(x²+x-1)(x+2)+(-3)
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Answers
Answer:
step 1
((x2)-x)-(1/2)((x-3)+3x2))
Step 2
((x2) - x) - (1/2 • (3x2 + x - 3))
Step 3
Trying to factor by splitting the middle term
Factoring 3x2+x-3
The first term is, 3x2 its coefficient is 3 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 3 • -3 = -9
Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 1 .
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
Conclusion : Trinomial can not be factored
Equation at the end of step 3 :
(3x2 + x - 3)
((x2) - x) - —————————————
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 :
x2 - x (x2 - x) • 2
x2 - x = —————— = ————————————
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
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
x2 - x = x • (x - 1)
Adding fractions that have a common denominator :
5.2 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 • (x-1) • 2 - ((3x2+x-3)) -x2 - 3x + 3
2 2
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-x2 - 3x + 3 = -1 • (x2 + 3x - 3)
Trying to factor by splitting the middle term
6.2 Factoring x2 + 3x - 3
The first term is, x2 its coefficient is 1 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 3 .
-3 + 1 = -2
-1 + 3 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-x2 - 3x + 3
————————————
2