Monday, August 17, 1998

Algebra 1 factoring help?

I need some help with these problems:

1. x^2 – 8x + 15
2. a^2 – a – 20
3. a^2 – 5a – 20
4. a^2 + 12ab + 27b^2
5. 2a^2 + 30a + 100

I don't know how to do them. I can easily find the answers, but I'd like to know the process so I don't have to keep asking on here.

Thanks

Answer on Algebra 1 factoring help?

Factoring decomposition yields:

1. x? - 5x - 3x + 15 . . Split -8x into two terms w/product of 15 and sum of -8
= x(x - 5) - 3(x - 5) . . Factor like terms
= (x - 3)(x - 5). . . . . . Group the common factors of x - 5 and collect the terms.

Do the same for the rest of the problem!

2. a? - a - 20
= a? - 5a + 4a - 20 [Sum: -1 and Product: -20]
= a(a - 5) + 4(a - 5)
= (a + 4)(a - 5)

3. a? - 5a - 20 - Unfactorable since you can't determine two real numbers with product of -20 and sum of -5.

4. a? + 12ab + 27b?
= a? + 9ab + 3ab + 27b? [Sum: 12 and Product: 27]
= a(a + 9b) + 3b(a + 9b)
= (a + 9b)(a + 3b)

5. 2a? + 30a + 100
= 2(a? + 15a + 50)
= 2(a? + 10a + 5a + 50) [Sum: 15 and Product: 50]
= 2(a(a + 10) + 5(a + 10))
= 2(a + 10)(a + 5)

I hope this helps!