Objective: Factor trinomials of the type x2 + bx + c.
Trinomials can be factored using a process different than the GCF method and the Grouping method. For example, the polynomial x2+7x + 10 cannot be factored using either method we have observed so far, but it still can be factored. In this lesson, we will learn how to factor trinomials of this type, where the coefficient in front of the x2 term is 1.
To factor trinomials of this type we must recall that often trinomials are the products of two binomials. For example:
(x+2)(x+5) = x2+5x+2x+10 = x2+7x +10
Since this is true, then the trinomial x2+7x +10 can be factored back into the two binomials (x+2)(x+5). What we observe from this type of trinomial is that the factored form will always contain two binomials where the first terms of the two binomials are "x" and the constants terms of the binomials will always multiply to give the "c" term of trinomial and add to give the "b" coefficient of the trinomial. We use this pattern to factor trinomials of this type. See the process shown in the video below.
Now that we learned how to factor basic trinomials of the type x2 + bx + c, we must learn how to factor trinomials when they appear slightly different then that given form. This will often require an additional step in the problem in order to ensure we are factoring the trinomial accurately. And lastly, though the trinomial process helps us factor many more types of polynomials, still not every polynomial (and in this case trinomial) can be factored. If a polynomial cannot be factored at all it is said to be prime. To see examples of all of these trinomial variations and prime polynomials, watch the video below.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.