How do you multiply #(5x^3-x^2+x-4) (x+1)#?

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Answer 1 · 2015-07-04T22:45:40

Use distributivity to find:

#(5x^3-x^2+x-4)(x+1) = 5x^4+4x^3-3x-4#

#(5x^3-x^2+x-4)(x+1)#

#=(5x^3-x^2+x-4)*x + (5x^3-x^2+x-4)*1#

#=5x^4-x^3+x^2-4x+5x^3-x^2+x-4#

#=5x^4-x^3+5x^3+x^2-x^2-4x+x-4#

#=5x^4+(-1+5)x^3+(1-1)x^2+(1-4)x-4#

#=5x^4+4x^3-3x-4#

Alternatively, look at each power of #x# in descending order and total up the relevant products of the coefficients:

#x^4# : #5*1 = 5#

#x^3# : #(5*1) + (-1*1) = 4#

#x^2# : #(-1*1) + (1*1) = 0#

#x# : #(1*1) + (-4*1) = -3#

#1#: #-4*1 = -4#

Hence: #5x^4+4x^3-3x-4#