Question

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)

Answer 1

The correct answer is x2(x+4) + 5(x+4)
That is the second choice.

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Answer 2

Answer:

Option (b) is correct

The factored form of polynomial $x^3+4x^2+5x+20$ by grouping terms is $x^2(x+4)+5(x+4)$

Step-by-step explanation:

Given  polynomial  $x^3+4x^2+5x+20$

We have to determine the factor of given polynomial using grouping.

Grouping is done by taking greatest common factor common  from different terms.

Consider the given polynomial $x^3+4x^2+5x+20$

Here, we can take $x^2$ common from first two terms and 5 common from last two terms, we get,

$x^3+4x^2+5x+20$

$\Rightarrow x^2(x+4)+5(x+4)$

$\Rightarrow (x^2+5)(x+4)$

Thus, the factored form of polynomial $x^3+4x^2+5x+20$ by grouping terms is $x^2(x+4)+5(x+4)$

Thus, Option (b) is correct.