factored form.
To factor the trinomial z^2 - 6z + 5, we need to find two binomials that multiply to give the trinomial. We look for two numbers whose product is 5 and whose sum is -6.
The possible pairs of numbers are (-5, -1) and (5, 1). However, since the coefficient of z is negative, we need the sum to be negative. So the pair (-5, -1) is the correct pair.
Therefore, we can factor z^2 - 6z + 5 as (z - 5)(z - 1).
The sum of rational expressions 11 - 2z / (z^2 - 6z + 5) + (z^2 - 3) / (z - 5) can be simplified as follows:
11 - 2z / (z - 5)(z - 1) + (z^2 - 3) / (z - 5)
Since the denominators have a common factor of (z - 5), we can combine the expressions by finding a common denominator:
11 - 2z / (z - 5)(z - 1) + (z^2 - 3)(z - 1) / (z - 5)(z - 1)
= (11 - 2z + (z^2 - 3)(z - 1)) / (z - 5)(z - 1)
Simplifying the numerator:
= (11 - 2z + z^3 - z^2 - 3z + 3) / (z - 5)(z - 1)
= (z^3 - z^2 - 5z + 14) / (z - 5)(z - 1)
Therefore, the simplified sum of rational expressions is (z^3 - z^2 - 5z + 14) / (z - 5)(z - 1).
Consider the sum of rational expressions: 11−2z/z^2−6z+5 + z^2−3/z−5
.
The trinomial z^2−6z+5
can be factored into two binomials. Write the trinomial in
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1 answer