What is the difference between 8x3 – 2x2 + 5x – 7
and 5x3 – 3x2 – 2x + 4?

First polynomial minus the second polynomial:

3 x³ + x² + 7 x - 11.

Step-by-step explanation:

The question asks for the difference between the two cubic polynomials (maximum power of x is three.) As the other answerer mentioned, the question doesn't say anything about the value of x. In that case, the difference between the two polynomials will still be a polynomial about x.

The power x in the difference can be as high as three. Assume that to be a cubic polynomial.

? x³ + ? x² + ? x + ?.

What are the values of each coefficient?

For example, the coefficient in front of x³ in the difference is the difference between the coefficients of x³ in the two original polynomials.

Subtract the second coefficient from the first. 8 - 5 = 3. In other words, 3 is the value of the x³ coefficient in the difference.

3 x³ + ? x² + ? x + ?.

Repeat this step for the x² and x coefficients.

3 x³ + x² + 7x + ?.

The constant in the difference is the difference between the two constants.

-7 - 4 = -11.

Hence the difference:

3 x³ + x² + 7x - 11.

Alternatively, group the terms by the power of x:

(8 x³ - 2 x² + 5 x - 7) - (5 x³ - 3 x² - 2 x + 4)

= (8 x³ - 5 x³) + (-2 x² + 3 x²) + (5 x + 2 x) + (-7 - 4)

= 3 x³ + x² + 7 x - 11.

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