Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
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Answer:
a=2, b=0
Step-by-step explanation:
Given:
f(x) = x^3 + x^2 - ax +b is divisible by (x^2 -x)
Need to find:
Values of a and b.
Solution:
Factor
(x^2-x) = (x)(x-1)
if x^3 + x^2 - ax +b is divisible by (x)(x-1), then
both x and (x-1) are roots to f(x), therefore
x=0 or x=1 are roots to f(x).
Using the factor theorem,
f(x=0) = 0 => 0+0-0+b = 0 => b=0
f(x=1)=0 => 1+1-a+b=0 => 1+1-a+0 = 0 => a=2
That is a=2, b=0
Now factor f(x) with a=2, b=0
f(x) = x^3 + x^2 - ax +b
= x^3 + x^2 - 2x
= x (x^2 + x - 2)
= x (x+2) (x-1)
Thus both x and (x-1) are factors... checks.
the answer is negative two over zero
<span><span>The least common multiple or LCM of 30 and 42 is:
30: 2, 3, 5
</span><span>42: 2. 3, 7
</span><span>LCM: 2, 3, 5, 7
</span></span><span>The Least Common Multiple (LCM) is: 2 x 3 x 5 x 7 = 210</span>