0
Give the first 3 non-zero terms of the Taylor polynomial approximation to sin x about the point x equals 0?
3
What else can I help you with?
Let N be the second last digit of your student number so N equals 3 Use the Taylor polynomial of Q2 to give an approximation to sin n?
So taking a student number to make the second to last number be N which will t equal 3 in the Taylor Polynomial for sin. So if N=3, we can calculate that sin(N) = sin(3) =0.05233596.
If a polynomial is divided by (x - a) and the remainder equals zero then (x - a) is a factor of the polynomial.?
Yes, that's correct. According to the Factor Theorem, if a polynomial ( P(x) ) is divided by ( (x - a) ) and the remainder is zero, then ( (x - a) ) is indeed a factor of the polynomial. This means that ( P(a) = 0 ), indicating that ( a ) is a root of the polynomial. Thus, the polynomial can be expressed as ( P(x) = (x - a)Q(x) ) for some polynomial ( Q(x) ).
What is a polynomial with a single root at x equals 2 and a double root at x equals 5?
That would be (x - 2) ( x - 5) ( x - 5). If you like, you can multiply these polynomials to get a single polynomial in standard form (i.e., not factored).
What is any nonzero number raised to the zero power is one?
Any nonzero number raised to the zero power equals one due to the properties of exponents. Specifically, according to the exponent rules, ( a^m / a^m = a^{m-m} = a^0 ), and since ( a^m / a^m ) equals one (as long as ( a \neq 0 )), it follows that ( a^0 = 1 ). This principle holds true for all nonzero numbers, illustrating a consistent and fundamental rule in mathematics.
Which binomial is a factor of the polynomial below?
To determine which binomial is a factor of a given polynomial, you can apply the Factor Theorem. According to this theorem, if you substitute a value ( c ) into the polynomial and it equals zero, then ( (x - c) ) is a factor. Alternatively, you can perform polynomial long division or synthetic division with the given binomials to see if any of them divides the polynomial without a remainder. If you provide the specific polynomial and the binomials you're considering, I can assist further.
If N be the second last digit of your student number so N equals 3 Use the Taylor polynomial of quarter 2 to give an approximation to sin n?
4 units
Let N be the second last digit of your student number so N equals 3 Use the Taylor polynomial of Q2 to give an approximation to sin n?
So taking a student number to make the second to last number be N which will t equal 3 in the Taylor Polynomial for sin. So if N=3, we can calculate that sin(N) = sin(3) =0.05233596.
When a nonzero integer is divided by it's opposite is -1?
Yes, when a nonzero integer is divided by it's opposite it's value equals -1
If a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
false - apex
The exponential expression b0 equals for any nonzero base b?
1
The polynomial x - 2 is a factor of the polynomial Fx equals 5x2 - 6x plus 4?
False
Any nonzero integer divided by 0 equals 0?
No. Division by 0 is not permitted.
What Degree of a polynomial is -18x2y2z equals 8x3y-5xz3?
5xZ3
If a polynomial is divided by (x - a) and the remainder equals zero then (x - a) is a factor of the polynomial.?
Yes, that's correct. According to the Factor Theorem, if a polynomial ( P(x) ) is divided by ( (x - a) ) and the remainder is zero, then ( (x - a) ) is indeed a factor of the polynomial. This means that ( P(a) = 0 ), indicating that ( a ) is a root of the polynomial. Thus, the polynomial can be expressed as ( P(x) = (x - a)Q(x) ) for some polynomial ( Q(x) ).
What is a polynomial with a single root at x equals 2 and a double root at x equals 5?
That would be (x - 2) ( x - 5) ( x - 5). If you like, you can multiply these polynomials to get a single polynomial in standard form (i.e., not factored).
What is any nonzero number raised to the zero power is one?
Any nonzero number raised to the zero power equals one due to the properties of exponents. Specifically, according to the exponent rules, ( a^m / a^m = a^{m-m} = a^0 ), and since ( a^m / a^m ) equals one (as long as ( a \neq 0 )), it follows that ( a^0 = 1 ). This principle holds true for all nonzero numbers, illustrating a consistent and fundamental rule in mathematics.
Is it false if a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
No, it’s true. It’s the same as saying if 60 is divided by 2 and the remainder equals zero (no remainder, so it divides perfectly), 2 is a factor of 60.
