How do you factor #8x ^ { 3} + 7x ^ { 2} - 32x + 28# completely?
1 Answer
Cannot be factored. (See explanation for alternate problem which was possibly the question intended.)
Explanation:
The problem as stated is irreducible and cannot be factored as written. However, it's incredibly close to a problem which CAN indeed be factored, assuming there's a typo and the problem mean for either the
Factor
When you come across factoring problems like this, there are many methods you can use. One thing to immediately look for is to see if there's any pattern in the coefficients than can be exploited in factoring.
For instance, the coefficients are 8, 7, -32, and -28. Can those be grouped in some manner where a number and a multiple of that number are together? If so, can you group them so that each pair has the same multiplier?
If we rearrange the terms such that we put the
That suggests we can use a practice known as factoring by grouping. Let's rewrite the terms to group them together as we talked about:
Notice how both groupings have factored in a way that leaves behind
Lastly, we can recognize that
Special note
Had I chosen to show the problem with a positive