SOLUTION: I am struggling with this problem, Can someone please help? Megan factored the expression 28x^2-25x+3 as (7x-3)(4x-1). But when Jacob applied the FOIL principle and mulitiplied

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am struggling with this problem, Can someone please help? Megan factored the expression 28x^2-25x+3 as (7x-3)(4x-1). But when Jacob applied the FOIL principle and mulitiplied      Log On


   

Question 407811: I am struggling with this problem, Can someone please help?
Megan factored the expression 28x^2-25x+3 as (7x-3)(4x-1). But when Jacob applied the FOIL principle and mulitiplied out (7x-3)(4x-1), he got 28x^2-19x+3; thus, Megan's solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!



28x%5E2-25x%2B3 as %287x-3%29%284x-1%29...let' multiply this
%287x%2A4x%2B7x%2A%28-1%29-3%2A4x+-3%2A%28-1%29%29
28x%5E2+-7x+-12x+%2B3
28x%5E2+-19x+%2B3...........Jacob was right

28x%5E2-25x%2B3....here Megan needed to replace -25x with sum or difference of two numbers in order to group terms (she needed four terms in this expression)
she took -7x+-12x which makes -19x
she needed to replace -25x with a pair of numbers that add to -25
first of all she needed to multiply the leading coefficient 28 and the last term 3,-she would have 84
second of all she needed to list all of the possible factors of 84 and next
these factors pair up to multiply to 84 and see which of these pairs add to -25
1*84=84
2*42=84
3*28=84
4*21=84
6*14=84
7*12=84
(-1)*(-84)=84
(-2)*(-42)=84
(-3)*(-28)=84
(-4)*(-21)=84
(-6)*(-14)=84
(-7)*(-12)=84
We can see from the table that -4 and -21 add to -25; so, she needed them to use
let's try it:
28x%5E2-25x%2B3
28x%5E2+-4x+-21x%2B3...group terms
%2828x%5E2+-4x%29%2B%28+-21x%2B3%29
4x%287x+-1%29-3%287x-1%29...%287x-1%29 is a common term
%284x-3%29%287x-1%29.......this would be her correct solution