Understanding zeroes and factors of polynomials

If the binomial (x -7) is a factor of the polynomial function f(x), which statement must be true?

• f(7) = -7
• f(7) = 0
• f(-7) = 0
• f(-7) = -7

      Is  $(x-2)$  a factor of  $f(x)=x^3-8x^2+14x-4?$  

• 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. 

If (x+2) is a factor of f(x), then which statement BEST represents f(x)?

• x=-2 is a zero of f(x)

• x=-2 is not a zero of f(x)

• x=2 is a zero of f(x)

• x=2 is not a zero of f(x)

In the equation
 (x + 2)(x - 3) = 0, the binomials are called...?

• Factors
• Products
• Multiples
• Zeros

Determine if  $\left(x-1\right)$   is a factor of  $5x^4-2x^3+3x-6$  .

• Yes

• No

What is b so that x - 3 is a factor of $x^4-2x^3+x^2-bx-12$  ?

b = _____

If $\alpha,\ \beta\$ and  $\gamma$ are zeroes of the polynomial  $2x^3+x^2-13x+6$ , then evaluate  $\left(\alpha\beta+\beta\gamma+\gamma\alpha\right)$ .

• 13

• -13

•  $\frac{13}{2}$  

•  $\frac{-13}{2}$  

What is the factor theorem?

• The factor theorem states that a polynomial f(x) has a factor (x + a) if and only if f(a) = 0.

• The factor theorem states that a polynomial f(x) has a factor (x - a) if and only if f(a) = 0.

• The factor theorem states that a polynomial f(x) has a factor (x + a) if and only if f(a) = 1.

• The factor theorem states that a polynomial f(x) has a factor (x - a) if and only if f(a) = 1.

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.

Find all the factors of x³ - 3x² - 4x + 12 given that -2 is a zero.

• (x-2) (x+2) (x+3)

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)