Function is p(x)=(x-4)^5(x^2-16)(x^2-5x+4)(x^3-64)
first factor into (x-r1)(x-r2)... form
p(x)=(x-4)^5(x-4)(x+4)(x-4)(x-1)(x-4)(x^2+4x+16)
group the like ones
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
multiplicity is how many times the root repeats in the function
for a root r₁, the root r₁ multiplicity 1 would be (x-r₁)^1, multility 2 would be (x-r₁)^2
so
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
(x^2+4x+16) is not on the real plane, but the roots are -2+2i√3 and -2-2i√3, each multiplicity 1 (but don't count them because they aren't real
baseically
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
<span>Simplify the fractions if not in lowest terms.Multiply the numerators of the fractions to get the new numerator.<span>Multiply the denominators of the fractions to get the new denominator.</span></span>
Thus, the final answers are 1 and -1/8.
Answer:
r = 44
Step-by-step explanation:
12 = r - (34 - 2)
Solve for r
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To solve, we need to isolate r.
Distribute the negative sign with the numbers within the parenthesis :
12 = r - 34 + 2
Add like terms :
12 = r - 32
Add 32 to both sides :
44 = r
r = 44
