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

7 0

2 years ago

Help me pleaseee ejejie

Elina [12.6K]

Answer:

The answer is A

Step-by-step explanation:

when you see x and y side by side in a table, each row is one point on a graph. hope this helps!

7 0

2 years ago

Lorenzo is planning a 285-mile trip. His car’s EPA rating is 18 mpg. The number of gallons of gas that Lorenzo will need for the

SpyIntel [72]

It would require 15.8333333 to make that trip.

4 0

2 years ago

Read 2 more answers

0.2(x+50)-6=0.4(3x+20) ( show work please)

garri49 [273]

Let's solve your equation step-by-step.0.2(x+50)−6=0.4(3x+20)Step 1: Simplify both sides of the equation.0.2(x+50)−6=0.4(3x+20)(0.2)(x)+(0.2)(50)+−6=(0.4)(3x)+(0.4)(20)(Distribute)0.2x+10+−6=1.2x+8(0.2x)+(10+−6)=1.2x+8(Combine Like Terms)0.2x+4=1.2x+80.2x+4=1.2x+8Step 2: Subtract 1.2x from both sides.0.2x+4−1.2x=1.2x+8−1.2x−1x+4=8Step 3: Subtract 4 from both sides.−1x+4−4=8−4−1x=4Step 4: Divide both sides by -1.−1x−1=4−1x=−4Answer:x=−4

7 0

3 years ago

Read 2 more answers