Exercises
Challenge your understanding of polynomials and factoring with this knowledge test. Practice identifying the degree of a polynomial, finding factors, expanding binomials, evaluating polynomial functions, and solving for roots and zeros. You will also work with difference of squares, perfect-square trinomials, quadratic factoring, and simplifying expressions such as squared binomials. Whether you are reviewing algebra fundamentals or preparing for a math assessment, this quiz offers a focused way to check your skills and build confidence with polynomial operations.
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The degree of a polynomial is the highest power of the variable in the expression. In the given polynomial, 4x^3, the highest power is 3.
The polynomial x^2 - 5x + 6 can be factored as (x-2)(x-3). Thus, x-2 is a factor of the polynomial.
Utilizing the distributive property, multiply 2x with both x and -2, and do the same for 3. The result is 2x^2 - 4x + 3x - 6, which simplifies to 2x^2 - x - 6.
Substituting -2 into the function, we have f(-2) = (-2)^2 + 4(-2) + 4 = 4 - 8 + 4 = 0.
The polynomial factors as (x-3)(x+1), yielding roots at x = 3 and x = -1.
Using the difference of squares formula, the product is x^2 - 1.
The polynomial can be expressed as (x+3)(x+4) since the factors of 12 that sum to 7 are 3 and 4.
Using the difference of squares formula, the product is 9x^2 - 16.
The polynomial x^2 - 9 can be factored as (x-3)(x+3), resulting in zeros at x = 3 and x = -3.
Using the square of a binomial formula, expand the expression to x^2 - 4x + 4.
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