Explain, in complete sentences, how to factor 4x2 – 4x – 48. Explain how your factors could be checked for accuracy
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let f(x)= 4x^2 – 4x – 48=4(x^2-x-12)
therefore, x-4 is a factor of f(x)
therefore, x+3 is a factor of f(x)
deg(f(x))=2 therefore, it has two roots
therefore, f(x) =4(x-4)(x+3)
Extract the common factor 4 getting
then factor the remainder getting: (x-4)(x+3) put them together and get
To check for accuracy simply multiply your results to determine if you end up with the original expression
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The first step to factorization is to take out a highest common factor, which in your case is 4 .
Now you have to ask yourself what multiplys to give -12 and and adds to give -1, well its right, -4,3
to check you can expand again and you should end up with a original question