What it means to factor a polynomial?

Question

1) What it means to factor a polynomial?

2) When do you try to factor by grouping?

3) How to determine the binomial factors of 6x2+5x-25? (2 menas square two)

4) How to solved 9t3 = 16t? (3 means cube)

Answer 1

1) to factor a polynomial means to find One of two or more quantities that divides a given polynomial without a remainder.

2) Factoring by grouping is usually done when you have at least 4 terms and they do not look to have anything in common. The procedure for that is:
bulletRemove the GCF if possible.
bulletGroup terms with common factors.
bulletRemove the GCF of each group.
bulletUse the distributive law to rewrite the expression.

3) 6x^2+5x-25 this one is hard. it's a trinomial in the form ax^2+bx+c where a does not equal 1

in this case, you'll have to use the trial and error method which means you have to guess the factors in order to get the binomial factors. to make it easier, find all the factors of c part which is -25. the factors are: +/-1,+/-5,+/-25. and find all the factors of a part which is 6. the factors are: +/-1,+/-2,+/-3,+/-6.

now, i won't go into trouble showing you all my solutions. i'll just give you the right answer. the correct answer is (3x-5) (2x+5). you can check to see if this solution is correct.

4) for this one, i suppose you're trying to solve for t. here's the solution:

9t^3 = 16t
9t^3 - 16 t = 0 make this an equation by transferring 16t to the left side and make it negative. make everything equals to zero.
t(9t^2 - 16) =0 factor the left side
t= 0 9t^2 -16 = 0
9t^2 = 16
t^2 = 16/9
t= + or - 4/3 get the square roots of both the right and left side

the possible answers are x=0, x= - 4/3, and x= 4/3

now, if you check these solutions, you'll see that only positive and negative 4/3 (+or - 4/3) will work.

hope these help you! ^_^

Answer 2

1) Factoring a polynomial means putting it in the form of a product of factors.
x^2 - 4x + 3 factors as (x - 3)(x - 1).

x^2 - 4x + 3 is written as a sum (and/or differences) of product of terms.
(x - 3)(x - 1) is written as a product of sums (and/or differences.

Answer 3

factorising the polynomial means converting into leanir equaiton. if you want help in future also come and sign up here http://www.mylot.com/?ref=helpme901 it is also a mesage borad. I am able to solve your each problem but it would be benifiacial for us both if you will ask me question there

Answer 4

factoring basically skill breaking an equation down into areas that are greater handy to artwork with. it generally contains changing a term it rather is squared or cubed, or in spite of, into 2 words of first degree (to the 1st skill) that, while accelerated mutually, equivalent your commencing equation. desire that enables!