Question 139024: OK.
MY QUESTION IS ABOUT POLYNOMIALS AND FACTORING.
I ONLY HAVE 3 QUESTIONS.
PROBLEM 1: Z^2+65+1000
[I NEED A NUMBER THAT MAKES BOTH WHEN ADDED OR MULTIPLIED.]
PROBLEM 2: X^2-45X+450
[I NEED A NUMBER THAT MAKES BOTH WHEN ADDED OR MULTIPLIED.]
PROBLEM 3: D^2-33D-280
[I NEED A NUMBER THAT MAKES BOTH WHEN ADDED OR MULTIPLIED.]
THATS ALL I NEED TO KNOW.
I CAN FIGURE OUT THE REST.
THANK YOU.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Do me a big favor and stop typing your questions in all caps. Thanks.
Factors of 1000:
1, 2, 2, 2, 5, 5, 5, 1000
1 and 1000, nope
2 and 500, nope
4 and 250, nope
5 and 100, nope
8 and 125, nope
10 and 100, nope
20 and 50, nope but closer
25 and 40. Aha!
Work out number 2 the same way.
Number 3 is a little tricker because you have to find the difference rather than the sum. But you have a clue. Because the sign on the constant term is negative, you know the signs on your two factors must be opposite -- one positive and the other negative. Also, since the coefficient on the first degree term is other than zero, you know that your two factors must be different. Since the sign on the first degree term is negative, the larger of the two factors must be negative.
Factors of 280
1, 2, 2, 2, 5, 7, 280
1 and -280, nope
2 and -140, nope
4 and -70, nope
5 and -56, nope but getting closer
7 and -40 Aha!!!
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