how do i factor this
y=x to the power of 2 -2x-5?
thanks in advance!
y = x^2 - 2 x - 5
That can not be factored with whole numbers
try solving quadratic
[ 2 +/- sqrt (4+20) ] /2
= 1 +/- sqrt(6)
so try
(x - 1+sqrt6)(x - 1-sqrt(6))
To factor the quadratic equation y = x^2 - 2x - 5, you can follow these steps:
Step 1: Split the middle term (-2x) into two terms whose coefficients multiply to give the product of the square term (x^2) and the constant term (-5). The product is -5x^2.
In this case, the factors should be -5x^2 and -5, since (-5)x(x^2) leads to -5x^3 term, which doesn't exist in the original equation.
Step 2: Determine two numbers whose sum is equal to the coefficient of the middle term (-2x) and whose product is equal to the product of the square term (x^2) and the constant term (-5).
In this case, we need to find two numbers whose sum is -2 and whose product is -5.
The numbers that satisfy these conditions are -5 and +1, since (-5) + (+1) = -4, and (-5)(+1) = -5.
Step 3: Rewrite the equation by replacing the middle term (-2x) with the sum of the two numbers found in Step 2.
y = x^2 - 5x + x - 5
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
y = (x^2 - 5x) + (x - 5)
Step 5: Factor the greatest common factor from each group.
y = x(x - 5) + 1(x - 5)
Step 6: Factor out the common binomial (x - 5).
y = (x + 1)(x - 5)
Therefore, the factored form of the quadratic equation y = x^2 - 2x - 5 is y = (x + 1)(x - 5).