State if it is a polynomial. If yes, say the degree.
2.f(x)=5x^2 +4x^4
4.f(x)=3-(1/2x)
6.f(x)=x(x-1)
8.f(x)=sqaure oot of x (square root of x-1)
10.f(x)=(x^2-5)/x^3
12. f(x)=-3x^2(x+2)^3
my answers
2.yes, 6
4.yes, 1
6.yes, 3
8.no
10.no
12.yes, 5
thanks!!
2. yes, 4 (the highest degree is of the term 4x^4)
4. good! as long as 1/2x means 0.5* x and not 1 / (2*x)
6. Expanding x(x-1) = x^2 - x; the degree is 2 (from the term x^2)
8. good
10. good
2. yes, 4 (the highest degree is of the term 4x^4)
4. good! as long as 1/2x means 0.5* x and not 1 / (2*x)
6. Expanding x(x-1) = x^2 - x; the degree is 2 (from the term x^2)
8. good
10. good
12. good
Thanks, so is the degree all of the x added together or jut the greatst one bcause tthen wouldnt 12 be 3 instead of 5?
greatest power of x. No on your comment on 12.
you have x^2(x+..)^3= x^2*(x^3+...) or hightest degree will be x^5
ohhhh gotcha thanks!!
To determine if a function is a polynomial, we need to identify if each term includes a variable raised to a non-negative integer power and if the coefficients are constants.
Let's go through each function to determine if it is a polynomial and find its degree:
2. f(x) = 5x^2 + 4x^4
Yes, it is a polynomial. The highest power of x is 4, so the degree is 4.
4. f(x) = 3 - (1/2x)
Yes, it is a polynomial. Although it is fractionally written, the degree is still determined by the highest power of x, which is 1.
6. f(x) = x(x-1)
Yes, it is a polynomial. Expanding the expression, we have x^2 - x, which implies that the highest power of x is 2. Therefore, the degree is 2.
8. f(x) = square root of x (square root of x-1)
No, it is not a polynomial. The square root operation makes it non-polynomial.
10. f(x) = (x^2-5)/x^3
No, it is not a polynomial. The presence of the term x^(-3) in the denominator makes it non-polynomial.
12. f(x) = -3x^2(x+2)^3
Yes, it is a polynomial. The degree is determined by the highest power of x, which is 5 (x^2 * x^3 = x^5).
Therefore, the correct answers are:
2. Yes, degree 4
4. Yes, degree 1
6. Yes, degree 2
8. No (not a polynomial)
10. No (not a polynomial)
12. Yes, degree 5