Factoring a=1

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials. This is typically done by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the factored form of the expression x² - 25?

Back

(x + 5)(x - 5)

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression x² + 9x - 36?

Back

To factor x² + 9x - 36, find two numbers that multiply to -36 and add to 9. The factored form is (x + 12)(x - 3).

Front

What is the factored form of d² - 10d + 25?

Back

(d - 5)(d - 5) or (d - 5)².

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression n² + 16n + 63?

Back

To factor n² + 16n + 63, find two numbers that multiply to 63 and add to 16. The factored form is (n + 7)(n + 9).

Front

What is a factor of the expression x² - 10x + 24?

Back

x - 4 is a factor of x² - 10x + 24.

Tags

CCSS.HSA.APR.B.2

Front

What is the difference of squares, and how is it factored?

Back

The difference of squares is a special case of factoring where an expression is in the form a² - b². It can be factored as (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

What is the significance of the leading coefficient in factoring quadratics?

Back

When the leading coefficient (the coefficient of x²) is 1, the factoring process is simpler, as you only need to find two numbers that multiply to the constant term.

Front

What are the steps to factor a trinomial of the form x² + bx + c?

Back

1. Identify two numbers that multiply to c and add to b. 2. Rewrite the trinomial as (x + m)(x + n), where m and n are the identified numbers.

Front

What is the role of the zero product property in solving quadratic equations?

Back

The zero product property states that if the product of two factors equals zero, then at least one of the factors must equal zero. This is used to solve quadratic equations after factoring.

Tags

CCSS.HSA-REI.B.4B