Question

The HCF and LCM of two quadratic expressions are (x - 5) and x3 – 19x - 30
Find the expressions.​

Answer 1

Answer:

x^2 - 2x - 15, x^2 - 3x - 10

Step-by-step explanation:

Its Specified that:

• H.C.F. = (x−5)
• L.C.M. = x^3 −19x−30

now, by vanishing method,

=) x^3 −19x−30

=) x^3 - 5x^2 + 5x^2 - 25x + 6x - 30

=) x^2(x - 5) + 5x(x - 5) + 6(x - 5)

=) (x^2 + 5x + 6)(x - 5)

=) (x^2 + 3x + 2x + 6)(x - 5)

=) (x + 3)(x + 2)(x - 5)

now, (x-5) being H.C.F. and (x+3)(x+2)(x-5) being the L.C.M.,

(x-5) becomes a common factor of both the expressions.

So,

First expression: (x-5)(x+3) = x^2 - 2x - 15

Second expression: (x-5)(x+2) = x^2 - 3x - 10

Hope it helps buddy.....

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