Methods of Factorization

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SamzeeTyro

Asked: March 24, 20212021-03-24T19:12:11+00:00 2021-03-24T19:12:11+00:00In: Algebra, High School/Senior Secondary School

What are the three common methods to do factorization?? Explain with examples.

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acedstud · Answer 1 · 2021-03-24T22:04:21+00:00

There are many methods of factorisation.

The three commonest types are:

1) Factorisation by factoring out the GCD.

Example: Factor $3x^2+6x$ .

Here, the GCD (the greatest factor both terms have in common) is $3x$ . So, factoring out $3x$ gives $3x(x+2)$ .

Therefore, $3x^2+6x=3x(x+2)$ .

2) Factorisation by grouping.

Example: to factor $3x^3+2x^2+9x+6$ , we group it as follows: $x^2(3x+2)+3(3x+2)=(x^2+3)(3x+2)$ .

Therefore, $3x^3+2x^2+9x+6=(x^2+3)(3x+2)$ .

3.) Factoring quadratic trinomials by trial and error.

Example: To factor $x^2+5x+6$ , we use the formula $x^2+(a+b)x+ab=(x+a)(x+b)$ . So, here, we have $x^2+5x+6=x^2+(2+3)x+2\times3=(x+2)(x+3)$ .

Therefore, $x^2+5x+6=(x+2)(x+3)$ .

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