algebra
posted by lee on .
Can someone please explain these problems to me I have tried and cannot figure them out.
1)Use synthetic division to find p(3) for p(x)=x^42x^34x+4
2)Find all the zeroes of the equation
x^46x^27x6=0

1. X = 3.
x+3 = 0.
Using synthetic division, divide the given expression by x+3. You will get
x^3  5x^2 + 15x  49. + 151 Remainder.
The fact that we got a remainder, means that x+3 is not a factor of the given
expression and 3 is not a zero. Which
means it will not give zero output when plugged into the Eq.
2. All values of X that satisfy the given Eq is a "zero" of the Eq.
x^4  6x^2  7x  6 = 0.
It was determined by trial and error that 2 satisfies the given Eq.
X = 2.
x+2 = 0
Divide the given Eq by x+2 and get
x^3  2x^2  2x 3. + 0 Remainder.
(x+2)(x^32x^22x3) = 0.
3 satisfies the cubic polynomial:
x = 3.
x3 = 0.
Divide the cubic polynomial by x3 and
get x^2+x+1 + 0 Remainder.
Our Eq 1s: (x+2)(x3)(x^2+x+1) = 0.
The 2nd degree polynomial cannot be
factored and has no zeroes, because
B^2 < 4AC. Therefore, the original Eq
has only 2 zeroes: 2, and 3.
OR
(x,y)
(2,0)
(3,0).