Either r or s will be negative, but not both. O If the c term is a negative number, then one factor of c will be positive, and one factor of c will be negative. In other words, r and s will have the same sign. O If the c term is a positive number, then the factors of c will both be positive or both be negative. When factoring a trinomial in the form x 2 + bx + c, consider the following tips. While there is no foolproof way to find the right combination on the first guess, there are some tips that can ease the way. And, there are times when the trinomial cannot be factored. Sometimes, the appropriate number combinations will just pop out and seem so obvious! Other times, despite trying many possibilities, the correct combinations are hard to find. Since multiplication is commutative, this is the same answer.įactoring trinomials is a matter of practice and patience. Then factor x( x – 3) + 4( x – 3), and factor out ( x – 3) getting ( x – 3 )( x + 4). In the above example, you could also rewrite x 2 + x – 12 as x 2 – 3 x + 4 x – 12 first. On the left, list all possible factors of the c term, 6 on the right you'll find the sums. A chart will help us organize possibilities. In this polynomial, the b part of the middle term is 5 and the c term is 6. Let’s factor the trinomial x 2 + 5 x + 6. Note that you can also rewrite 7 x as 5 x + 2 x.
So you can rewrite 7 x as 2 x + 5 x, and continue factoring as in the example above. Do either of these pairs have a sum of 7? Yes, 2 and 5. Look at factor pairs of 10: 1 and 10, 2 and 5. The resulting factors will be ( x + r) and ( x + s).įor example, to factor x 2 + 7 x +10, you are looking for two numbers whose sum is 7 (the coefficient of the middle term) and whose product is 10 (the last term). Rewrite the trinomial as x 2 + rx + sx + c and then use grouping and the distributive property to factor the polynomial. To factor a trinomial in the form x 2 + bx + c, find two integers, r and s, whose product is c and whose sum is b. Fortunately, there's a rule for that.įactoring Trinomials in the form x 2 + bx + c If you rewrite 7 x as 6 x + x, this method won’t work.
#Quadratic trinomial how to
How do you know how to rewrite the middle term? Unfortunately, you can’t rewrite it just any way. Group the pairs and factor out the common factor x from the first pair and 2 from the second pair. Rewrite the middle term 7 x as 5 x + 2 x.
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