Vocabulary
monomial- An expression that is either a number, a variable, or the product of a number and one or more variables with whole number exponents.
Essential Information
To factor ax^2+bx+c when a does not equal, find integers, k, l, m, and n such that:
ax^2+bx=c=(kx+m)(lx+n)=klx^2+(kn+lm)x+mn
kl=a mn=c
ax^2+bx=c=(kx+m)(lx+n)=klx^2+(kn+lm)x+mn
kl=a mn=c
Factoring Special Products
If the values of a and c in ax^2+bx+c are perfect squares, check to see whether you can use one of the special factoring patterns to factor the expression.
If the values of a and c in ax^2+bx+c are perfect squares, check to see whether you can use one of the special factoring patterns to factor the expression.
Factoring out Monomials
When factoring an expression, first check to see whether the terms have a common monomial factor.
When factoring an expression, first check to see whether the terms have a common monomial factor.
Solving Quadratic Equations
If the left side of the quadratic equation ax^2+bx+c=0 can be factored, then the equation can be solved using the zero product property.
If the left side of the quadratic equation ax^2+bx+c=0 can be factored, then the equation can be solved using the zero product property.
Factoring and Zeros
The maximum or minimum value of a quadratic function can be found by first using factoring to write the function in intercept form, y=a(x-p)(x-q). Because the function's vertex lies on the axis of symmetry, x=(p+q)/2, the maximum or minimum occurs ar the average of the zeros p and q.
The maximum or minimum value of a quadratic function can be found by first using factoring to write the function in intercept form, y=a(x-p)(x-q). Because the function's vertex lies on the axis of symmetry, x=(p+q)/2, the maximum or minimum occurs ar the average of the zeros p and q.