Problem 21
Question
Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+4 x+12$$
Step-by-Step Solution
Verified Answer
The trinomial \(x^{2}+4x+12\) is prime and cannot be factored.
1Step 1: Analyze the trinomial
Our trinomial is \(x^{2}+4x+12\). We need to find two numbers that multiply to give 12 and also add to give 4.
2Step 2: Attempt to factor
It's not possible to find any two numbers that multiply to give 12 and add up to 4. Because of this, the trinomial is considered prime and cannot be factored.
3Step 3: Checking with FOIL
As the trinomial cannot be factored further, there is no need to apply the FOIL (First, Outer, Inner, Last) method.
Other exercises in this chapter
Problem 20
Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$32 x-24$$
View solution Problem 20
Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$6 w^{2}-17 w
View solution Problem 21
Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$x^{2}=4 x$$
View solution Problem 21
Factor each difference of two squares. $$x^{4}-y^{10}$$
View solution