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)
( 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.
[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.
To simplify and write the given polynomial in standard form, we'll first remove the parentheses and combine like terms.
(5x^3 + 3x^2 - 7x + 10) - (3x^3 -x^2 + 4x- 1)
Expanding the parentheses:
5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Now, let’s combine like terms:
(5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
2x^3 + 4x^2 - 11x + 11
The polynomial written in standard form is 2x^3 + 4x^2 - 11x + 11.
Now, let’s classify this polynomial by degree and number of terms:
The degree of the polynomial is determined by the highest exponent of x, which is 3.
The number of terms in the polynomial is determined by the number of separate expressions added together, which is 4.
Therefore, the polynomial 2x^3 + 4x^2 - 11x + 11 is classified as a cubic polynomial (degree 3) with four terms.
To simplify the expression and write it in standard form, we first remove the parentheses by distributing the subtraction operation:
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
= 5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Now, we can combine like terms by adding or subtracting coefficients of the same degree:
(5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
= 2x^3 + 4x^2 - 11x + 11
The simplified expression in standard form is 2x^3 + 4x^2 - 11x + 11.
To classify the polynomial by degree and number of terms:
- The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent of x is 3, so the degree of the polynomial is 3.
- The number of terms in a polynomial is the total count of individual terms. In this case, there are 4 terms: 2x^3, 4x^2, -11x, and 11.
Therefore, the polynomial can be classified as a degree 3 polynomial with 4 terms.