To aspect ax2 + bx + c whenever that factors, you desire to break-up the linear term bx together b1x + b2x such that b1b2= ac and b1 and b2are integers.

You are watching: X2-2x-24 0

With your case of x2- 2x - 24, us haveb1+b2 =-2 and also b1b2 = 1*(-24) = -24.

By factoring -24 we discover several choices: (1,-24), (2,-12), (3,-8), (4,-6), (6,-4), (8,-3), (12,-2), and also (24,-1)

notice that in the pair (4,-6), the 4+(-6) = -2

Thus we deserve to take b1 = 4 and also b2 = -6 and we get

x2-2x - 24 = x2 + 4x - 6x - 24 = x(x+4) - 6(x+4) = (x - 6)(x + 4)

So the equationx2 - 2x - 24 = 0 becomes (x - 6)(x + 4) = 0.

Thus through Euclid"s Lemma, we have actually x - 6 = 0 or x + 4 = 0, so that x = -4 or x = 6.

Note: Euclid"s Lemma states that if friend multiply 2 or much more numbers together and also the product is 0 then at least one of the number is 0.


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Slight Correction:

Euclid"s Lemma actually says that if a*b is divisible by a prime number p then either a or b is divisible through p.

In the situation of abdominal muscle = 0, the fact that either a or b is 0 is called the "Zero-Divisor Property". It have the right to be displayed easily by using Euclid"s Lemma and also Euclid"s Theorem.

Euclid"s theorem simply says the there space infinitely many prime numbers.


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