Chapter 6: Q 6.45TI. (page 593)

Factor: $4 x^{2} + 12 x + 9$ .

Short Answer

Expert verified

The Factors of $4 x^{2} + 12 x + 9$ is ${(2 x + 3)}^{2}$ , that is $(2 x + 3) (2 x + 3)$ .

Step by step solution

Step 1. Given information.

Given an expression $4 x^{2} + 12 x + 9$ .

Step 2. Find if first and last term are perfect squares or not.

First term is $4 x^{2}$ which can be expressed as ${(2 x)}^{2}$ .

Last term is 9 which can be expressed as $3^{2}$ .

Consider $a = 2 x$ and $b = 3$ .

So, first and last term are perfect squares.

Step 3. Check if the middle term is of the form ±2ab.

Here, middle term is 12x which can be expressed as $2 \times 2 x \times 3$ .

It follows that middle term is of the form $2 a b$ .

Step 4. Write the square of the binomial.

So, $4 x^{2} + 12 x + 9$ is a perfect square trinomial of the form $a^{2} + 2 a b + b^{2}$ .

Note that ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ .

Therefore, $4 x^{2} + 12 x + 9 = {(2 x + 3)}^{2}$ .

Step 5. Check by multiplying.

Verification can be obtained as follows.

$\begin{array}{rcl} {(2 x + 3)}^{2} & = & {(2 x)}^{2} + 2 \times 2 x \times 3 + 3^{2} \\ = & 4 x^{2} + 12 x + 9 \end{array}$

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Factor: $4 x^{2} + 12 x + 9$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if first and last term are perfect squares or not.

Step 3. Check if the middle term is of the form ±2ab.

Step 4. Write the square of the binomial.

Step 5. Check by multiplying.

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Factor:4x2+12x+9.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if first and last term are perfect squares or not.

Step 3. Check if the middle term is of the form ±2ab.

Step 4. Write the square of the binomial.

Step 5. Check by multiplying.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Pure Maths

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Factor: $4 x^{2} + 12 x + 9$ .