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How do you factor #x^2-8x-20#?

Answer 1

Eli Assouline

# ( x + 2 ) ( x - 10 ) # is the factorised form of the expression.

#x^2 - 8x - 20 #

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*-20 =- 20 #

AND

#N_1 +N_2 = b = -8#

After trying out a few numbers we get #N_1 = 2 # and #N_2 =-10# #2 * (-10) = -20#, and #2+(-10)= - 8#

#x^2 - 8x - 20 = x^2 - 10x + 2x - 20 #

#=x ( x - 10 ) + 2 ( x - 1 0)#

# ( x + 2 ) ( x - 10 ) # is the factorised form of the expression.

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Answer 2

Avery Alexander

To factor the quadratic expression ( x^2 - 8x - 20 ), we need to find two numbers that multiply to give ( -20 ) and add to give ( -8 ). These numbers are ( -10 ) and ( 2 ). Then, we rewrite the quadratic expression as:

[ x^2 - 10x + 2x - 20 ]

Next, we group the terms and factor by grouping:

[ (x^2 - 10x) + (2x - 20) ] [ x(x - 10) + 2(x - 10) ]

Now, we can factor out the common factor ( (x - 10) ):

[ (x - 10)(x + 2) ]

So, the factored form of ( x^2 - 8x - 20 ) is ( (x - 10)(x + 2) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.