(Solved) How to factor quadratics with?

Fedorfan76

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11 years ago

5x squared + 2x + 3

How to factor with a number on the first part? I am stuck when there is a number in the first part. The problem is just an example. It may not be factorable.

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!JRon@n

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11 years ago

5x^2+2x+3 I think not+3 but -3 so
5x^2+2x-3=(5x-3)(x+1)

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JulieA

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11 years ago

This verified answer contains over 160 words.

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Julie Appleton

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rjframe

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11 years ago

Say, it is of the form:

ax² + bx + c = 0,.................(1), where a, b and c are constants.

(i) Multiply "a" and "c"& factorize the product (ac) into ALL POSSIBLE factors.

(ii) Amongst all these, choose combination of a pair of those two factors whose sum or difference is b. Let's say "m" and "n", so that b = m ± n, (of course mn = ac) and write (1) as:

ax² + (m ± n) x + c = 0 or ax² + mx ± n x + c = 0.

(iii) Group as under & take highest common factor in each group:

{Ist} + {IInd}

(ax² + mx) ± (n x + c) = 0.

Say it is like: px(rx + s) + q(rx + s) = 0, where p, q, r, and s are constants.

Then, finally, factors of the quadratic (1) will be:

(px + q)(rx + s) = 0.

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fireman2101

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11 years ago

just get its factors..for your example, it just has one pair of factor, 5x and x..

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