Polynomials
Math ⇒ Algebra
Polynomials starts at 7 and continues till grade 12.
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See sample questions for grade 12
Describe the process of synthetic division for dividing polynomials.
Divide the polynomial x3 + 2x2 - 5x + 6 by (x - 1) and state the remainder.
Explain why x-2 + 3 is not a polynomial.
Find the sum of the roots of the polynomial 2x2 - 5x + 3.
Find the value of k so that x2 + kx + 9 has equal roots.
Given the polynomial f(x) = x3 - 6x2 + 11x - 6, find all its integer roots.
If the product of the roots of a quadratic polynomial ax2 + bx + c is 6 and a = 2, c = 12, what is the value of b?
If the remainder when f(x) is divided by (x - 1) is 5, and the remainder when f(x) is divided by (x - 2) is 3, what is the remainder when f(x) is divided by (x - 1)(x - 2)?
If a polynomial has a double root at x = 2, which of the following is true?
(1) (x - 2) is a factor
(2) (x - 2)2 is a factor
(3) (x - 2)3 is a factor
(4) (x + 2) is a factor
Which of the following is a monic polynomial?
(1) x2 + 3x + 2
(2) 2x2 - x + 1
(3) 5x3 + 2x
(4) 4x - 7
Which of the following is a polynomial?
(1) 3x2 + 2x - 5
(2) 2/x + 1
(3) √x + 4
(4) x3 - 7x + 6
Which of the following is a zero polynomial?
(1) 0
(2) x
(3) x2
(4) 1
A polynomial of degree 3 is called a _______.
Fill in the blank: The graph of a quadratic polynomial is a _______.
The degree of the polynomial 5x4 - 3x2 + 7x - 2 is _______.
The zeros of the polynomial x2 - 5x + 6 are _______ and _______.
True or False: Every polynomial equation of degree n has exactly n real roots.
True or False: The product of two polynomials is always a polynomial.
True or False: The set of all polynomials forms a vector space over the field of real numbers.
True or False: The sum of two polynomials is always a polynomial.
