15X^(5/2)-2x^(3/2)-24x^(1/2) can someone please show how to factor this problem using GCF?
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15 * x^(5/2) - 2 * x^(3/2) - 24 * x^(1/2) =>
x^(1/2) * (15 * x^(4/2) - 2 * x^(2/2) - 24) =>
x^(1/2) * (15x^2 - 2x - 24)
Let's see if we can factor 15x^2 - 2x - 24
a = 15
b = -2
c = -24
b^2 - 4ac =>
4 - 4 * 15 * (-24) =>
4 * (1 + 15 * 24) =>
4 * (1 + 360) =>
4 * 361
Since 4 * 361 is a perfect square, then we can factor it:
(-b +/- sqrt(b^2 - 4ac)) / (2a) =>
(2 +/- sqrt(4 * 361)) / (2 * 15) =>
(2 +/- 2 * 19) / (2 * 15) =>
(1 +/- 19) / 15 =>
20/15 , -18/15 =>
4/3 , -6/5
(3x - 4) * (5x + 6) is the factorization of 15x^2 - 2x - 24
x^(1/2) * (3x - 4) * (5x + 6) is the complete factorization
x^(1/2) * (15 * x^(4/2) - 2 * x^(2/2) - 24) =>
x^(1/2) * (15x^2 - 2x - 24)
Let's see if we can factor 15x^2 - 2x - 24
a = 15
b = -2
c = -24
b^2 - 4ac =>
4 - 4 * 15 * (-24) =>
4 * (1 + 15 * 24) =>
4 * (1 + 360) =>
4 * 361
Since 4 * 361 is a perfect square, then we can factor it:
(-b +/- sqrt(b^2 - 4ac)) / (2a) =>
(2 +/- sqrt(4 * 361)) / (2 * 15) =>
(2 +/- 2 * 19) / (2 * 15) =>
(1 +/- 19) / 15 =>
20/15 , -18/15 =>
4/3 , -6/5
(3x - 4) * (5x + 6) is the factorization of 15x^2 - 2x - 24
x^(1/2) * (3x - 4) * (5x + 6) is the complete factorization
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x^(1/2)(15x^2-2x-24)