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.

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Solution

Let $A$ be the other polynomial. It is given that one of the polynomial is $3 x + 7$ and the product of the polynomials is $6 x^{3} + 29 x^{2} + 44 x + 21$ that is:

$(3 x + 7) \times A = 6 x^{3} + 29 x^{2} + 44 x + 21 A = \frac{6 x^{3} + 29 x^{2} + 44 x + 21}{3 x + 7}$

We now divide $6 x^{3} + 29 x^{2} + 44 x + 21$ by $(3 x + 7)$ as shown below:

From the division, we observe that the quotient is $2 x^{2} + 5 x + 3$ and the remainder is $0$ .

Hence, the other polynomial is $2 x^{2} + 5 x + 3$ .

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