Simplify and write in standard form. Then, classify the polynomial by degree and number of terms.
(5x3 + 3x2 7x + 10) (3x3 x2 + 4x 1)
Simplify and write in standard form. Then, classify the polynomial by degree and number of terms.
(5x3 + 3x2 7x + 10) (3x3 x2 + 4x 1)
To simplify and write in standard form, we need to combine like terms.
First, let's simplify the expression inside the parentheses by distributing the negative sign:
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
This becomes:
5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Now, let's group the like terms:
(5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
Simplifying further:
2x^3 + 4x^2 - 11x + 11
The simplified expression in standard form is:
2x^3 + 4x^2 - 11x + 11
Now, let's classify the polynomial by degree and number of terms.
Degree: The highest power of x is 3, so the degree is 3.
Number of terms: There are 4 terms in the polynomial.
Therefore, the polynomial is classified as a cubic polynomial (degree 3) and it has 4 terms.
To simplify and write the given expression in standard form, we can start by combining like terms within the parentheses.
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
First, distribute the negative sign inside the second parentheses:
5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Next, combine like terms:
(5x^3 - 3x^3) + (3x^2 + x^2) + (-7x - 4x) + (10 + 1)
= 2x^3 + 4x^2 - 11x + 11
Now, let's classify this polynomial by its degree and number of terms.
Degree:
The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 3, so the degree of the polynomial is 3.
Number of terms:
To determine the number of terms, count the number of separate algebraic expressions separated by addition or subtraction signs. In this case, there are four terms: 2x^3, 4x^2, -11x, 11.
Therefore, the simplified and written expression in standard form is 2x^3 + 4x^2 - 11x + 11, and it is a polynomial of degree 3 with four terms.
I'm assuming you meant
(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)
so, first, get rid of the parentheses:
5x^3 + 3x^2 - 7x + 10 - 3x^3 + x^2 - 4x + 1
Now collect like powers:
(5-3)x^3 + (3+1)x^2 + (-7-4)x + (10+1)
2x^3 + 4x^2 - 11x + 11
Since the powers are descending, that's standard form.
degree is the highest power
terms are separated by + or - signs, so just count them.