We are given polynomial: [tex]5x^3+8x^2-7x-6[/tex].
We need to explain why the binomial (x + 2) IS a factor of this polynomial expression and why the binomial (x + 1) IS NOT a factor of this polynomial expression.
Let us set first factor equal to 0 and solve for x.
x+2=0
x=-2.
Plugging x=-2 in given polynomial, we get
[tex]5(-2)^3+8(-2)^2-7(-2)-6 = 5(-8) +8(4)+14-6[/tex]
[tex]= -40 +32+14-6[/tex]
[tex]=0[/tex]
Because x=-2 gives 0 on plugging in given polynomial, so it's factor of given polynomial expression.
Now, let us check second factor x+1=0
x=-1.
Plugging x=-1 in given polynomial, we get
[tex]5(-1)^3+8(-1)^2-7(-1)-6 = 5(-1) +8(1)+7-6[/tex]
=-5+8+7-6.
= -4.
Because x=-1 doesn't gives 0 on plugging in given polynomial, so it's not a factor of given polynomial expression.
