THE ANSWER IS
(x(3)+250x(2)+100x)/((1)/(2)x(2)+25x+9)
Final result :
2x • (x2 + 250x + 100) —————————————————————— x2 + 50x + 18
Step by step solution :
Step 1 :
1 Simplify — 2
Equation at the end of step 1 :
x)1 ————•x2)+25x)+9) (((2
Step 2 :
Equation at the end of step 2 :
)x2 ———+25x)+9) ((2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 2 as the denominator :
25x 25x • 2 25x = ——— = ——————— 1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x2 + 25x • 2 x2 + 50x ———————————— = ———————— 2 2
Equation at the end of step 3 :
(x2+50x) ————————+9) (2
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 2 as the denominator :
9 9 • 2 9 = — = ————— 1 2
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
x2 + 50x = x • (x + 50)
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
x • (x+50) + 9 • 2 x2 + 50x + 18 —————————————————— = ————————————— 2 2
Equation at the end of step 5 :
(x2+50x+18) ——————————— 2
Step 6 :
Equation at the end of step 6 :
(x2 + 50x + 18) ——————————————— 2
Step 7 :
x2+50x+18 Divide x3+250x2+100x by ————————— 2
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
x3 + 250x2 + 100x = x • (x2 + 250x + 100)
Trying to factor by splitting the middle term
8.2 Factoring x2 + 250x + 100
The first term is, x2 its coefficient is 1 .
The middle term is, +250x its coefficient is 250 .
The last term, "the constant", is +100
Step-1 : Multiply the coefficient of the first term by the constant 1 • 100 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is 250 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20
-5 + -20 = -25
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Trying to factor by splitting the middle term
8.3 Factoring x2+50x+18
The first term is, x2 its coefficient is 1 .
The middle term is, +50x its coefficient is 50 .
The last term, "the constant", is +18
Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18
Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is 50 .
-18 + -1 = -19
-9 + -2 = -11
-6 + -3 = -9
-3 + -6 = -9
-2 + -9 = -11
-1 + -18 = -19
1 + 18 = 19
2 + 9 = 11
3 + 6 = 9
6 + 3 = 9
9 + 2 = 11
18 + 1 = 19
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
2x • (x2 + 250x + 100) —————————————————————— x2 + 50x + 18
