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Chapter 11: Q. 3 (page 764)

Factor completely:3x4+6x3+3x2

Short Answer

Expert verified

The factors in the given expression is3x2(x+1)2

Step by step solution

01

Step 1. Check for a common factor

The given expression is3x4+6x3+3x2

Here we can see that the expression has a common factor, 3x2.

That is

3x4+6x3+3x2=3x2x2+2x+1

02

Step 2. Write as a perfect square

Here, in the trinomial x2+2x+1, the first term x2and the third term localid="1647515831673" 1=12are perfect squares. The middle term is twice the product of localid="1647515850045" xand localid="1647515868323" 1,

Therefore, we have a perfect square.

Factoring the perfect square, we get the expression localid="1647515891415" (x+1)2

Hence,localid="1647515879792" 3x4+6x3+3x2=3x2(x+1)2

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Most popular questions from this chapter

Solve each system of equations. If the system has no solution, say that it is inconsistent.
x+3y=52x-3y=-8

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

y=x-1;y=x2-6x+9

solve each system of equations. If the system has no solution, say that it is inconsistent

x + 4y - 3z = -8

3x - y + 3z = 12

x + y + 6z = 1

In Problems 35鈥�42, graph each system of inequalities by hand.

x2+y2鈮�9x+y鈮�3

In Problems, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

x5+x4-x2+2x4-2x2+1
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