SOLUTION: Factor each of the following polynomials completely: -3s^2 - 10s + 8 I do not even know where to start because I do not understnd the text book.

Question 107590: Factor each of the following polynomials completely:
-3s^2 - 10s + 8
I do not even know where to start because I do not understnd the text book.
Found 3 solutions by stanbon, checkley71, scott8148:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
-3s^2 - 10s + 8
Find two numbers whse product = ac = -24 and whose sum = b= -10
the numbers are -12 and +2
Replace -10s by -12s+2s
-----------------------
= -3s^2-12s+2s+8
Factor the 1st two and the last two terms separately
=-3s(s+4)+2(s+4)
Factor again to get:
=(s+4)(-3s+2)
================
Cheers,
Stan H.

Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
-3S^2-10S+8 YOU NEED TO FIND 2 FACTORS OF -3 & 2 FACTORS OF 8 THAT WHEN MULTIPLIED & THEN ADDED = -10.
FACTORS OF -3 ARE (1,-3). FACTORS OF 8 ARE (1,8),(-1,-8),(2,4),(-2,-4).
YOU CAN ELIMINATE THE 1&8 BECAUSE 8+3=11, 8-3=5. SO IT MUST BE THE (2,4) FACTORS. TRY 1*4+-3*2=4-6=-2 NOT A GOOD TRY. 1*2+(-3*4)=2-12=-10 LOOKS LIKE A WINNER.
SO WE HAVE:
(-3S+2)(S+4)
PROOF
-3S+2
S+4 WHEN MULTIPLIED
-------------------------------
-3S^2+2S-12S+8 COMBINING LIKE TERMS WE GET
-3X^2-10S+8
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
factor means to find the quantities that are multiplied to get the quantity you are factoring

example: (x+1)(x+2)=x^2+3x+2 ... (x+1) and (x+2) are factors of x^2+3x+2

notice that the constant term (2) is the product of the constant terms in the factors
...and the x coefficient (3) is the sum of the constant terms of the factors

one technique is grouping ... x^2+3x+2 ... (x^2+x)+(2x+2) ... (x(x+1))+(2(x+1)) ... (x+2)(x+1)
...factoring the groups is easier than the whole expression

-3s^2-10s+8 ... (-3s^2-12s)+(2s+8) ... (-3s(s+4))+(2(s+4))

it takes time and practice to spot the patterns easily ... good luck
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