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
Peter's present age is 6 years and John's present age is 17 years.
let
Peter's age = x
John is 11 years older than Peter. Therefore,
In 5years time, John will be twice as old as peter. Therefore,
<h3 /><h3>Present age equation:</h3>
2(x + 5) = x + 16
2x + 10 = x + 16
2x - x = 16 - 10
x = 6
Therefore, Peter's present age is 6 years and John's present age is 17 years.
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Step-by-step explanation:
<h2><u>Given :-</u></h2>
x-1-(x-1)²+ax-a
<h2><u>To find :-</u></h2>
Factorize the expression ?
<h2><u>Solution :-</u></h2>
Given expression is x-1-(x-1)²+ax-a
It can be written as
(x-1)-(x-1)²+(ax-a)
=> (x-1)-(x-1)(x-1)+a(x-1)
=> (x-1)[1-(x-1)+a]
=> (x-1)(1-x+1+a)
=> (x-1)(2-x+a)
<h2><u>Answer:-</u></h2>
x-1-(x-1)²+ax-a = (x-1)(2-x+a)
Hope this helps!!
Answer:
The value of given expression is 1.
Step-by-step explanation:
The given expression is
If a is a real number, then .
Using exponent property we get,
Therefore the value of given expression is 1.
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