Home
Class 10
MATHS
Using Division Algorithm prove that the ...

Using Division Algorithm prove that the polynomial ` g(x) = x^(2) + 3x + 1 ` is a factor of `f(x) = 3 x^(4) + 5 x^(3) - 7 x^(2) + 2x + 2`

Text Solution

Verified by Experts

The correct Answer is:
i.e., g (x) is a factor of f(x)
Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    ZEN PUBLICATION|Exercise TEXTUAL EXERCISE ( Exercise 9 . 1 )|1 Videos

  • POLYNOMIALS

    ZEN PUBLICATION|Exercise TEXTUAL EXERCISE ( Exercise 9 . 2 )|2 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    ZEN PUBLICATION|Exercise ADDITIONAL QUESTIONS - HIGHER ORDER THINKING SKILLS (HOTS)|12 Videos

  • PROBABILITY

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS HOTS [HIGHER ORDER THINKING SKILLS]-QUESTIONS|24 Videos

Similar Questions

Explore conceptually related problems

Check if g(x) = x^(3) - 3x + 1 is a factor of p(x) = x^(5) - 4x^(3) + x^(2) +3x + 1 .

If x - 1 is a factor of x^(5) - 4x^(3) +2 x^(2) - 3x + k = 0 then k is

Divide the polynomial 2x ^(4) - 4x ^(3) - 3x -1 by (x-1)

lim _ ( xto infty ) ( 3x^(2) -4x + 5)/( 7x^(2) + 2x +3)

Check whether (x-2) is a factor of x ^(3) - 2x ^(2) - 5x +4

Find the Factor Theorem, x +2 is a factor of x ^(3) + 2x ^(2) + 3x + 6.

If x = 1 is a zeru of the polynomial f(x) = x^(3) - 2x^(2) + 4x + k , write the value of k.

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : i] p(x) = x^(3) - 3x^(2) + 5x - 3, g(x) = x^(2) - 2 ii] p(x) = x^(4) - 3x^(2) + 4x + 5, g(x) = x^(2) + 1 - x iii] p (x) = x^(4) - 5 x + 6 g(x) = 2 - x^(2)

Show that (x +4) ,(x-3) and (x-7) are factors of x ^(3) - 6x ^(2) - 19 x + 84.