HELp Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values.

Answers:

There are eight items in that list above.

Explanation:

We'll use the AC method of factoring.

The first term has coefficient 3. The last term is -8. Multiply them to get 3*(-8) = -24.

Now let's list all the ways to multiply two integers to get -24

For each pair of factors listed, we'll add up those pairs. Each sum we get represents a possible value of k

Note the symmetry. For instance we have 10 as one sum and -10 as another sum.

Let's go over an example. Let's say that k = 10

The expression 3x^2+kx-8 turns into 3x^2+10x-8

From the list above, we see that -2+12 = 10. So the two values -2 and 12 will help us factor.

Break up the 10x into -2x+12x and then factor by grouping like so

3x^2 + 10x - 8

3x^2 - 2x + 12x - 8

(3x^2 - 2x) + (12x - 8)

x(3x-2) + (12x - 8)

x(3x-2) + 4(3x - 2)

(x+4)(3x-2)

Therefore, 3x^2 + 10x - 8 factors into (x+4)(3x-2)

We can use the FOIL rule, distribution, or the box method to confirm this.

I'll let you try out other values of k to see how 3x^2+kx-8 factors.

nlgqer

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