Name four values of b which make the expression factorable:

x^2 - 3x + b

just find two numbers where one is 3 more than the other:

1,4
7,10
etc.

Then use them to make the factors
(x+1)(x-4) = x^2-3x-4
(x+7)(x-10) = x^2-3x-70
etc.

so b becomes -4,-70, etc.

-4,-10,-18,-42

thank you

Thank you, Steve

To determine the values of b which make the expression factorable, we need to find the values of b for which the quadratic expression x^2 - 3x + b can be factored into two binomials.

In order for a quadratic expression to be factorable, the quadratic equation should have two real roots or solutions. This means that the discriminant of the quadratic equation must be greater than or equal to zero.

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula: discriminant = b^2 - 4ac.

In our case, the quadratic equation is x^2 - 3x + b = 0. Comparing it to the general quadratic equation form ax^2 + bx + c = 0, we have a = 1, b = -3, and c = b.

The discriminant for this quadratic equation becomes: discriminant = (-3)^2 - 4(1)(b) = 9 - 4b.

To make the expression factorable, the discriminant should be greater than or equal to zero. Therefore, we need to solve the inequality 9 - 4b ≥ 0.

Solving this inequality, we have:

9 - 4b ≥ 0
4b ≤ 9
b ≤ 9/4

So, the values of b that make the expression factorable are any values less than or equal to 9/4.

To summarize, four values of b which make the expression x^2 - 3x + b factorable are any values less than or equal to 9/4.

Very helpful

Thank You! :)

name four values of b which makethe expression factorable x^2-3x+b.