Factor 15x3 – 5x2 + 6x – 2 by grouping. what is the resulting expression?

(5x2 + 2)(3x – 1)

(5x2 – 2)(3x + 1)

(15x2 + 2)(x – 1)

(15x2 – 2)(x + 1)

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 our expression into tow pairs:

Step 1. Look for common multiples between the factors of our expression:

Notice that 15 is a multiple of 5 and 6 is a multiple of 2, so we should group the factors 15x3 and 5x2 into a pair, and the factors 6x and 2 into another pair. To do it, we just need to group the terms using parenthesis:

Step 2. Identify the common factor of each pair:

Notice that the least common multiple of 15 and 5 is 5, so 5 is part of the common factor of ; now the common factor between the variables (in this case ) is the variable with the least exponent, so . Putting all together we realize that the common factor of the pair is . The common factor of the pair is just 2 since we have no variables there.

Step 3. Factor out the common factor of each pair:

Step 4. Factor out the common binomial factor and group the remaining terms in a parenthesis:

We can conclude that the correct answer is: (5x2 + 2)(3x – 1)

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