How do you factor by grouping $10 x^{3} + 20 x^{2} + x + 2$ $10x^3+20x^2+x+2$ ?

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How do you factor by grouping $10 x^{3} + 20 x^{2} + x + 2$ $10x^3+20x^2+x+2$ ?

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Answer 1 · 2015-04-11T09:47:52

We can factorise the following expression by making groups of 2

$(10 x^{3} + 20 x^{2}) + (x + 2)$ $(10x^3+20x^2)+(x+2)$

In the first group, $10 x^{2}$ $10x^2$ is common to both the terms, and in the second, $1$ $1$ is the only factor common to both the terms.

So we write the expression as

$(10 x^{2}) (x + 2) + 1 \cdot (x + 2)$ $(10x^2)(x+2)+1*(x+2)$

$= (x + 2) (10 x^{2} + 1)$ $= color(green)((x+2)(10x^2+1)$

As $10 x^{2} + 1$ $10x^2 + 1$ cannot be factorised further, the above will be the factorised form of the expression $10 x^{3} + 20 x^{2} + x + 2$ $10x^3+20x^2+x+2$

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How do you factor by grouping $10 x^{3} + 20 x^{2} + x + 2$ $10x^3+20x^2+x+2$ ?

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