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
Answer:
d=e
Step-by-step explanation:
The expression 7•3x is not equal to the expression 21x. You might think that the two expressions are the same since 7x3 is 21 but the first expression is a dot product. This kind of expression includes the magnitude and direction of the vector in an expression, for example, <span>7•3x. The second expression, 21x, expresses only the magnitude and does not include the direction.</span>
Answer:
y=3x- 3/2
Step-by-step explanation:
4.2x−1.4y=2.1
Subtract 4.2x from each side
4.2x-4.2x−1.4y=-4.2x+2.1
-1.4y = -4.2x +2.1
divide each side by -1.4
-1.4y/-1.4y = -4.2x/ -1.4 +2.1/-1.4y
y=3x- 3/2
