Factoring(3): Factoring Quadratic Trinomials With a Leading Coefficient of 1
1) A trinomial is a polynomial with three terms.
2) A quadratic polynomial is a 2nd degree polynomial in one variable (the highest power of the variable is 2).
3) The linear term in a polynomial is the 1st degree term (the exponent of the variable is 1).
4) The constant term in a polynomial is the term without a variable.
5) “Coefficient” means the number part of a term.
6) “Sum” means the result of addition
7) “Product” means the result of addition
HOW TO FACTOR A QUADRATIC TRINOMIAL WITH A LEADING COEFFICIENT OF 1:
1) Make sure that the polynomial is, in fact, in the correct form: x2 + bx + c
(Note: Since we can’t see the coefficient of the first term, we know the leading coefficient is 1)
2) Think of two numbers, p and q, whose SUM is the coefficient of the linear term (b) and whose PRODUCT is the constant term (c).
3) Write the binomial factors – both factors begin with x, one factor ends with p, and one factor ends with q.
(Note: Because of the commutative property, the order of the factors doesn’t matter)
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