Answer:
-4x2 + 3x - 225
———————————————
3
Step-by-step explanation:
Step 1 :
4
Simplify —
3
Equation at the end of step 1 :
4
(x - (— • x2)) - 75
3
Step 2 :
Equation at the end of step 2 :
4x2
(x - ———) - 75
3
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
x x • 3
x = — = —————
1 3
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:
x • 3 - (4x2) 3x - 4x2
————————————— = ————————
3 3
Equation at the end of step 3 :
(3x - 4x2)
—————————— - 75
3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
75 75 • 3
75 = —— = ——————
1 3
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
3x - 4x2 = -x • (4x - 3)
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
-x • (4x-3) - (75 • 3) -4x2 + 3x - 225
—————————————————————— = ———————————————
3 3
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-4x2 + 3x - 225 = -1 • (4x2 - 3x + 225)
Trying to factor by splitting the middle term
6.2 Factoring 4x2 - 3x + 225
The first term is, 4x2 its coefficient is 4 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is +225
Step-1 : Multiply the coefficient of the first term by the constant 4 • 225 = 900
Step-2 : Find two factors of 900 whose sum equals the coefficient of the middle term, which is -3 .
-900 + -1 = -901
-450 + -2 = -452
-300 + -3 = -303
-225 + -4 = -229
-180 + -5 = -185
-150 + -6 = -156
For tidiness, printing of 48 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-4x2 + 3x - 225
———————————————
3
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