ACT Math : How to factor a polynomial
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Example Question #11 : How To Factor A Polynomial
Which expression is equivalent to the following polynomial:
This question calls for us to factor the polynomial into two binomials. Since the first term is and the last term is a number without a variable, we know that how answer will be of the form where a and b are positive or negative numbers.
To find a and b we look at the second and third term. Since the second term is not present, we know . (The x comes from a and b multiplying by x and then adding with each other).
The term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that -81 & 1, 81 & -1, and -9 & 9 are the possible pairs. Now we can look and see which one adds up to make 0.
This gives us the pair -9 & 9 and we plug that into the equation as a and b to get our final answer.
Example Question #81 : Polynomials
Factor the following polynomial:
To factor a polynomial of the form begin by factoring both and .
Since we are done.
When you factor your two factors need to add together to get .
Since:
and the two factors we want are and .
Simply plug them into the parentheses and you have:
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