To write the polynomial in standard form, we first need to combine like terms and arrange the terms in descending order of the variable's exponents. Given the polynomial:
\[ 6 - 2x^3 - 3x + 6x^3 \]
First, combine the \( -2x^3 \) and \( 6x^3 \) terms:
\[ -2x^3 + 6x^3 = 4x^3 \]
Now, rewrite the polynomial with the combined terms:
\[ 4x^3 - 3x + 6 \]
The polynomial in standard form is:
\[ 4x^3 - 3x + 6 \]
Next, we need to identify the polynomial based on its degree and the number of terms.
1. **Degree**: The degree of the polynomial is the highest power of \( x \) present in the polynomial. Here, the highest power of \( x \) is 3. Therefore, the polynomial is of degree 3, which makes it a cubic polynomial.
2. **Number of Terms**: There are three terms: \( 4x^3 \), \( -3x \), and \( 6 \). Therefore, it is a trinomial.
Thus, the polynomial \( 4x^3 - 3x + 6 \) in standard form is a cubic trinomial.
So, the correct answer is:
\[ 4x^3 - 3x + 6; \, \text{cubic trinomial} \]
4.
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
6 – 2x3 – 3x + 6x3
–4x3 – 3x + 6; quadratic trinomial
4x3 – 3x + 6; cubic trinomial
8x3 – 3x + 6; cubic polynomial
4x3 – 3x + 6; quadratic binomial
1 answer
1 answer