How do you factor #y= x^2 – 14x – 32#?

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Answer 1 · 2016-03-21T16:50:39

# color(blue)((x + 2) ( x -16)# is the factorised form of the expression.

#y = x^2 - 14x - 32#

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

In this technique, if 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 * (-32) = -32#

AND

#N_1 +N_2 = b = -14#

After trying out a few numbers we get #N_1 = -16# and #N_2 =2#

#(-16 ) * 2 = -32# and # 2 +(- 16)= -14#

# x^2 - color(green)(14x) - 32 =x^2 color(green)(- 16x + 2x) - 32#

# = x ( x -16) + 2 ( x - 16)#

# = color(blue)((x + 2) ( x -16)#

# color(blue)((x + 2) ( x -16)# is the factorised form of the expression.