Math Tutoring on Factoring Trinomials with a Leading Coefficient Not 1
To factor a trinomial ax²+bx+1, when the leading coefficient, “a", does not equal to 1 we will be using the Trial and Error Method and the Grouping Technique. In trial and error method or reverse FOIL method,
1. Place the factors of ax² in the first positions of the two sets of parentheses that represent the factors.
2. Place two possible factors of c into the second positions of the parentheses.
3. Find the inner and outer products of the two sets of parentheses.
4. Keep doing this until the inner and outer products that add to the middle term, bx is found.
In factor by grouping,
1. Divide the polynomial into two groups, the first half, and the second half.
2. Factor the g.c.f. out of the first half, and then factor the g.c.f. out of the second half.
3. Notice a common binomial or trinomial factor.
4. Factor out the common binomial or trinomial factor.
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4. What does it mean to factor a polynomial?
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