Answer:
-17x2 - 14x + 10
————————————————
2
Explanation:
STEP
1
:
25
Simplify ——
2
Equation at the end of step
1
:
25
(((4•(x2))-(——•x2))-7x)+5
2
STEP
2
:
Equation at the end of step 2
25x2
(((4 • (x2)) - ————) - 7x) + 5
2
STEP
3
:
Equation at the end of step
3
:
25x2
((22x2 - ————) - 7x) + 5
2
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
22x2 22x2 • 2
22x2 = ———— = ————————
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 :
4.2 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:
22x2 • 2 - (25x2) -17x2
————————————————— = —————
2 2
Equation at the end of step
4
:
-17x2
(————— - 7x) + 5
2
STEP
5
:
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
7x 7x • 2
7x = —— = ——————
1 2
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
-17x2 - (7x • 2) -17x2 - 14x
———————————————— = ———————————
2 2
Equation at the end of step
5
:
(-17x2 - 14x)
————————————— + 5
2
STEP
6
:
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 2 as the denominator :
5 5 • 2
5 = — = —————
1 2
STEP
7
:
Pulling out like terms :
7.1 Pull out like factors :
-17x2 - 14x = -x • (17x + 14)
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
-x • (17x+14) + 5 • 2 -17x2 - 14x + 10
————————————————————— = ————————————————
2 2
STEP
8
:
Pulling out like terms :
8.1 Pull out like factors :
-17x2 - 14x + 10 = -1 • (17x2 + 14x - 10)
Trying to factor by splitting the middle term
8.2 Factoring 17x2 + 14x - 10
The first term is, 17x2 its coefficient is 17 .
The middle term is, +14x its coefficient is 14 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 17 • -10 = -170
Step-2 : Find two factors of -170 whose sum equals the coefficient of the middle term, which is 14 .
-170 + 1 = -169
-85 + 2 = -83
-34 + 5 = -29
-17 + 10 = -7
-10 + 17 = 7
-5 + 34 = 29
-2 + 85 = 83
-1 + 170 = 169
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-17x2 - 14x + 10
————————————————
2