c ti a r d a u q g n ri to c a F expressions 1 of 8
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Quadratic expressions A quadratic expression is an expression in which the highest power of the variable is 2. For example, 2 t x2 – 2, w2 + 3w + 1, 4 – 5g2 , 2 The general form of a quadratic expression in x is: ax2 + bx + c
(where a = 0)
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. 2 of 8
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Factoring expressions Remember: factoring an expression is the opposite of multiplying it. Multiplying
a2 + 3a + 2
(a + 1)(a + 2)
Factoring
Often: When we multiply an expression we remove the parentheses. When we factor an expression we write it with parentheses. 3 of 8
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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 + c we 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. 4 of 8
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Factoring quadratic expressions 1
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Matching quadratic expressions
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Factoring quadratic expressions Quadratic expressions of the form ax2 + bx + c can be factored if they can be written using parentheses as (dx + e)(fx + g) where d, e, f and g are integers. If we multiply (dx + e)(fx + g) we have, (dx + e)(fx + g) = dfx2 + dgx + efx + eg = dfx2 + (dg + ef)x + eg Comparing this to ax2 + bx + c we can see that: a = df b = (dg + ef) c = eg 7 of 8
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Factoring quadratic expressions
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