# ACT Math : Polynomials

## Example Questions

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### Example Question #6 : Factoring Polynomials

Factor the following polynomial:

Explanation:

To factor the polynomial, factor the last term into two numbers that sum to the middle term.  and  so we simply place those into parentheses to obtain:

### Example Question #7 : Factoring Polynomials

The polynomial  is equal to which of the following expressions.

Explanation:

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  we know . (The x comes from a and b multiplying by x and then adding with each other). The +4 term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & 4, 2 & 2, -1 & -4, and -2 & -2 are the possible pairs.

Now we can look and see which one adds up to make -4.

This gives us the pair -2 & -2.

### Example Question #101 : Variables

Which expression is equivalent to the following polynomial:

Explanation:

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 #11 : Factoring Polynomials

Factor the following polynomial:

Explanation:

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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