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We are given the quadratic expression:

\[
x^2 + ax - 40
\]

To find the value of \(a\) for which the trinomial is factorable, we need to ensure that the trinomial can be factored into two binomials of the form:

\[
(x + p)(x + q) = x^2 + (p+q)x + pq
\]

From this, we know:
- \(pq = -40\) (the constant term)
- \(p + q = a\) (the coefficient of the middle term)

So, we need to find pairs of integers \(p\) and \(q\) whose product is \(-40\). These integer pairs will then sum up to give the value of \(a\).

The factor pairs of \(-40\) are:
\[
(1, -40), (-1, 40), (2, -20), (-2, 20), (4, -10), (-4, 10), (5, -8), (-5, 8)
\]

Now, calculate the sums \(p + q\) for each pair:

\[
1 + (-40) = -39
\]
\[
-1 + 40 = 39
\]
\[
2 + (-20) = -18
\]
\[
-2 + 20 = 18
\]
\[
4 + (-10) = -6
\]
\[
-4 + 10 = 6
\]
\[
5 + (-8) = -3
\]
\[
-5 + 8 = 3
\]

Thus, the possible values of \(a\) for which the trinomial is factorable are:

\[
a = -39, 39, -18, 18, -6, 6, -3, 3
\]

Would you like more details on the factoring process or help with something else?

Here are 5 related questions:
1. How do you determine if a quadratic trinomial is factorable?
2. Can every quadratic expression be factored over integers?
3. What happens when the discriminant is negative in a quadratic equation?
4. How do you factor a quadratic expression when the leading coefficient is not 1?
5. How does factoring help in solving quadratic equations?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) to see if a quadratic is factorable over the real numbers.

For which value of a will the trinomial be factorable? x^2 + ax - 40

Learn how to factor the quadratic trinomial x^2 + ax - 40 by determining possible values of a. This solution explains how to use factor pairs and factorization techniques. Ideal for students in Grades 8-10.

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