The book says:
Find three different values that complete the expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials.
4g^2+___g+10
Okay, I tried Hotmath, but it didn't explain ALL the steps. I just simply COULD NOT figure it out. I will be able to factor the trinomials, I just need help finding the values that go in the blank. Any help is greatly appreciated! (note: this homework is due by Friday, so please answer soon. TYVM!)
Emily, I don't know if there is any fancier way of doing this other than trial and errror.
I just set up 2 polynomials:
(4g + )(g + ), and used for the blanks the factors of 10, (5,2 and 10 and 1). Then I did the same for:
(2g + )(g + ).
Does this make sense to you?
Thank you very much!
Yes, I can help you find the values that complete the expression in the trinomial. To factor the trinomial 4g^2 + ___g + 10 into the product of two binomials, we need to find two numbers that multiply to give you the constant term (10) and add up to the coefficient of the middle term (g).
Here's how you can do it step-by-step:
1. Write down the trinomial: 4g^2 + ___g + 10
2. Start by factoring out the common factor, if there is any. In this case, there is no common factor other than 1.
3. Now, we need to find two numbers that multiply to give you 10 and add up to give you g. Since 10 can be factored as (1, 10) and (2, 5), we can try these pairs of numbers.
4. Place these pairs of numbers in the blanks and check if they work.
a) First pair: (4g + 1)(g + 10)
Multiply the outer and inner terms: 4g * 10 = 40g and 1 * g = g
The middle term doesn't match the coefficient g, so this is not correct.
b) Second pair: (4g + 2)(g + 5)
Multiply the outer and inner terms: 4g * 5 = 20g and 2 * g = 2g
Add the middle terms: 20g + 2g = 22g
The middle term matches the coefficient g, so this is the correct factorization.
5. So, the trinomial 4g^2 + ___g + 10 factors into (4g + 2)(g + 5).
You can use this process of trial and error to find the correct values that complete the expression in other similar trinomials as well. Remember to look for pairs of numbers that multiply to give you the constant term and add up to give you the coefficient of the middle term.