Question 1:
\[ \text{If } P(x) = x^3 – 4x^2 + 3x + 5, \text{ what is } P(2)? \] \[ \text{(a) } 1, \quad \text{(b) } 3, \quad \text{(c) } 5, \quad \text{(d) } 7 \] Answer: C
Question 2:
\[ \text{Which of the following is a polynomial?} \] \[ \text{(a) } x^2 + \frac{1}{x}, \quad \text{(b) } 3x^4 + 2x – 7, \quad \text{(c) } \sqrt{x} + 5, \quad \text{(d) } x^{-3} + x \] Answer: B
Question 3:
\[ \text{If } x-2 \text{ is a factor of } P(x) = x^3 – 5x^2 + ax + 10, \text{ find } a. \] \[ \text{(a) } 3, \quad \text{(b) } 5, \quad \text{(c) } 7, \quad \text{(d) } 9 \] Answer: A
Question 4:
\[ \text{The degree of the polynomial } 7x^5 – 3x^3 + 2x^8 + 4 \text{ is:} \] \[ \text{(a) } 3, \quad \text{(b) } 5, \quad \text{(c) } 8, \quad \text{(d) } 4 \] Answer: C
Question 5:
\[ \text{What is the remainder when } x^4 + 3x^3 – 2x + 7 \text{ is divided by } x – 1? \] \[ \text{(a) } 7, \quad \text{(b) } 9, \quad \text{(c) } 6, \quad \text{(d) } 5 \] Answer: A
Question 6:
\[ \text{Which polynomial identity represents } (a+b)^3? \] \[ \text{(a) } a^3 + 3a^2b + 3ab^2 + b^3, \quad \text{(b) } a^3 – b^3, \] \[ \text{(c) } (a+b)(a-b), \quad \text{(d) } a^3 – 3a^2b + 3ab^2 – b^3 \] Answer: A
Question 7:
\[ \text{Which of the following is a monomial?} \] \[ \text{(a) } x^2 + 2x, \quad \text{(b) } 4x^3, \quad \text{(c) } 3x^2 + 5x + 7, \quad \text{(d) } x – 1 \] Answer: B
Question 8:
\[ \text{If } P(x) = x^3 + ax^2 + bx + 6 \text{ has roots } 1, 2, 3, \text{ find } a + b. \] \[ \text{(a) } -5, \quad \text{(b) } -6, \quad \text{(c) } -7, \quad \text{(d) } -8 \] Answer: B
Question 9:
\[ \text{If } P(x) = x^3 – 2x + 5, \text{ then the coefficient of } x \text{ is:} \] \[ \text{(a) } -2, \quad \text{(b) } 3, \quad \text{(c) } 5, \quad \text{(d) } 1 \] Answer: A
Question 10:
\[ \text{If } P(x) = x^4 – 3x^3 + 2x^2 – 4x + 7, \text{ then the leading coefficient is:} \] \[ \text{(a) } -3, \quad \text{(b) } 2, \quad \text{(c) } 1, \quad \text{(d) } 4 \] Answer: C
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