Unit 4.2b HW: Factoring in Quadratic Form

Front

What is the factored form of x^4 - 10x^2 + 9?

Back

(x+3)(x-3)(x+1)(x-1)

Front

How do you solve x^4 - 26x^2 + 25 = 0 by factoring?

Back

x = -1, 1, -5, 5

Front

What are the solutions for x^4 - 256 = 0?

Back

x = 4, x = -4, x = 4i, x = -4i

Front

Define a quadratic equation.

Back

A polynomial equation of the form ax^2 + bx + c = 0, where a ≠ 0.

Front

What is the purpose of factoring in algebra?

Back

To simplify expressions and solve equations by breaking them down into simpler components.

Front

What is the difference of squares formula?

Back

a^2 - b^2 = (a - b)(a + b)

Front

What is a perfect square trinomial?

Back

An expression of the form a^2 ± 2ab + b^2, which factors to (a ± b)^2.

Front

How do you factor x^4 - 10x^2 + 9?

Back

Substitute y = x^2, then factor as (y - 9)(y - 1) and revert back to x.

Front

What is the first step in factoring a polynomial?

Back

Look for a common factor in all terms.

Front

What does it mean to factor completely?

Back

To break down a polynomial into irreducible factors.