Advertisements
Advertisements
प्रश्न
Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm g(x) = 2x2 − x + 3, f(x) = 6x5 − x4 + 4x3 − 5x2 − x − 15
उत्तर
3x2 + x2 − 2x − 5
`2x^2 - x + 3)overline(6x^5 - x^4 + 4x^3 - 5x^2 - x - 15)`
6x3 − 3x4 + 9x3
− + −
2x4 − 5x3 − 5x2
2x4 − x3 + 3x2
− + −
− 4x3 − 8x2 − x
− 4x3 + 2x2 − 6x
+ − +
−10x2 + 5x − 15
−10x2 + 5x − 15
+ − +
0
Since the remainder is 0,
Hence, 2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
APPEARS IN
संबंधित प्रश्न
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following
p(x) = x4 – 5x + 6, g(x) = 2 – x2
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
t2 – 3, 2t4 + 3t3 – 2t2 – 9t – 12
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 4x3 + 8x2 + 8x + 7, g(x) = 2x2 − x + 1
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 15x3 − 20x2 + 13x − 12; g(x) = x2 − 2x + 2
Find all zeros of the polynomial 2x4 + 7x3 − 19x2 − 14x + 30, if two of its zeros are `sqrt2` and `-sqrt2`.
If (a-b) , a and (a + b) are zeros of the polynomial `2x^3-6x^2+5x-7` write the value of a.
State Division Algorithm for Polynomials.
Find the quotient and remainder of the following.
(4x3 + 6x2 – 23x + 18) ÷ (x + 3)
Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?
