Answer:
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 <em>cubic</em> 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 <em>cubic</em> 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.
- The coefficient of x³ in the first polynomial 8 x³ - 2 x² + 5 x - 7 is 8.
- The coefficient of x³ in the second polynomial 5 x³ - 3 x² - 2 x + 4 is 5.
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.
- x²: -2 - (-3) = -2 + 3 = 1.
- x: 5 - (-2) = 5 + 2 = 7.
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.
