X^2-2x-15
The given expression can be factored as follows:
x^2 - 2x - 15 = (x - 5)(x + 3)
X^2-2x-15
=X^2+5x-3x-15
X(x+5)-3(x-5)
Factoring we have
(X-3)(x+5)
So therefore the factors are -3 and +5.
Actually, the correct factorization of the expression x^2 - 2x - 15 is (x - 5)(x + 3). The factors are 5 and -3, not -3 and 5 as you stated.
X^2-2x-15
=X^2-5x-3x-15
X(x-5)-3(x-5)
Factoring we have
(X+3)(x-5)
So therefore the factors are +3 and -5.
No, that is incorrect. The correct factorization of x^2 - 2x - 15 is indeed (x - 5)(x + 3), not (x + 3)(x - 5). The factors are 5 and -3, not 3 and -5 as you stated.
To factor the quadratic expression X^2 - 2x - 15, you need to find two numbers that multiply to give -15 and add up to -2.
First, list all the pairs of factors of -15:
(-1, 15), (1, -15), (-3, 5), (3, -5)
Among these pairs, (-3, 5) is the pair where the sum is -2.
Now, rewrite the middle term -2x as the sum of -3x and 5x:
X^2 - 3x + 5x - 15
Group the terms:
(X^2 - 3x) + (5x - 15)
Factor out the greatest common factor from each group:
x(x - 3) + 5(x - 3)
Now, notice that (x - 3) is common to both terms. Factor out this common factor:
(x - 3)(x + 5)
Therefore, the factored form of the quadratic expression X^2 - 2x - 15 is (x - 3)(x + 5).
To solve the quadratic equation X^2 - 2x - 15, we can use the quadratic formula. The quadratic formula is given by:
X = (-b ± √(b^2 - 4ac)) / (2a)
In our case, the equation is in the form of Ax^2 + Bx + C, where:
A = 1, B = -2, and C = -15.
Now let's plug these values into the quadratic formula:
X = (-(-2) ± √((-2)^2 - 4(1)(-15))) / (2(1))
Simplifying further:
X = (2 ± √(4 + 60)) / 2
X = (2 ± √64) / 2
X = (2 ± 8) / 2
Now we have two solutions:
X = (2 + 8) / 2 => X = 10 / 2 => X = 5
X = (2 - 8) / 2 => X = -6 / 2 => X = -3
So the solutions to the quadratic equation X^2 - 2x - 15 are X = 5 and X = -3.