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)   (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)   (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



Does that work?

 

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
 You can avoid the fraction this way:







Now collect like terms





Now substitute 





Hope I got it 

Answer by Theo(13342)   (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) 



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.





 

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