5x³+8x²-7x-6 1.explain why the binomial (x + 2) is a factor of this polynomial expression. 2.explain why the binomial (x + 1) is not a factor of this polynomial expression.

Step-by-step explanation:

Whether we divide using long division or using synthetic division, the rule is the same:  If, after division, there is no remainder (i. e., the remainder is zero), the divisor binomial is a factor or the associated root is indeed a root/zero/solution.

Divide 5x³+8x²-7x-6 by (x+2) using synthetic division.  Use the divisor -2 (which comes from letting x+2 = 0):

-2   /    5    8    -7    -6

                -10    4     6

          5      -2    -3    0          Since the remainder here is 0, we know that

                                               -2 is a root of 5x³+8x²-7x-6 and that (x+2) is

                                                a factor of 5x³+8x²-7x-6.

Now check out the possibility that (x+1) is a factor of  5x^3 + 8x^2 - 7x - 6:

Use -1 as the divisor in synthetic division:    

-1   /    5    8    -7    -6

                -5   -3     10

          5      3   -10    4        

Since there is a non-zero remainder (4), we can conclude that (x + 1) is NOT a factor of the given polynomial expression.  

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