My question is Simplify (8x²+3x-4) (5x+4) -2x(3x²+5x
Answers
Answer:
x3+8x2+24x+45/x4+3x3-27x-81
Final result :
4x7 + 8x6 - 3x5 - 81x4 + 45
———————————————————————————
x4
Step by step solution :
Step 1 :
Equation at the end of step 1 :
45
((((((x3)+(8•(x2)))+24x)+————)+3x3)-27x)-81
(x4)
Step 2 :
45
Simplify ——
x4
Equation at the end of step 2 :
45
((((((x3)+(8•(x2)))+24x)+——)+3x3)-27x)-81
x4
Step 3 :
Equation at the end of step 3 :
45
((((((x3)+23x2)+24x)+——)+3x3)-27x)-81
x4
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using x4 as the denominator :
x3 + 8x2 + 24x (x3 + 8x2 + 24x) • x4
x3 + 8x2 + 24x = —————————————— = —————————————————————
1 x4
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 :
x3 + 8x2 + 24x = x • (x2 + 8x + 24)
Trying to factor by splitting the middle term
5.2 Factoring x2 + 8x + 24
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 1 • 24 = 24
Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is 8 .
-24 + -1 = -25
-12 + -2 = -14
-8 + -3 = -11
-6 + -4 = -10
-4 + -6 = -10
-3 + -8 = -11
-2 + -12 = -14
-1 + -24 = -25
1 + 24 = 25
2 + 12 = 14
3 + 8 = 11
4 + 6 = 10
6 + 4 = 10
8 + 3 = 11
12 + 2 = 14
24 + 1 = 25
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
5.3 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 • (x2+8x+24) • x4 + 45 x7 + 8x6 + 24x5 + 45
———————————————————————— = ————————————————————
x4 x4
Equation at the end of step 5 :
(x7 + 8x6 + 24x5 + 45)
((—————————————————————— + 3x3) - 27x) - 81
x4
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x4 as the denominator :
3x3 3x3 • x4
3x3 = ——— = ————————
1 x4
Checking for a perfect cube :
6.2 x7 + 8x6 + 24x5 + 45 is not a perfect cube
Trying to factor by pulling out :
6.3 Factoring: x7 + 8x6 + 24x5 + 45
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x7 + 45
Group 2: 8x6 + 24x5
Pull out from each group separately :
Group 1: (x7 + 45) • (1)
Group 2: (x + 3) • (8x5)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.