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ACT Math : Polynomials

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Example Questions

Example Question #2 : Factoring Polynomials

Factor the following polynomial:
x^2 + 6x - 27

Possible Answers:

$\textup{The polynomial cannot be factored}$

(x+9)(x-3)

(x-9)(x+3)

(x+27)(x-1)

(x+2)(x+3)

Correct answer:

(x+9)(x-3)

Explanation:

To factor the polynomial, factor the last term into two numbers that sum to the middle term. (9)*(-3) = -27 and 9 + -3 = 6 so we simply place those into parentheses to obtain:

(x+9)(x-3)

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Example Question #81 : Polynomials

The polynomial x^2-4x+4 is equal to which of the following expressions.

Possible Answers:

$(x-2)^{2}$

(x-4)(x+1)

$(x-4)^{2}$

(x-1)(x+4)

(x-2)(x+2)

Correct answer:

$(x-2)^{2}$

Explanation:

This question calls for us to factor the polynomial into two binomials.

Since the first term is x^2 and the last term is a number without a variable, we know that how answer will be of the form (x+ a)(x+ b) 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 -4x we know a+b=-4 . (The x comes from a and b multiplying by x and then adding with each other). The +4 term tells us that a*b=4 . 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.

(x-2)(x-2)=(x-2)^2

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Example Question #101 : Variables

Which expression is equivalent to the following polynomial:

x^2-81

Possible Answers:

(x+80)(x+1)

(x-9)^2

(x-90)(x+9)

(x-9)(x+9)

x(x-81)

Correct answer:

(x-9)(x+9)

Explanation:

This question calls for us to factor the polynomial into two binomials. Since the first term is x^2 and the last term is a number without a variable, we know that how answer will be of the form (x+ a)(x+ b) 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 a+b=0 . (The x comes from a and b multiplying by x and then adding with each other).

The term tells us that a*b=-81 . 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.

(x-9)(x+9)

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Example Question #101 : Variables

Factor the following polynomial:

x^2 -14x + 33

Possible Answers:

(x-33)(x+1)

(x-11)(x-3)

(x+11)(x-3)

(x-11)(x+3)

(x-7)(x+2)

Correct answer:

(x-11)(x-3)

Explanation:

To factor a polynomial of the form ax^2 + bx + c begin by factoring both and .

Since a=1 we are done.

When you factor your two factors need to add together to get .

Since:

-11*-3 = 33 and -11 +-3=-14 the two factors we want are and .

Simply plug them into the parentheses and you have:

(x-11)(x-3)

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ACT Math : Polynomials

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2 : Factoring Polynomials

Example Question #81 : Polynomials

Example Question #101 : Variables

Example Question #101 : Variables

All ACT Math Resources

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