Respuesta :

znk

Answer:

3(x + 5)(x+ 5)  

Step-by-step explanation:

3x² + 30x + 75

Here's one way to do it.

Step 1. Factor out the highest common factor of all three terms.

You can factor out a 3.

3(x² +10x +25) = 0

Step 2. Factor the remaining polynomial

We must find two numbers whose product is 25 and whose sum is 10.

A little trial-and-error gives us 5 and 5.  

5 × 5 = 25; 5 + 5 = 10

We can factor the expression as

3(x + 5)(x + 5)

MrRoyal

To factorize a polynomial implies that, we want to get several algebraic expressions from the polynomial.

When [tex]3x^2 +30x + 75[/tex] is factored, the result is: [tex]3(x + 5)(x + 5)[/tex]

Given

[tex]3x^2 +30x + 75[/tex]

Factor out 3

[tex]3x^2 +30x + 75 = 3 \times (x^2 + 10x + 25)[/tex]

Expand the bracket

[tex]3x^2 +30x + 75 = 3 \times (x^2 + 5x + 5x + 25)[/tex]

Factorize

[tex]3x^2 +30x + 75 = 3 \times (x(x + 5) + 5(x + 5))[/tex]

Factor out x + 5

[tex]3x^2 +30x + 75 = 3 \times ((x + 5)(x + 5))[/tex]

So, we have:

[tex]3x^2 +30x + 75 = 3(x + 5)(x + 5)[/tex]

Hence, the factors of [tex]3x^2 +30x + 75[/tex] are 3 and (x + 5)

Read more about factors of polynomials at:

https://brainly.com/question/16865029

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