the value of f(5) is 10, which is option (b) ,  the value of f(-2) is -12, which is option (d).  To find the value of f(5) usingsynthetic substitution,we first set up the synthetic division table as follows:5 | 3  -9  -20|||___|   |   |We write the coefficients of the polynomial in the top row of the table and the root (in this case, 5) outside the division symbol. We then bring down the first coefficient (3) and multiply it by the root to get 15, which we write below thesecond coefficient(-9). We add 15 and -9 to get 6, which we then multiply by the root to get 30, which we write below the third coefficient (-20). We add 30 and -20 to get 10, which is the remainder. Therefore, the value of f(5) is 10, which is option (b).6) To find f(-2) using synthetic substitution, we set up the synthetic division table as follows:-2 | 1   0   8   24|_||||    |   |   |We write the coefficients of thepolynomialin the top row of the table and the root (in this case, -2) outside thedivision symbol.We then bring down the first coefficient (1) and multiply it by the root to get -2, which we write below the second coefficient (0). We add -2 and 0 to get -2, which we then multiply by the root to get 4, which we write below the third coefficient (8). We add 4 and 8 to get 12, which we then multiply by the root to get -24, which we write below the fourth coefficient (24). We add 12 and -24 to get -12, which is the remainder. Therefore, the value of f(-2) is -12, which is option (d).To know more aboutsynthetic substitution,click here:brainly.com/question/29253953#SPJ4...

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