(完整版)ALevel数学2

Factorizing quadratic expressions
No constant term
Quadratic expressions of the form ax2 + bx can always be factorized by taking out the common factor x. For example:
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Quadratic expressions
A quadratic expression is an expression in which the highest power of the variable is 2. For example:
x2 – 2
w2 + 3w + 1
t2 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 the coefficient of x2. b is the coefficient of x.
(x + d)(x + e) = x2 + dx + ex + de = x2 + (d + e)x + de
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Factorizing quadratic expressions
The general form Quadratic expressions of the general form ax2 + bx + c can be factorized if they can be written using brackets as
the identity
a2 – b2 = (a + b)(a – b)
to factorize it. For example:
9x2 – 49 = (3x + 7)(3x – 7)
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Factorizing quadratic expressions
x2 + 3x + 2
Factorizing When we expand an expression we multiply out the brackets. When we factorize an expression we write it with brackets.
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c is a constant term.
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Contents
Factorizing quadratics
Quadratic expressions Factorizing quadratics Completing the square Solving quadratic equations The discriminant Graphs of quadratic functions Examination-style questions
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3x2 – 5x = x(3x – 5)
The difference between two squares
When a quadratic has no term in x and the other two terms can
be written as the difference between two squares, we can use
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Factorizing quadratic expressions
Factorizing an expression is the inverse of expanding it. Expanding or multiplying out
(x + 1)(x + 2)
AS-Level Maths:
Core 1
for Edexcel
C1.2 Algebra and functions 2
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(dx + e)(fx + g) where d, e, f and g are integers. If we expand (dx + e)(fx + g), we have
(dx + e)(fx + g)= dfx2 + dgx + efx + eg = dfx2 + (dg + ef)x + eg
Quadratic expressions with a = 1 Quadratic expressions of the form x2 + bx + c can be factorized if they can be written using brackets as
(x + d)(x + e) where d and e are integers. If we expand (x + d)(x + e), we have
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Contents
Quadratic expressions
Quadratic expressions Factorizing quadratics Completing the square Solving quadratic equations The discriminant Graphs of quadratic functions Examination-style questions