Factoring polynomials?

Question

I need help with factoring second degree polynomials.
The first question looks like this b^2+4b-60.

Answer 1

Solve the quadratic equation b^2+4b-60=0
Once you found the two answers - b1 and b2 (6 and -10 in this case) - you can write your expression as A(b-b1)(b-2), where A is the costant that goes with x^2 (1 - or nothing - in this case).
So, the answer to this problem is, as it is said already (b-6)(b+10).

If the equation had only one solution, then ot would factor as a full square - for example (x^2+2x+1) = (x-1)^2 - just imagine that there are two solutions, like before, but they both happen to be the sane.

and if there are no real solutions at all, then the expression cannot be factored at all (not in real numbers anyway).

Answer 2

Its quite simple. First u take the sole number that is present (without any x etc). In this case it is -60. Now you have to find two numbers who's multiplication is -60 and addition is +4. Try out various combinations. U will be able to do it in a jiffy once u get practice. Then u hv to split the middle portion into the addition of those two nos v found out. (that is the one hving single degree x or y.....)

In the case of the polynomial b^2 + 4b- 60=0 (its normally 0 for simple eq, if its mentioned otherwise do the small changes)
the two numbers are 10 and -6. Notice that it matches the criterion i mentioned. That is 10 * -6 is -60 and their addition that is 10 - 6 is 4. So now since v hv found the nos v can solve the problem.

b^2+ 4b - 60
Now divide 4b into 10b - 6b (as those r the nos v hv found out)

b^2 + 10b - 6b - 60 = 0
now group the first two terms and the last two terms and take out the common factor (take out the common terms in such a way that two brackets r same, as u can c below)

b(b+10) - 6(b+10) = 0

now since two brackets r same take them common

(b+10) (b-6) = 0

hence either b = -10 OR b = 6 (as v shifted the nos to the other side the signs changed.)

Hope it helped.

Answer 3

b^2 + 4b-60 Do the following:

try (b+x)(b+y) where x and y are to be determined

xy=-60 and x+y =4. x=6 y=-10 possible since xy=-60, but NO
because x+y=-4 not +4
try x=+10 and y= -6. That does it!

b^2 +4b-60=(b+10)(b-6)

Answer 4

You need to look for (b + m)(b + n), where mn = -60 and m + n = 4. For mn to equal -60, they must be of opposite signs. I think you'll find that 10 and -6 do the trick. In general, mn needs to equal the constant term, and m + n needs to equal the coefficient of b. It's harder when b^2 has a coefficient other than 1.

Answer 5

there is a great website that can offer help it is purplemath.com you could find help there. The is also a box algorithm that works for factoring polynomials that works every time. good luck I know math suck, cause I am doing the same thing right now!!!

Answer 6

if you want to find out really easily, just use a ti-89 calculator, there is a Factor option. This way it will solve any factorization you need.

Answer 7

(b+10)(b-6)

Answer 8

im studying the same stuff. go on

http://education.yahoo.com/homework_help/math_help/algebra1

it really helps. theres like a tutor explaining stuff.

Answer 9

(b+10)(b-6). Use foil "first, inner, outer, last" to multiply it out.