Question

Simplify and write in standard form. Then classify the polynomial by degree and number of terms:
(5x^3 + 3x^2 - 7x + 10) - (3x^3 -x^2 + 4x- 1)

Answer 1

[5x³ + 3x² - 7x + 10] + [3x³ - x² + 4x - 1]
= 5x³+3x³ + 3x²-x² -7x+4x + 10-1
now just add up the coefficients for like powers and arrange the powers in descending order. (They already are)
Terms are separated by + and - signs
The degree is the highest power.

Answer 2

( 5 x³ + 3 x² - 7 x + 10) - ( 3 x³ - x² + 4 x - 1 ) =

5 x³ + 3 x² - 7 x + 10 - 3 x³ - ( - x² ) - 4 x - ( - 1 ) =

5 x³ + 3 x² - 7 x + 10 - 3 x³ + x² - 4 x + 1 =

5 x³ - 3 x³ + 3 x² + x² - 7 x - 4 x + 10 + 1 =

2 x³ + 4 x² - 11 x + 11

The degree of the polynomial is found by looking at the term with the highest exponent on its variable.

2 x³ + 4 x² - 11 x + 11 is a third-degree ( cubic ) polynomial.

A polynomial of four terms is called a quadrinomial.