How do you factor #x² - 8x + 7#?

2 Answers
Don't Memorise
Jun 30, 2015

# color(green)((x-1)(x-7 )# is the factorised form.

Explanation:

#x^2 - 8x +7#

We can Split the Middle Term of this expression to factorise it.

In this technique, since we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*7 =7#
AND
#N_1 +N_2 = b = -8#

After trying out a few numbers we get #N_1 = -1# and #N_2 =-7#
#(-1)*(-7) = 7#, and #-1+(-7)= -8#

#x^2 - 8x +7 = x^2 color(green)(-1x - 7x) +7 #

# = x(x-1) - 7(x-1 )#

#(x-1)# is a common factor to each of the terms

# color(green)((x-1)(x-7 )# is the factorised form.

Nghi N. · Nghi N
Jun 30, 2015

Factor #y = x^2 - 8x + 7#

Explanation:

Because ( a + b + c = 0), use the shortcut:
One real root is 1, and the factor is (x - 1)
The other real root is #c/a = 7#, then, the corresponding factor is
(x - 7).
Factorised form:
y = (x - 1)(x - 7)

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