What are the factor of 80k^2_45
80k^2 - 45
= 5(16k^2 - 9), factoring out the GCF of the two terms, which is 5.
= 5(4k+3)(4k-3), since 16k^2 - 9 can be represented by the difference of two squares (4k)^2 - 3^2
What are the factor of 80k^2_45
80k^2 - 45
= 5(16k^2 - 9), factoring out the GCF of the two terms, which is 5.
= 5(4k+3)(4k-3), since 16k^2 - 9 can be represented by the difference of two squares (4k)^2 - 3^2
Not sure i'm reading this correctly, but assuming the expression is:
80K^{2} - 45 then use the quadratic formula to get the roots. (-b + sqrt(b^{2}-4ac)/2a = formula
where a,b,c are the coefficients of the first,second,third term.
NOTE: there is NO 'b' term, just a = 80 and c = 45
so we have 0 + sqrt(0^{2 }- 4(80)(-45)) all divided by 160
thus we have 0 + sqrt(1440) all divided by 160.
remember: the sqrt(1440) = sqrt(144) times sqrt(100), so we have 12 times 10
thus we have +(120)/160
Now we have TWO roots. .75 and -.75
so.......
the factors of the expression are (k+.75) and (k-.75)
there are other ways to do this as well by just factoring, but use of the quadratic is easier to see.
Comments
Stuart,
I agree that the solutions are .75 and -.75 if we were trying to solve an equation; however, this is an expression and the student is being asked to factor it. Robert is definitely correct. The answer is 5(4k +3)(4k - 3), because it is completely broken down to its smallest factors using only integers.
Sincerely,
Phillip H, NBCT