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The volume of a cuboid given by the polynomial 8x³+12x²-2x-3.find possible expressions for the dimensions of the cuboid.verify the result by taking x=5units
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Given Equation is f(x) = 8x^3 + 12x^2 - 2x - 3.
It can be factorized as:
= > 4x^2(2x + 3) - (2x + 3)
= > (4x^2 - 1)(2x + 3)
= > (2x + 1)(2x - 1)(2x + 3).
Consider (2x + 1)(2x - 1)(2x + 3) as g(x).
Now,
substitute x = 5 in f(x), we get
= > 8(5)^3 + 12(5)^2 - 2(5) - 3
= > 1000 + 300 - 10 - 3
= > 1300 - 13
= > 1287.
Now,
substitute x = 5 in g(x), we get
= > (2(5) + 1)(2(5) - 1)(2(5) + 3)
= > (10 + 1)(10 - 1)(10 + 3)
= > (11)(9)(13)
= > 1287.
Therefore, f(x) = g(x).
Hope this helps!
siddhartharao77:
no no..straightaway factorization\
okk..tell me which step u didnt understand
8x^3+12x²-2x-3
= > 4x^2(2x + 3) - 1(2x + 3)
= > (4x^2 - 1)(2x + 3)
= > ((2x)^2 - 1^2)(2x + 3)
We know that a^2 - b^2 = (a + b)(a - b)
= > (2x + 1)(2x - 1)(2x + 3)
= > 4x^2(2x + 3) - 1(2x + 3)
= > (4x^2 - 1)(2x + 3)
= > ((2x)^2 - 1^2)(2x + 3)
We know that a^2 - b^2 = (a + b)(a - b)
= > (2x + 1)(2x - 1)(2x + 3)
Force P, 2P and 3P are acting along three sides of an equilateral triangle ABC in cyclic order. Find the magnitude and d...
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