Factor the polynomial: $$x^3 - 4x^2 - 2x + 8$$

The factored form is: $$ (x - 4)(x^2 - 2) $$ .

What is the factored form of $$d^3 + 3d^2 - 9d - 27 $$ ?

The factored form is: $$ (d + 3)^2 (d - 3) $$ .

What is the formula for factoring a quadratic trinomial?

The formula for factoring a quadratic trinomial $$ax^2 + bx + c$$ is to find two numbers that multiply to $$ac$$ and add to $$b$$ .

What is the difference between a polynomial and a monomial?

A polynomial is a sum of two or more monomials. A monomial is a single term that can be a constant, variable, or a product of constants and variables.

What is the factored form of $$5n^3 - 10n^2 + 3n - 6$$ ?

The factored form is: $$ (5n^2 + 3)(n - 2) $$ .

What is the significance of the number 64 in relation to perfect squares and cubes?

64 is significant because it is both a perfect square (8^2) and a perfect cube (4^3).

What does it mean for a polynomial to be unfactorable?

A polynomial is unfactorable if it cannot be expressed as a product of simpler polynomials with real coefficients.

What is the role of the GCF in factoring polynomials?

The GCF helps simplify the polynomial by factoring out the largest common factor from all terms, making it easier to factor further.

How do you identify the Sum/Difference of Two Squares?

The Sum of Two Squares is expressed as $$a^2 + b^2$$ , and the Difference of Two Squares is expressed as $$a^2 - b^2 = (a - b)(a + b)$$ .

What is the process of factoring by substitution?

Factoring by substitution involves replacing a variable or expression with a single variable to simplify the polynomial, then factoring it, and substituting back.

Factoring Polynomials - Review Flashcards

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What is the Sum/Difference of Two Cubes formula?

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