Factor Completely: GCF, Trinomial, and DOTS

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms in the expression and divide each term by this factor, then write the expression as the GCF multiplied by the resulting expression.

Tags

CCSS.7.EE.A.1

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

What is the process of factoring a trinomial?

Back

To factor a trinomial, find two numbers that multiply to 'ac' (the product of the coefficient of x^2 and the constant term) and add to 'b' (the coefficient of x). Use these numbers to split the middle term and factor by grouping.

Front

What does DOTS stand for in factoring?

Back

DOTS stands for Difference of Two Squares, a factoring technique used for expressions in the form a^2 - b^2.

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a difference of two squares?

Back

To factor a difference of two squares, use the formula a^2 - b^2 = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of 6m^2 + 16m?

Back

The factored form is 2m(3m + 8).

Front

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

Back

Factor out x^2 to get x^2(x^2 - 9), then recognize x^2 - 9 as a difference of squares: x^2(x + 3)(x - 3).

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of 3x^5 - 27x^3?

Back

The factored form is 3x^3(x - 3)(x + 3).

Front

How do you factor 8x^4 + 22x^3 - 6x^2?

Back

Factor out the GCF, which is 2x^2, to get 2x^2(4x^2 + 11x - 3), then factor the quadratic to get 2x^2(4x - 1)(x + 3).