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Bunuel
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If the least common multiple and the highest common factor of two expr 10 Aug 2021, 03:15
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If the least common multiple and the highest common factor of two expressions are (x^2 + 6x + 8)(x + 1) and (x + 1) respectively and one of the expressions is (x^2 + 3x + 2), what it the other?

(A) x^2 + 5x + 4
(B) x^2 − 5x + 4
(C) x^2 + 4x + 5
(D) x^2 − 4x + 5
(E) x^2 − 8x + 5
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If the least common multiple and the highest common factor of two expr Updated on: 10 Aug 2021, 03:46
Originally posted by sj296 on 10 Aug 2021, 03:32.
Last edited by sj296 on 10 Aug 2021, 03:46, edited 1 time in total.
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Bunuel
If the least common multiple and the highest common factor of two expressions are (x^2 + 6x + 8)(x + 1) and (x + 1) respectively and one of the expressions is (x^2 + 3x + 2), what it the other?

(A) x^2 + 5x + 5
(B) x^2 − 5x + 4
(C) x^2 + 4x + 5
(D) x^2 − 4x + 5
(E) x^2 − 8x + 5
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Hey @Bunnel I am getting x^2 + 5x + 4. Could you pls check the options.

HCF = (x + 1)

LCM = (x^2 + 6x + 8)(x + 1) => (x+4)(x+2)(x+1)

One of the expressions = (x^2 + 3x + 2) => (x+2)(x+1)

HCF*LCM = multiplication of the two numbers

=> (x+4)(x+2)(x+1)*(x + 1) = (x+2)(x+1) * Another expression

=> Another expression = (x+4)(x+1) = x^2 + 5x + 4

There is no option :?
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If the least common multiple and the highest common factor of two expr 10 Aug 2021, 03:38
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Two fractions are equivalent if they express the same part of a whole. ... Then divide both the numerator and the denominator by the greatest common factor.
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If the least common multiple and the highest common factor of two expr 10 Aug 2021, 03:43
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Solution:

We are given \(LCM\) \(= (x^2 + 6x + 8)(x + 1)\) and \(HCF\) \(= x+1\).

One of the expression \(= x^2 + 3x + 2\). We are asked the other expression.

We know a property: Product of 2 number = product of their LCM and HCF

We can write: \((x^2 + 6x + 8)(x + 1)\times (x+1) = x^2 + 3x + 2 \times second expression\).

\(⇒ (x^2 + 6x + 8)(x + 1)^2=x^2+3x+2 \times A\) (Assuming the other expression be A)

\(⇒ (x^2+4x+2x+8)(x+1)^2=x^2+2x+x+2 \times A\)

\(⇒ (x+2)(x+4)(x+1)^2=(x+1)(x+2)\times A\)

\(⇒ (x+4)(x+1)=A\)

\(⇒ A=x^2+5x+4\)

Bunuel please change one of the answer options to \(x^2+5x+4\).

Hence the right answer will be \(x^2+5x+4\).
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If the least common multiple and the highest common factor of two expr 13 Sep 2024, 22:42
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x+1 is a factor of the equation, substitute x = -1 in the equations and see if it leads to 0. A is the only one.
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If the least common multiple and the highest common factor of two expr 08 Oct 2024, 07:06
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The only option that can give you the hcf i.e x+1 is option A
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If the least common multiple and the highest common factor of two expr 27 Mar 2026, 07:30
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