Factorise:
2 answers:
Answer:
(5x -a +5)(2x -a -2)
Step-by-step explanation:
We assume you want to factor this to two linear factors in x and a. A graphing calculator can help immensely (see attached) by showing you the lines you get by setting each factor to zero.
Those lines can be found by considering the x- and a- intercepts.
<u>x-intercepts</u>
Set a=0 and solve for x.
10x² -10 = 0
(x -1)(x +1) = 0 . . . . divide by 10; factor the difference of squares
x = 1 or -1 . . . . . . . . . . zero-product rule
<u>a-intercepts</u>
Set x=0 and solve for a.
(a +2)(a -5) = 0
a = -2 or +5 . . . . . . by the zero-product rule
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The intercept form of the equation for a line is ...
x/p +y/q = 1 . . . . . . x-intercept = p; y-intercept = q
Possible lines through these intercept points are ...
x/1 +a/-2 = 1 ⇒ 2x -a -2 = 0
x/-1 +a/-2 = 1 ⇒ 2x +a +2 = 0
x/1 +a/5 = 1 ⇒ 5x +a -5 = 0
x/-1 +a/5 = 1 ⇒ 5x -a +5 = 0
These can be paired up two ways. The one of interest can be found by considering the resulting ax term.
(5x +a -5)(2x +a +2) ⇒ ax term is 7ax
(5x -a +5)(2x -a -2) ⇒ ax term is -7ax, as in the given expression
The factorization is (5x -a +5)(2x -a -2).
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