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Write the polynomial in standard form and identify the leading coefficient.6 + 9t 4 – 5t + t 5?
t^5 +9t^4 -5t +6; 1
What else can I help you with?
What is the leading coefficient in a polynomial?
It is the number (coefficient) that belongs to the variable of the highest degree in a polynomial.
What is the leading term in a polynomial?
The leading term in a polynomial is the term with the highest degree, which determines the polynomial's end behavior and its classification (e.g., linear, quadratic, cubic). It is typically expressed in the form ( ax^n ), where ( a ) is a non-zero coefficient and ( n ) is a non-negative integer. The leading term is crucial for understanding the polynomial's growth as the input values become very large or very small.
Where p is a factor of the leading coefficient of the polynomial and q is a factor of the constant term.?
Anywhere. Provided it is not zero, and number p can be the leading coefficient of a polynomial. And any number q can be the constant term.
How do you find the leading term of a polynomial?
If the polynomial is in terms of the variable x, then look for the term with the biggest power (the suffix after the x) of x. That term is the leading term. So the leading term of x2 + 5 + 4x + 3x6 + 2x3 is 3x6 If you are likely to do any further work with the polynomial, it would be a good idea to arrange it in order of the descending powers of x anyway.
The rational roots of a polynomial function F(x) can be written in the form where p is a factor of the constant term of the polynomial and q is a factor of the leading coefficient.?
TRue
Would you identify the leading digit 0.00693 of the decimal and then roundto the leading digit?
Identify the leading digit of the decimal and then round to the leading digit. 0.00693
Does a polynomial with a leading term with an even exponent must have at least one real zero?
No.
What is the number in front of the term with the highest degree in a polynomial?
It is the Coefficient. It only refers to the given term that it is front. e.g. 2x^2 - 3x + 1 The '2' in front of 'x^2' only refers to 'x^2'. The '-3' in front of 'x' is the coefficient of '-3' The '1' is a constant.
Which polynomial has rational coefficients a leading leading coefficient of 1 and the zeros at 2-3i and 4?
There cannot be such a polynomial. If a polynomial has rational coefficients, then any complex roots must come in conjugate pairs. In this case the conjugate for 2-3i is not a root. Consequently, either (a) the function is not a polynomial, or (b) it does not have rational coefficients, or (c) 2 - 3i is not a root (nor any other complex number), or (d) there are other roots that have not been mentioned. In the last case, the polynomial could have any number of additional (unlisted) roots and is therefore indeterminate.
What is a possible leading coefficient and degree for a polynomial starting in quadrant 3 and ending in quadrant 4?
Leading coefficient: Negative. Order: Any even integer.
How do you identify 0.0024 the leading digit of the decimal and then round to the leading digit?
0.002
What is a polynomial function f of least degree that has rational coefficient a leading coefficient of 1 and the given zeros -7 -4?
A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).
