-a) =0, then ____R___ is a factor of P (x).

A

`{:(P, Q, R),(""(x - a) , (x -a) , (x +a) ):}`

B

`{:(P, Q, R),(""(x + a) , (x -a) , (x +a) ):}`

C

`{:(P, Q, R),(""(x - a) , (x +a) , (x -a) ):}`

D

`{:(P, Q, R),(""(x + a) , (x -a) , (x -a) ):}`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we need to fill in the blanks based on the properties of polynomials and the Remainder Theorem. ### Step-by-Step Solution: **(i)** When \( P(x) \) is divided by _____, the remainder is \( P(a) \). According to the Remainder Theorem, when a polynomial \( P(x) \) is divided by \( x - a \), the remainder is \( P(a) \). So, we fill in the blank with: **Answer:** \( x - a \) **(ii)** If \( P(a) = 0 \), then ____ is a factor of \( P(x) \). If \( P(a) = 0 \), it means that \( a \) is a root of the polynomial \( P(x) \). Therefore, by the Factor Theorem, \( x - a \) is a factor of \( P(x) \). So, we fill in the blank with: **Answer:** \( x - a \) **(iii)** If \( P(-a) = 0 \), then ____ is a factor of \( P(x) \). If \( P(-a) = 0 \), it means that \( -a \) is a root of the polynomial \( P(x) \). Therefore, by the Factor Theorem, \( x + a \) is a factor of \( P(x) \). So, we fill in the blank with: **Answer:** \( x + a \) ### Final Answers: (i) \( x - a \) (ii) \( x - a \) (iii) \( x + a \)
Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC EXPRESSIONS AND POLYNOMIALS

    CENGAGE|Exercise TEST YOURSELF (LEVEL 3) (MULTIPLE CHOICE QUESTIONS) |40 Videos

  • CIRCLES

    CENGAGE|Exercise OLYMPIAD AND NTSE LEVEL EXERCISES|6 Videos

Similar Questions

Explore conceptually related problems

When (p^(2)-p-29) is divided by (p-6) the remainder is 1.

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(0) is

Find the quotient and remainder when p(x) is divided by q(x)

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(5) is

If we divide a polynomial p(x) by x-alpha, the remainder obtained is p(alpha) Note that if p(alpha)=0, then x-alpha is a factor of p(x)

Find all cubic polnomials p(x) such that (x-1)^(2) is a factor of p(x)+2 and (x+1)^(2) is a factor of p(x)-2 .

When a polynomial p(x) is divided by x-1, the remainder is 3. When p(x) is divided by x-3, the remainder is 5. If r(x) isthe remainder when p(x) is divided by (x-1)(x-3), then thevalue of r(-2) is

Suppose p(x) is a polynomial with integer coefficients.The remainder when p(x) is divided by x-1 is 1 and the remainder when p(x) is divided cby x-4 is 10. If r(x) is the remainder when p(x) is divided by (x-1)(x-4) then find the value of r(2006)

Suppose p(x) is a polynomial with integer coefficients.The remainder when p(x) is divided by x-1 is 1 and the remainder when p(x) is divided cby x-4 is 10. If r(x) is the remainder when p(x) is divided by (x-1)(x-4) then find the value of r(2006)