Question

Factor completely: 2x3 + 14x2 + 6x + 42

Answer 1

Answer:

$2\cdot{(x+1)\cdot{(x^2+3)}$

Step-by-step explanation:

We can take out 2 to as this is common in each term:

$2\cdot{x^3}+14\cdot{x^2}+6\cdot{x}+42$

$2\cdot{(x^3+7\cdot{x^2}+3\cdot{x}+21)}$

We can see that the use factors of 21 which are 1, 3, 7 and 21 (all ± values). We can use -7 and the coefficients of the simplified expression to determine if one of the values is zero when -7 is multiplied and added to the coefficients:

-7] 1  7   3   21

Bring down 1

-7] 1  7   3   21

____-7_ 0_-21____

    1  0   3    0

We can see that the factor of -7 yields two zeros, but the final answer is zero and therefore we can use 7 factor and the answers it yielded:

We can simplify the expression using 1, 0 and 3.

$2\cdot{(x+7)\cdot{(x^2+0\cdot{x}+3)}$

$2\cdot{(x+7)\cdot{(x^2+3)}$

Answer 2

To factor all you do is...
Factor 2x3+14x2+6x+422x3+14x2+6x+42=2(x+7)(x2+3)Answer:2(x+7)(x2+3)