SOLUTION: Factor the trinomial using the AC method. 4x^2-7x+5

Algebra.Com
Question 718705: Factor the trinomial using the AC method.
4x^2-7x+5
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?



To find these two numbers, we need to list all of the factors of (the previous product).



Factors of :

1,2,4,5,10,20

-1,-2,-4,-5,-10,-20



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to .

1*20 = 20
2*10 = 20
4*5 = 20
(-1)*(-20) = 20
(-2)*(-10) = 20
(-4)*(-5) = 20


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1201+20=21
2102+10=12
454+5=9
-1-20-1+(-20)=-21
-2-10-2+(-10)=-12
-4-5-4+(-5)=-9




From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.



===============================================================





Answer:



So doesn't factor at all (over the rational numbers).



So is prime.
RELATED QUESTIONS

Factor each trinomial using the ac Method 15x² - 7x -2 (answered by stanbon)
Factor each Trinomial using the “ac” method. Showing work and solution. 15x² - 7x... (answered by fractalier)
Factor each trinomial using the ac method... (answered by checkley77)
Factor each trinomial using the ac method... (answered by KnightOwlTutor)
Factor each trinomial using the ac method. 21x^2 + 2x -... (answered by mananth)
Factor the trinomial... (answered by lynnlo)
7x^2+26x-8 factor the trinomial or state if it's prime. Using the FOIL... (answered by Alan3354)
please help! Fact the trinomial using the ac method. 2x^2 + 11x +... (answered by Alan3354)
5x^2-9x-2 How do you identify a factor of this trinomial using the AC... (answered by Nate)