Question

Please help!!!
Determine two different values of “b” in x2 + bx + 30 so that the expression can be factored into the product of two binomials. Explain how you determined those values and show each factorization. Explain how your process would change if the expression was 2x2 + bx + 30.

Answer 1

What you want, is to open two sets of parenthesis, so that x is in the first position, and since the constant is 30, you could have (+3)(+10), then you would have (x + 3)(x+10) = x^2 + 13x + 30, so b = 13 in this case.
Or, you can have (x + 6)(x + 5) which also yields x^ + bx + 30. And specifically, you would have x^2 + 11x + 30, so b = 11 in this case. Other possibilities are possible. So 2 possible values for b is b = 10 and b = 11.

Answer 2

I don't understand at all ): @Easyaspi314

Answer 3

When you want to factor x^2 + bx + 30, you are looking for two numbers that when you multiply them you get +30, and when you add them up, you get b.

Answer 4

okay, so 10 and 3? @Easyaspi314

Answer 5

Thats one possibility...so (x+10)(x+3) is a possibility...and when you multiple (x+10)(x+3) you get x^2 + 13x + 30...so b = 13.

Answer 6

I used 5 and 6 which is also fine.
I also used 5 and 6, which is also fine.

You could also use 1 and 30.

Answer 7

Or even 2 and 15 is fine.

Many ways.

Answer 8

oh okay I think I get it! Thank you!

Answer 9

I got:

x^2+bx+30 or x^2+bx+30
2*15=30 3*10=30
(x+2)(x+15) (x+3)(x+10)
x^2+2x+15x+30 x^2+3x+10x+30
b=17 b=13

good so far? @Easyaspi314

Answer 10

I had to give 2 examples

Answer 11

Correct. You were just asked to give 2 possible values for b, although there are more than 2 possible, as discussed.

Answer 12

It says to explain how the process would change if the expression was 2x^2+bx+30

"I would have to multiply 30 and 2 and get 60. Then I would have to determine the possibility of b from the factors of 60, instead of 30."

Is this answer good? or do I need more detail, explaining, etc.? @Easyaspi314