Question

The area of a rectangle is 2x^3 + 5x^2 - x - 6 sq. cm. Write a polynomial that represents its width if its length is 2x^2 + x - 3.

Answer 1

Required Answer :

→ ( x + 2 ) cm

Given :

• Area of a rectangle = $\sf { {2x}^{3} +{5x}^{2} - x - 6 \: {cm}^{2}}$

• Length = $\sf { {2x}^{2} + x -3}$

To calculate :

• Width

Calculation :

As we know that :

★ $\boxed{\sf{{Area}_{(Rectangle)} = Length \times Width}}$

So, according to the question :

$\sf{ \longrightarrow {2x}^{3} +{5x}^{2} - x - 6 ={2x}^{2} + x -3 \times width }$

$\sf{ \longrightarrow \dfrac{ {2x}^{3} +{5x}^{2} - x - 6 }{{2x}^{2} + x -3 } = width }$

Clearly, here we have to divide a polynomial by a polynomial.

→ Refer to the attachment for the last step (division of the polynomial according to the question).

How I divided?

• Firstly arrange the polynomials in descending order.

• Then, set up them in a form of a long division.

• After that, we divided the first term of the dividend $\rm {({2x}^{3})}$ by the first term of the divisor $\rm {({2x}^{2})}$.

• Then, multiply the divisor $\rm {({2x}^{2} + x -3)}$ by the quotient (x).

• Then, write the product below the dividend and subtract as an ordinary division.

• Now, remainder we got is the new dividend. Same as the 3rd step , divide the first term of the remainder (4x²) by (2x²) and the write the quotient.

• After that, we multiplied the divisor (2x² + x - 3) by 2 and subtracted.

At last we got the answer that is the quotient (x + 2)cm.

Therefore, width of the rectangle is (x + 2) cm.

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