Synthetic Division, Remainder Theorem and Factor Theorem

When setting up this problem using synthetic division, what numbers should fill in the squares?

• -1, 3, 15, -19, -30

• 1, -3, -15, 19, 30

• 1, 3, -15, 19, 30

• 1, -3, 15, -19, 30

Use synthetic division to determine whether the first polynomial is a factor of the second. (katex latex="(x-5),(x^5-3x^4-13x^3+19x^2-17x+15)") ​ (a)   the binomial ​ (b)   a factor of the polynomial, because ​ (c)  

• No

• is not

• Yes

• is

Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is  not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is  not a factor. There is a remainder. 

• No

• is not

• Yes

• is

Divide by using synthetic division

When setting this problem up using synthetic division, what order of numbers should fill in the squares?

• 1, 6, 9, -3

• -1, 0, -6, 0, -9, 3

• -1, -6, -9, 3

• 1, 0, 6, 0, 9, -3

• 0

• -8

• -28

• 26