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Remainder Theorem

Prove that 3x...

Question

Prove that (3x + 7) is a factor of $(6 x^{3} + 29 x^{2} + 44 x + 21)$ .

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Solution

$∵$ The remainder is $0$
Therefore, $(3 x + 7)$ is a factor of $(6 x^{3} + 29 x^{2} + 44 x + 21)$

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Similar questions

Q. The product of two polynomials is

6 x^{3} + 29 x^{2} + 44 x + 21

and one of the polynomials is

3 x + 7

. Find the other polynomial.

Q. For polynomial

P (x) = 6 x^{3} + 29 x^{2} + 44 x + 21

\frac{3 x + 5}{4 x + 2} = \frac{3 x + 4}{4 x + 7}

Q. Without actual division, prove that 2x⁴ − 6x³ + 3x² + 3x − 2 is exactly divisible by x² − 3x + 2.

Q. Solve the following equation and verify your answer:

\frac{3 x + 5}{4 x + 2} = \frac{3 x + 4}{4 x + 7}

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