Mathematics, 26.11.2019 07:31 ale3133

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)

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Answer from: smortandsons

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

Learn moreWhich expression is equivalent to the product of a binomial and a trinomial after it has been fully simplified The y-intercept of the quadratic function f(x) = (x – 6)(x – 2) Which is the graph of f(x) = (x - 1)(x + 4)

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

Answer from: Allahmere

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.

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

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 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

2. Learn more about logarithm model

3. Learn more about the product of binomial and trinomial

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.

Answer from: Quest

the balance is found at the link

step-by-step explanation:

Answer from: Quest

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

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