Synethetic substitution is the process of using synthetic division to find g(x). To find g(-3), use synthetic division with a divisor of -3. The remainder equals g(-3)
Use the coefficients of the polynomial as the dividend. Note that the x^2 term has a coefficient of zero.
g(x)=color(red)1x^3+color(red)0x^2color(red)(-8)x+color(red)6
-3| color(red)1color(white)(aaaa)color(red)0color(white)(aa)color(red)(-8)color(white)(aaa)color(red)6
color(white)(aaa^2)darrcolor(white)(aaaaaaaaaaaaaaaa)Pull down the color(red)1
color(white)(aaa^2a)color(magenta)1
-3| color(red)1color(white)(aaaa)color(red)0color(white)(aa)color(red)(-8)color(white)(aaa)color(red)6
color(white)(aaa^2)darrcolor(white)(a^2)color(blue)(-3)color(white)(aaaaaaaaaa) Multiply -3 * color(magenta)1=color(blue)(-3)
color(white)(aaaa^2color(magenta)1color(white)(aa)color(magenta)(-3)color(white)(aaaaaaaaaaa)Add color(red)0 +color(blue)(-3) =color(magenta)(-3)
Repeat the process of multiplying by -3 and adding to the coefficient.
-3| color(red)1color(white)(aaaa)color(red)0color(white)(aa)color(red)(-8)color(white)(aaa)color(red)6
color(white)(aaa^2)darrcolor(white)(a^2)color(blue)(-3)color(white)(aaa)color(blue)9color(white)(aa)color(blue)(-3)
color(white)(aaaa^2color(magenta)1color(white)(aa)color(magenta)(-3)color(white)(aaa)color(magenta)1color(white)(aa)aacolor(orange)3
The remainder color(orange)3= g(-3)
