p(x)=x^3+2x^2-3x+20
one of this functions zeros is -4
When using synthetic division to find all the zeros of a polynomial function, would you plug in 4 or -4 into the actual equation?
Or rather, what would I do to find all the zeros for this equation?
When using synthetic division to find the zeros of a polynomial function, you would plug in the value that corresponds to the zero you are trying to test. In this case, since one of the zeros is -4, you would plug in -4 into the actual equation, not 4.
To explain further, the process of synthetic division involves dividing the polynomial function by a linear factor (x - a), where "a" represents the value you want to test as a zero. This process allows us to simplify the polynomial and determine if the value of "a" is indeed a zero.
So, in your example, the polynomial function is p(x) = x^3 + 2x^2 - 3x + 20, and you want to find out if -4 is a zero. To test this, you would perform synthetic division by dividing the polynomial by (x - (-4)), which simplifies to (x + 4). Plugging in -4 into the polynomial equation would be the first step in synthetic division to carry out the calculations.
Keep in mind that synthetic division is a method used to test for rational zeros, which are values that can be expressed as fractions of two integers. If you are dealing with irrational or complex zeros, synthetic division would not be appropriate, and other methods like factoring or the quadratic formula might be more suitable.