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Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.
Concept: undefined >> undefined
In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)
f(x) = x3 + 4x2 − 3x + 10, g(x) = x + 4
Concept: undefined >> undefined
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f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
Concept: undefined >> undefined
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
Concept: undefined >> undefined
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
Concept: undefined >> undefined
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
Concept: undefined >> undefined
f(x) = x4 − 3x2 + 4, g(x) = x − 2
Concept: undefined >> undefined
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
Concept: undefined >> undefined
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Concept: undefined >> undefined
If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.
Concept: undefined >> undefined
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
Concept: undefined >> undefined
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
Concept: undefined >> undefined
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
Concept: undefined >> undefined
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Concept: undefined >> undefined
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
Concept: undefined >> undefined
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x .
Concept: undefined >> undefined
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the value of the following case, if R1 = R2.
Concept: undefined >> undefined
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following case, if R1 + R2 = 0.
Concept: undefined >> undefined
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following cases, if 2R1 − R2 = 0.
Concept: undefined >> undefined
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
Concept: undefined >> undefined
