Question

If a polynomial has four terms, 3x3 + 5x + 6x2 + 10, which factoring method can be considered?

Answer 1

Hello,

1) order the terms:

3x^3+6x^2+5x+10

2) method: grouping 2 to 2 the terms:

=(3x^3+6x^2)+(5x+10)
=3x^2(x+2)+5(x+2)=(x+2)(3x^2+5)

Answer 2

Answer:

We can factorize the polynomial using method of grouping terms.

Step-by-step explanation:

Consider the given polynomial $3x^3 + 5x + 6x^2 + 10$

We have to find the factoring method that can be considered to solve the given polynomial.

Consider the given polynomial $3x^3 + 5x + 6x^2 + 10$

Since, the polynomial involves 4 terms,

So we can factorize the polynomial using grouping terms,

First rearranging in standard form in decreasing order of degrees of x.

$3x^3  + 6x^2 + 5x + 10$

Grouping two terms together, we get,

$=\left(3x^3+6x^2\right)+\left(5x+10\right)$

Now taking $3x^2$ common from first two and 5 from last two , we have,

$=3x^2\left(x+2\right)+5\left(x+2\right)$

Now, taking (x+2) common, we have,

$=\left(x+2\right)\left(3x^2+5\right)$

$3x^3 + 5x + 6x^2 + 10=\left(x+2\right)\left(3x^2+5\right)$

Thus, We can factorize the polynomial using method of grouping terms.