factoring polynomials

When you factor polynomials, the factors will be..

Polynomials and monomials

ALWAYS try to factor out..

The GCF first

Common factor

A number or expression that is a factor of two or more numbers or polynomials

If first term is negative

Try and factor out the negative sign

Greatest Common Factor/GCF

The greatest number or expression that is a factor of two or more numbers or expressions

Grouping method

Separating the two terms of a polynomials, then factor out the GCF of each group. Then put those two GCFs as a binomial

Quadratic trinomial

ax² + bx + c, where a,b, and c are real numbers not equal to zero

x² + bx + c factors into

(x + p)(x + q)

The constant term of the trinomial, c

(p • q)

The coefficient of the x-term of the trinomial, b

(p + q)

If b is negative and c is positive,

Both p and q are negative

If both b and c are negative

Either p or q is negative and the other is positive

When factoring a trinomial in the form ax² + bx + c,

ALWAYS try and factor the GCF first and then factor the smaller equation

Leading coefficient

The coefficient of the term of the highest degree in the polynomial

Factoring out a -1 can help

ONLY when the leading coefficient is negative and there is NO GCF

(rx + p)(sx + q)

ax² + bx + c factored

The trinomials leading coefficient, a

r • s

The constant term, c

p • q

If c is positive

p AND q will both be positive or negative

If c is negative

p and q will have opposite signs

Best way factor this form if there is no multiples of c that add up to b?

Mental math..

Differences of squares

An expression that has two perfect squares, with one subtracted from the other, x² - 9 = (x)² - (3)²

for any number b, the polynomial x² - b² can be factored as

(x + b)(x - b)

A perfect square trinomial

The result of multiplying a binomial by itself

A perfect square trinomial can be factored as

(a + b)² or (a + b)²

In a perfect square trinomial,

a & b must be perfect squares and can’t be negative, and then the other term must be 2ab

x-intercepts

The points where the graph meets the x-axis

Roots/ the zeros of the function

The solutions to an equation/what x values make the equation true

To find the roots

Set the factorization of the equation to zero and solve, but on the graph keep it the equal value

Just because we have the zeros of a polynomial function,

Does not mean we have the polynomial itself

When polynomials have the same zeros,

The only differences in their equation is the constant factor

f(x) = x² has what amount of zeros

ONE