Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? x(x2 + 4) + 5(x2 + 4) x2(x + 4) + 5(x + 4) x2(x + 5) + 4(x + 5) x(x2 + 5) + 4x(x2 + 5)

Answers

Answer 1

Answer:

x²(x + 4) + 5(x + 4)

Further explanation

Factoring (also called factorization) is the reserve operation of multiplication. When we factor (or factorize) a polynomial, we write it as a product of its factors.

Grouping is one of the factoring methods. Other methods such as isolating common factors and identities.

Steps for grouping:

We group the terms with a common factor.
We can isolate a common factor and put it outside the parentheses.

Let’s start.

$\boxed{ \ x^3 + 4x^2 + 5x + 20 = \ ? \ }$

$\boxed{ \ = (x^3 + 4x^2) + (5x + 20) \ }$

$\boxed{\boxed{ \ = x^2(x + 4) + 5(x + 4) \ }}$

We can also group the terms as follows.

$\boxed{ \ x^3 + 4x^2 + 5x + 20 = \ ? \ }$

$\boxed{ \ = (x^3 + 5x) + (4x^2 + 20) \ }$

$\boxed{\boxed{ \ = x(x^2 + 5) + 4(x^2 + 5) \ }}$

We will get the same results from the two ways above. Let's see.

First group, $\boxed{ \ x^2(x + 4) + 5(x + 4) \ } \rightarrow \boxed{ \ (x + 4) (x^2 + 5) \ }$
Second group, $\boxed{ \ x(x^2 + 5) + 4(x^2 + 5) \ } \rightarrow \boxed{ \ (x^2 + 5) (x + 4) \ }$

Thus the part which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping is $\boxed{\boxed{ \ x^2(x + 4) + 5(x + 4) \ }}$

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Keywords: which shows, one way, to determine, the factors of x³ + 4x² + 5x + 20, by grouping, common factor, polynomial, identities

Answer 2

Answer:

The correct option is $\fbox{\text{Option B}}$ that is ${x^2}\left( {x + 4} \right) + 5\left( {x + 4} \right)$ that shows one way to determine the factors of ${x^3} + 4{x^2} + 5x + 20$ .

Further explanation:

Factors are the numbers if we multiply them we get the original number.

Factorization is finding the numbers if we multiply them we get the original number.

Prime factorization is finding the numbers if we multiply them we get the original number.

Given:

The polynomial is ${x^3} + 4{x^2} + 5x + 20$ .

The options are,

A. $x\left( {{x^2} + 4} \right) + 5\left( {{x^2} + 4} \right)$ .

B. ${x^2}\left( {x + 4} \right) + 5\left( {x + 4} \right)$ .

C. ${x^2}\left( {x + 5} \right) + 5\left( {x + 5} \right)$ .

D. $x\left( {{x^2} + 5} \right) + 4x\left( {{x^2} + 5} \right)$

Explanation:

Consider the polynomial ${x^3} + 4{x^2} + 5x + 20$ as $P\left( x \right)$ .

Steps involve in finding the factors of ${x^3} + 4{x^2} + 5x + 20$ are as follows,

First we have to make the groups of the terms as,

$P\left( x \right) = \left( {{x^3} + 4{x^2}} \right) + \left( {5x + 20} \right)$

Now factorize the above 2 groups.

$\begin{gathered}P\left( x \right) = {x^2}\left( {x + 4} \right)+5\left( {{x^2}+4} \right)\n= \left( {{x^2}+5} \right)\left( {x+4} \right) \n\end{gathered}$

The factors of ${x^3} + 4{x^2} + 5x + 20\text{ } \text{are} \left( {{x^2} + 5} \right) \text{and} \left( {x + 4} \right)$ .

Option A is not correct as the first common factor is $x$ from group one but it not the highest common factor.

$\fbox{\text{Option B}}$ is correct as the factors are same as the factors of the polynomial.

Option C is not correct as the factors are not same as the factors of the polynomial.

Option D is not correct as the factors are not same as the factors of the polynomial.

Learn more:

1. Learn more about the polynomial brainly.com/question/12996944

2. Learn more about logarithm model brainly.com/question/13005829

3. Learn more about the product of binomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Polynomials

Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

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Answers

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Step-by-step explanation:

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True
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Answers

False because 3/4 is equal to .75 which is not equivalent to .34 . Hope that helps!

Answer: False

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Answers

Answers:

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b. f(0)=0

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f. x when f(x)=0 answer: 0

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But I hope this helps and answers your question :)

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Answers

mark me brainiest please :)

You can find the answer by subtracting the
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