Problem 31
Question
Factor completely, or state that the polynomial is prime. $$x^{2}+36$$
Step-by-Step Solution
Verified Answer
The polynomial \(x^{2} + 36\) is a prime polynomial as it can't be factored using integer coefficients.
1Step 1
Identify the polynomial and its components: we have \(x^{2} + 36\)
2Step 2
Try to factor the polynomial: In our case, since there is no integral root which when squared gives 36, and the polynomial can't be expressed as difference of squares. It doesn't factor into two binomials with integral coefficients.
3Step 3
Conclude: As a result, the original polynomial \(x^{2} + 36\) can't be factored using non-integer coefficients, so it is a prime polynomial.
Other exercises in this chapter
Problem 31
Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. \(r^{2}+12 r+27\)
View solution Problem 31
Use factoring to solve each quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\) -intercepts. $$4 x^{2}=12 x-9$$
View solution Problem 31
Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations usin
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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. $$8 x^{2}-4
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