Fill in the blank;
•In the process of polynomial division (Divisor)(Quotient)+_______=_______
•When a polynomial function f is divided by x-c, the remainder is _______.
•If a function f, whose domain is all real numbers, is even and if 4 is a zero of f, then _______ is also a zero.
I don't like math.
Remainder, Dividend
f(c)
-4 (because it's even)
•In the process of polynomial division (Divisor)(Quotient)+ (Remainder) = (Dividend)
•When a polynomial function f is divided by x-c, the remainder is (f(c)).
•If a function f, whose domain is all real numbers, is even and if 4 is a zero of f, then -4 is also a zero.
• In the process of polynomial division (Divisor)(Quotient) + Remainder = Dividend
To find the missing value in the equation, you need to consider the polynomial division process.
1. To perform polynomial division, you divide a polynomial (the Dividend) by another polynomial (the Divisor). As a result, you obtain a Quotient and a Remainder. These values are combined with the product of the Divisor and Quotient to equal the original Dividend.
2. When a polynomial function f is divided by x-c, the remainder is equal to the value of the function evaluated at c. In other words, if you substitute the value c into the polynomial function f(x), the remainder is the resulting value.
3. If a function f, whose domain is all real numbers, is even and if 4 is a zero of f, then -4 is also a zero.
This is because for an even function, the graph is symmetric with respect to the y-axis (also known as the origin). When a function has a zero at 4, it means that the graph intersects the x-axis at x = 4. Due to the symmetry of the even function, it will also intersect the x-axis at x = -4. Consequently, -4 is also a zero of the function f.