what is y=xsquared+2x-15 in factored form?
y = x^2 + 2x - 15
y = (x - 3)(x + 5)
To express the quadratic equation y = x^2 + 2x - 15 in factored form, we need to find two binomials that, when multiplied together, give us the original equation.
To factor the quadratic equation, we are essentially looking for two numbers that multiply to -15 and add up to 2.
Let's find the factors of -15 and look for the appropriate pair:
1, -15,
-1, 15,
3, -5,
-3, 5.
Among these pairs, the pair that adds up to 2 is 3 and -5.
So, we can rewrite the equation as:
y = (x + 5)(x - 3).
Therefore, the factored form of the equation y = x^2 + 2x - 15 is (x + 5)(x - 3).
To find the factored form of the quadratic equation y = x² + 2x - 15, you need to factorize it. Here's the step-by-step process:
Step 1: Write down the equation: y = x² + 2x - 15
Step 2: Look at the coefficient of x², which is 1. Since it is positive, we know that both factors will have the same sign.
Step 3: Now, focus on the constant term, which is -15. We need to find two numbers that multiply to give -15 and add up to the coefficient of x, which is 2.
Step 4: The factors of -15 that add up to 2 are 5 and -3. So, we rewrite the equation using these factors:
y = (x + 5)(x - 3)
That's it! The factored form of the quadratic equation y = x² + 2x - 15 is (x + 5)(x - 3).