If x+2 is a factor of f(x)=2x^3-3x^2-4x+a , find the value of a?

Feb 28, 2018

$a = 20$

Explanation:

Use the Synthetic division method;

Write down the coefficient numbers in the first row in order of highest to lowest power and the factor.

$x + 2 \left(x - m\right) m = - 2$

Drag the first coefficient number down, $2 \times \left(- 2\right) = - 4$, write $- 4$ under the next coefficient number, $- 3 + \left(- 4\right) = - 7$, $\left(- 2\right) \times \left(- 7\right) = 14$, repeat...

We want the denominator to be zero, so

$a + \left(- 20\right) = 0$

$a = 20$

Feb 28, 2018

$a = 20$

Explanation:

$\text{given "x+2" is a factor then "x=-2" is a zero}$

$\Rightarrow f \left(- 2\right) = 2 {\left(- 2\right)}^{3} - 3 {\left(- 2\right)}^{2} - 4 \left(- 2\right) + a = 0$

$\Rightarrow - 16 - 12 + 8 + a = 0$

$\Rightarrow a = 20$