Which shows one way to determine the factors of x3 – 12x2 – 2x + 24 by grouping?

Asked by wiki @ 29/10/2020 in Mathematics viewed by 421 People

Answered by wiki @ 29/10/2020

When factoring by grouping also called factoring in pairs, we should split the expression into tow pairs that have something in common. The idea is that after we factor each pair, we get a binomial common factor. Now let's check how to split the expression into tow pairs:

Step 1. Look for common multiples among the the terms of the expression:

Notice that 24 is a multiple of 12 (12x2=24), so we should group 12x2 and 24

$x^3-12x^2-2x+24$

$(24-12x^2)+x^3-2x$

Step 2. Group the other therms:

$(24-12x^2)+(x^3-2x)$

Step 3. It is a good idea to express the higher variable in each of the pairs as the positive first term of the pair. Since the variable in the first pair is in second position and it's negative, we are going to multiply the first parenthesis by -1 to change the order and the sign of the variable:

$(24-12x^2)+(x^3-2x)$

$-(12x^2-24)+(x^3-2x)$

Step 4. Factor out the common terms of each pair:

$-(12x^2-24)+(x^3-2x)$

$-12(x^2-2)+x(x^2-2)$

Step 5. Factor out the common binomial term $(x^2-2)$ :

$-12(x^2-2)+x(x^2-2)$

$(x^2-2)(x-12)$

Which shows one way to determine the factors of x3 – 12x2 – 2x + 24 by grouping?

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