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# If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?

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Math Expert
Joined: 02 Sep 2009
Posts: 52230
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?  [#permalink]

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31 Oct 2018, 23:10
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:16) correct 53% (01:32) wrong based on 38 sessions

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If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?

(1) a = 1
(2) a and b are positive inte

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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?  [#permalink]

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01 Nov 2018, 00:29
Bunuel wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?

(1) a = 1
(2) a and b are positive inte

Question: c = ?

Given:$$x^2 + 3x + c = (x + a)(x + b)$$
i.e. $$x^2 + 3x + c = x^2 + (a+b)x + ab$$
Comparing the RHS with LHS we get,
$$a+b = 3$$ and $$a*b = c$$

Now we have one linear relation between a and b and we need to find a*b to find c

Question REPHRASED: What is the value of a or b or c?

Statement 1: a = 1

SUFFICIENT

Statement 2: a and b are positive inters
i.e. a and b must be 1 and 2 only hence
c = 1*2 = 2
SUFFICIENT

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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?  [#permalink]

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03 Nov 2018, 00:50
Dear Moderator,

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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c? &nbs [#permalink] 03 Nov 2018, 00:50
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