
Concept explainers
To calculate: The simplified form of (x4+5x3+3x2−8x+3)÷(x+3) ,

Answer to Problem 5PT
The simplified form of (x4+5x3+3x2−8x+3)÷(x+3) is x3+2x2−3x+1 .
Explanation of Solution
Given information:
The statement “ (x4+5x3+3x2−8x+3)÷(x+3) .”
Formula used:
When a polynomial is divided by its factor then dividend is the product of divisor and quotient increased by remainder.
Consider the provided statement “ (x4+5x3+3x2−8x+3)÷(x+3) .”
Recall that When a polynomial is divided by its factor then dividend is the product of divisor and quotient increased by remainder.
Apply the method of long division. First multiply the expression x+3 by x3 .subtract it from the dividend. Next multiply x+3 by 2x2 subtract the expression obtained. Next multiply x+3 by −3x subtract the expression from the dividend. Next multiply x+3 by 1 subtract the expression obtained
So, the given expression can be simplified as,
(x4+5x3+3x2−8x+3)÷(x+3)
Observe to solve the expression first open the brackets.
x+3x3+2x2−3x+1x4+5x3+3x2−8x+3x4+3x3 2x3+3x22x3+6x2 −3x2−8x3x2+9x x+3−x−3 0
Now since, Dividend=Quotent×Divisor+Remainder . Here, dividend is x4+5x3+3x2−8x+3 and quotient is x3+2x2−3x+1 , divisor is x+3 .
Therefore, x4+5x3+3x2−8x+3=(x+3)(x3+2x2−3x+1)+0 .
Since, the quotient is x3+2x2−3x+1 cannot be simplified further,
Thus, the simplified form of (x4+5x3+3x2−8x+3)÷(x+3) is (x+3)(x3+2x2−3x+1)+0 .
Chapter 6 Solutions
Algebra 2
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