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Answer:
Step-by-step explanation:
Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
Thus, we now have:
Step 2: Apply the concept of Partial Fraction
Let,
=
Multiply both sides by (x - 1)(x - 4)
=
Step 3:
Substituting x = 4 in
Substituting x = 1 in
Step 4: Plug in the values of A and B into the original equation in step 2
Answer:
A. 2x(x+1)(x-6); 0, -1, 6
Step-by-step explanation:
The zeros are the values of x that make the factors zero. That is, for binomial factors, they are the opposite of the constant in the binomial factor. For example, the factor (x+1) will be zero when x = -1, so that -1+1 = 0.
This observation eliminates choices B and C.
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The product of binomial factors looks like this:
(x +a)(x +b) = x² +(a+b)x +ab . . . . . x-coefficient is (a+b)
Once 2x is factored from the given polynomial, the resulting quadratic is ...
x^2 -5x -6
This means the sum of the constants in the binomial terms must be -5. That will only be the case for choice A.
