Chapter 11: Q. 3 (page 764)

Factor completely: $3 x^{4} + 6 x^{3} + 3 x^{2}$

Short Answer

Expert verified

The factors in the given expression is $3 x^{2} (x + 1)^{2}$

Step by step solution

Step 1. Check for a common factor

The given expression is $3 x^{4} + 6 x^{3} + 3 x^{2}$

Here we can see that the expression has a common factor, $3 x^{2}$ .

That is

$3 x^{4} + 6 x^{3} + 3 x^{2} = 3 x^{2} (x^{2} + 2 x + 1)$

Step 2. Write as a perfect square

Here, in the trinomial $x^{2} + 2 x + 1$ , the first term $x^{2}$ and the third term localid="1647515831673" $1 = 1^{2}$ are perfect squares. The middle term is twice the product of localid="1647515850045" $x$ and 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" $3 x^{4} + 6 x^{3} + 3 x^{2} = 3 x^{2} (x + 1)^{2}$

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Factor completely: $3 x^{4} + 6 x^{3} + 3 x^{2}$

Short Answer

Step by step solution

Step 1. Check for a common factor

Step 2. Write as a perfect square

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Factor completely:3x4+6x3+3x2

Short Answer

Step by step solution

Step 1. Check for a common factor

Step 2. Write as a perfect square

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor completely: $3 x^{4} + 6 x^{3} + 3 x^{2}$