Mona H.

asked • 12/02/20

can trinomials be factored by grouping?

John N.

Yes, but you have to convert it into a polynomial with 4 terms. If it is not prime, you can do this with a method I call "busting the B". A trinomial is of the form Ax^2+Bx+C, so "busting the B" means you will basically "uncombine" the x-term (you will have two x terms). The method is done by these steps: 1: Multiply A*C (include the negatives if any) 2: Create a factor chart of the product of A*C (ignore the signs for now) 3: If the product of A*C is POSITIVE, you will add the factors to see if you get the value of B as the sum (keep in mind that both factors can be negative). If the product of A*C is NEGATIVE, you will subtract the factors to see if you get the value of B as the difference (put the negative sign on the appropriate value, for example if B is negative, put the negative sign on the larger of the two factors). SIDE NOTE: the trinomial is prime if the sum or difference of these factors does not result in the value of B. 4: Whichever pair of factors gets you the value of B when you add or subtract them (depending on the situation in step 3), those will be the coefficients of your x-terms. Rewrite your polynomial with your new coefficients of x and proceed with grouping!
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12/03/20

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