Factor. 6a^4 + 3a^3 - a + 2 _____

Question

Bytelearn · Accepted Answer

Look for factors: Look for common factors in each term. We can see that there is no common factor for all terms, so we cannot factor by grouping directly. We need to look for a different approach.Factor by grouping: Try to factor by grouping. We can attempt to group the terms in pairs to see if we can factor anything out. Let's group the first two terms and the last two terms: (6a^4 + 3a^3) - (a - 2) Now, let's factor out the greatest common factor from each group.Factor out common factor: Factor out the greatest common factor from each group. From the first group (6a^4 + 3a^3), we can factor out 3a^3: 3a^3(2a + 1) From the second group (a - 2), we cannot factor anything out, so it remains as is: -(a - 2) Now we have: 3a^3(2a + 1) - (a - 2)Check for binomial factor: Check for a common binomial factor. Unfortunately, there is no common binomial factor between 3a^3(2a + 1) and -(a - 2). This means that our attempt to factor by grouping does not work, and we need to try a different method or check if the polynomial is prime (cannot be factored).Check for patterns: Check for patterns or special products. There are no obvious patterns such as a difference of squares, perfect square trinomials, or sum/difference of cubes. The polynomial does not seem to fit any special product patterns.Attempt synthetic division: Attempt synthetic division or use the Rational Root Theorem. Since the polynomial does not factor by grouping and does not fit any special patterns, we can try to find rational roots using the Rational Root Theorem or synthetic division. However, this process is beyond the scope of a simple step-by-step solution and requires trial and error with possible rational roots.

Factor. $\newline$ $6a^4 + 3a^3 - a + 2$ $\newline$ _____

Full solution

More problems from Factor by grouping

Related topics

Factor. \newline6a4+3a3−a+26a^4 + 3a^3 - a + 26a4+3a3−a+2\newline_____

Factor. $\newline$ $6a^4 + 3a^3 - a + 2$ $\newline$ _____