Question

fixt 3x3 + 5x2 - 16x - 2​

Answer 1

The factor of 3x3 + 5x2 - 16x - 2 is (3x + 2) • (x + 3) • (x - 2)

Explanation:

What is the factor of 3x3 + 5x2 - 16x - 12​

Solution:

= [3 • (x^3) +  5x^2) -  16x] -  12

= x^2 ( 3x - 5x) - ( 16 x + 12)

= x^2 ( 3x - 5x ) - 2 ( 8x + 6 )

= (x^2 - 2)  ( 3x - 5x ) (8x + 6 )

Or

= [3 • (x^3) +  5x^2) -  16x] -  12

= [(3x^3 +  5x^2) -  16 x] -  12

= [(3x^3 +  5x^2) -  16x] -  12  ( It is not a perfect cube)

= (3x + 2) • (x + 3) • (x - 2)

Answer 2

Given:

$\bold{3x^3 + 5x^2 - 16x - 12}$

To find:

Factor=?

Solution:

In the given question there is some mistyping error so the correct equation can be described as follows:

$\Rightarrow 3x^3 + 5x^2 - 16x - 12$

factor the above equation:

by hit and trail method we put the value  2 in the x so, wet get the value that is equal to: 0

$f(x)= 3x^3 + 5x^2 - 16x - 12\\\\x= 2\\\\f(2)=3 \times 2^3+5\times2^2-16 \times 2 -12\\\\f(2)=3 \times 8+5\times4-16 \times 2 -12\\\\f(2)= 24+20-32-12\\\\f(2)= 44-44\\\\f(2)=0$

$(x-2)$ is one factor of the equation and we divide the value by $(x-2)$ so it will give another fraction value and to factor that value we get the value that is: $(x+3)(3x+2)$

The final answer to this equation is: $(x-2) (x+3)(3x+2)$