In the polynomial 3x^4−3x^3+6x^2−3x+6, which term would represent the hundreds place, if this were an integer?
-3x
6
-3x^3
6x^2
Would it be 6x^2?
If not can it be explained how to figure this out?
I suspect we are talking about a base 10 system
1 = 1*10^0
10 = 1 * 10^1
100 = 1 * 10^2
1000 = 1*10^3 etc
so if that is it then the number is
3*10^4−3*10^3+6*10^2−3*10^1+6 *10^0
so yes, 6x is in the 6*10^2 or hundreds spot
Thanks :)
To determine which term represents the hundreds place in the polynomial 3x^4-3x^3+6x^2-3x+6, we need to recall the place value system in polynomials.
In a polynomial expression, each term is composed of a coefficient and a variable raised to a certain power. The power of the variable represents the place value. For example, in the term 6x^2, the variable x is raised to the power of 2, indicating that it represents the tens place. The coefficient 6 represents the value of the term at that place.
In our given polynomial, the terms are in decreasing order of powers of x. The highest power of x is 4 in the term 3x^4, which represents the thousands place. The second-highest power is 3 in the term -3x^3, representing the hundreds place.
Therefore, the term that represents the hundreds place in the polynomial is -3x^3.
To determine which term represents the hundreds place in a polynomial, we need to analyze the exponents of the variable. In this case, the variable is x.
Let's break down the polynomial: 3x^4 - 3x^3 + 6x^2 - 3x + 6
The term 6x^2 corresponds to the x^2 term, and it does not have any other variables or coefficients in front of it. Therefore, if this polynomial were representing an integer, the coefficient in front of the x^2 term, which is 6, would represent the hundreds place.
So, yes, your answer is correct. The term 6x^2 represents the hundreds place in the given polynomial.