Chapter 9: Q80. (page 535)

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.
$4 x^{2} - 20 x + 25$

Short Answer

Expert verified

Yes, the factor of a given trinomial is $(2 x - 5) (2 x - 5)$ .

Step by step solution

Step 1. Check.

Check whether the given trinomial is a perfect square or not.

Here, the first term is $4 x^{2} = {(2 x)}^{2}$ .

Middle term is $20 x = 2 (2 x) (5)$ , which is in the form of $2 a b$ .

The last term is $25 = 5^{2}$ .

So, the given trinomial is a perfect square.

Step 2. Factor the trinomial.

Factor the perfect square trinomial.

$4 x^{2} - 10 x - 10 x + 25 = 2 x (x - 5) - 5 (2 x - 5)$

Step 3. Simplify.

Simplify the above-obtained expression.

$(2 x - 5) (2 x - 5)$

Therefore, the factor $4 x^{2} - 20 x + 25$ is $(2 x - 5) (2 x - 5)$ .

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Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.
$4 x^{2} - 20 x + 25$

Short Answer

Step by step solution

Step 1. Check.

Step 2. Factor the trinomial.

Step 3. Simplify.

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Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.4x2−20x+25

Short Answer

Step by step solution

Step 1. Check.

Step 2. Factor the trinomial.

Step 3. Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Calculus

Mechanics Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.
$4 x^{2} - 20 x + 25$