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Factoring quadratic expressions. Quadratic expressions. t 2. ax 2 + bx + c (where a = 0). 2. A quadratic expression is an expression in which the highest power of the variable is 2. For example,. x 2 – 2,. w 2 + 3 w + 1,. 4 – 5 g 2 ,.
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Quadratic expressions t2 ax2 + bx + c (where a = 0) 2 A quadratic expression is an expression in which the highest power of the variable is 2. For example, x2 – 2, w2 + 3w + 1, 4 – 5g2 , The general form of a quadratic expression in x is: x is a variable. a is a fixed number and is the coefficient of x2. b is a fixed number and is the coefficient of x. c is a fixed number and is the constant term.
a2 + 3a + 2 (a + 1)(a + 2) Factoring Remember: factoring an expression is the opposite of multiplying it. Multiplying Factoring expressions Often: When we multiply an expression we remove the parentheses. When we factor an expression we write it with parentheses.
Factoring quadratic expressions Quadratic expressions of the form x2 + bx + c can be factored if they can be written using parentheses as (x + d)(x + e) where d and e are integers. If we multiply (x + d)(x + e) we have: (x + d)(x + e) = x2 + dx + ex + de = x2 + (d + e)x + de Comparing this to x2 + bx + cwe can see that: • The sum of d and e must be equal to b, the coefficient of x. • The product of d and e must be equal to c, the constant term.
