SOLUTION: Can you help me figure (x-1/2)(4x^3-2x^2+5x-6) Where 1/2 is a fraction. I can solve this without the fraction, but can you help me to solve when there is a fraction involved.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you help me figure (x-1/2)(4x^3-2x^2+5x-6) Where 1/2 is a fraction. I can solve this without the fraction, but can you help me to solve when there is a fraction involved.      Log On


   

Question 629303: Can you help me figure
(x-1/2)(4x^3-2x^2+5x-6)
Where 1/2 is a fraction. I can solve this without the fraction, but can you help me to solve when there is a fraction involved.
Found 5 solutions by ewatrrr, richwmiller, Alan3354, josmiceli, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

(x-1/2)(4x^3-2x^2+5x-6)   || Technique is the same

 x(4x^3-2x^2+5x-6) + -1/2(4x^3-2x^2+5x-6)

  4x^4 - 2x^3 + 5x^2 - 6x - 2x^3 + x^2 - 5/2x + 3  ||combine Like Terms

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
multiply (4x^3-2x^2+5x-6) by x
multiply (4x^3-2x^2+5x-6) by 1/2
add the two results together
4x^4-4x^3+6x^2-(17x)/2+3
If you don't like fractions, you can turn it into a decimal .5
(x-.5)(4x^3-2x^2+5x-6)
multiply (4x^3-2x^2+5x-6) by x
multiply (4x^3-2x^2+5x-6) by .5
add the two results together
4x^4-4x^3+6x^2-8.5x+3.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Can you help me figure
(x-1/2)(4x^3-2x^2+5x-6)
Where 1/2 is a fraction. I can solve this without the fraction, but can you help me to solve when there is a fraction involved.
--------------
Make it
%282x-1%29%284x%5E3-2x%5E2%2B5x-6%29%2F2
Does that work?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can avoid the fraction this way:
+a+=+1%2F2+
+%28+x+-+a+%29%2A%28+4x%5E3+-+2x%5E2+%2B+5x+-+6+%29+
+4x%5E4+-+2x%5E3+%2B+5x%5E2+-+6x+-+4%2Aa%2Ax%5E3+%2B+2%2Aa%2Ax%5E2+-+5%2Aa%2Ax+%2B+6a+
Now collect like terms
+4x%5E4+-+2x%5E3+-+4%2Aa%2Ax%5E3+%2B+5x%5E2+%2B+2%2Aa%2Ax%5E2+-+6x+-+5%2Aa%2Ax+%2B+6a+

Now substitute +a+=+1%2F2+

+4x%5E4+-+4x%5E3+%2B+6x%5E2+-+%2817%2F2%29%2Ax+%2B+3+
Hope I got it

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your expression is:
(x-1/2)(4x^3-2x^2+5x-6)
you use the distributive law of multiplication.
that law is:
(a + b ) * (c + d + e) equals:
a * (c + d + e) plus:
b * (c + d + e)
you use the distributive law of multiplication again to get:
a * (c + d + e) equals:
a*c + a*d + a*e
and:
b * (c + d + e) equals:
b*c + b*d + b*e.
put them together and you get:
(a + b) * (c + d + e) equals:
a*c + a*d + a*e + b*c + b*d + b*e
we can apply this to your expression of:
(x-1/2)(4x^3-2x^2+5x-6)
using the distributive law of multiplication, this becomes:
x*(4x^3-2x^2+5x-6) - (1/2)(4x^3-2x^2+5x-6)
using the distributive law of multiplication again, this becomes:
x*4x^3 - x*2x^2 + x*5x - x*6 - (1/2)*4x^3 + (1/2)*2x^2 - (1/2)*5x + (1/2)*6
simplifying each term gets you:
4x^4 - 2x^3 + 5x^2 - 6x -2x^3 + x^2 - (5/2)x + 3
you now want to combine like terms if there are any.
-2x^3 and -2x^3 combine into -4x^3
5x^2 and x^2 combine into 6x^2
-6x and -(5/2)x combine into (-17/2)x
putting all the combined terms together, you get:
4x^4 - 4x^3 + 6x^2 - (17/2)x + 3
that's your final expression.
i was able to confirm graphically that this expression and the starting expression are the same.
here's a graph of your starting expression of:
(x-1/2)(4x^3-2x^2+5x-6)
graph%28600%2C600%2C-10%2C10%2C-50%2C50%2C%28x-1%2F2%29%284x%5E3-2x%5E2%2B5x-6%29%29
here's a graph of your final expression of:
4x^4 - 4x^3 + 6x^2 - (17/2)x + 3

here's both expressions superimposed on the same graph:

since they superimpose on each other perfectly so that they look like one expression, they are identical to each other.
this confirms the solution is correct.