0
Factor a formula of form ax^2+bx by pulling out an x. This is called "factoring out a common factor."
For example, 3x^2+5x can be split up by pulling out the x and getting x*(3x+5), where the asterisk * indicates multiplication.
- 2
Factor a formula of form ax^2+bxy+cy^2+d--i.e., a form with at least two variables and at least four terms--by grouping.
For example, take 6x^3-9x^2+2xy-3y. Group terms that have variables in common: (6x^3-9x^2)+(2xy-3y). Pull out common terms: 3x^2(2x-3)+y(2x-3). Group again: (3x^2+y)(2x-3). This method doesn't always work. Usually the problem states to use grouping so that you don't waste a lot of time on a method that won't work.
- 3
Factor a formula of form ax^2+bx+c (with a, b, c constants) by grouping.
For example, for 6x^2+17x+12, we have a=6, b=17 and c=12. Use the following algorithm to factor it: find factors of ac that add to b; ac is 72. The first factorization that comes to most people's minds is 9*8. Fortunately, 9+8=17. Now rewrite the equation with b split up into 9 and 8, and then factor by grouping the four-term polynomial: 6x^2+(9+8)x+12 = 6x^2+9x+8x+12 = (6x^2+9x)+(8x+12) = 3x(2x+3)+4(2x+3). Group again to get (3x+4)(2x+3).
- 4
Refer to formulas when it helps. For example, the formula for x^2-y^2 is (x-y)(x+y), so, for instance, 9x^2-4=(3x-2)(3x+2).
The formula for factoring x^3-y^3 is (x-y)(x^2+xy+y^2). The formula for x^3+y^3 is (x+y)(x^2-xy+y^2).
- 5
Use two substitutions to solve cubics (single-variable polynomials of order 3), a method first published by Gerolamo Cardano. For the form x^3+ax^2+bx+c=0, substitute x=z-a/3, where z is a variable. Then regroup terms of the same order. (3b-a^2)/3 will end up being the coefficient of z. Then define p=(3b-a^2)/3. Make the substitution z=w-p/3x (called "Vieta's substitution"). Then regroup terms of common order again. The resulting formula is a quadratic in w^3. If the formula can't be factored using grouping as described above, factor quadratics using the quadratic equation.
Add your answer:
Earn +20 pts
What does the exponent indicate using the factor?
The exponent indicates the number of times the base is used as a factor.
What is the exponent indicates how many times that factor as used?
That is all that the exponent is.
What tells us how many times a number is used as a factor?
The exponent tells us how many times a number is used as a factor.
Is base used as a factor?
The exponent tells how many times the base is used as a factor.
What is the Factor 5x exponent 4 plus 25x exponent 2?
5x^2(x^2 + 5)
What is the common factor multiplied repeatedly by the exponent?
The base is the common factor multiplied repeatedly by the exponent.
What does the exponent indicate using the factor?
The exponent indicates the number of times the base is used as a factor.
What is the smallest raised number in a power that tells how many times the base is used as a factor?
The exponent.
What is the n in xn indicating the number of factor of x?
exponent exponent
What exponent tells how many times what is used as a factor?
The exponent tells how many times the base is used as a factor.
What is the exponent indicates how many times that factor as used?
That is all that the exponent is.
What tells how many times a number is used as a factor?
An exponent tells how many times a number is used as a factor.
What is an exponent that tells how many times blank is used in a factor?
The EXPONENT tells you how often the BASE is used as a factor.
Is the present value factor the exponent of the future value factor?
The present value factor is the exponent of the future value factor. this is the relationship between Present Value and Future Value.
What indicates the number of times the base is used a factor?
The exponent tells how many times to use the base as a factor.
Where is the exponent use for?
The exponent tells how many times the base is used as a factor.
What does an exponent represents?
An exponent tells how many times a factor is muliplied by itself.
