High School Math : Polynomials

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #31 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by rearranging the terms to group together the quadratic:

 

Now, convert the quadratic into a square:

 

Finally, distribute the :

Example Question #32 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by extracting  from the polynomial:

 

Now, rearrange to combine like terms:

 

Extract the like terms and factor the cubic:

 

Simplify by combining like terms:

Example Question #33 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by extracting  from the polynomial:

 

Now, rearrange to combine like terms:

 

Extract the like terms and factor the cubic:

 

Simplify by combining like terms:

Example Question #1 : Write A Polynomial Function From Its Zeros

Consider the equation .

According to the Rational Zeroes Theorem, if  are all integers, then, regardless of their values, which of the following cannot be a solution to the equation?

Possible Answers:

Correct answer:

Explanation:

By the Rational Zeroes Theorem, any rational solution must be a factor of the constant, 6, divided by the factor of the leading coefficient, 14. 

Four of the answer choices have this characteristic:

is in lowest terms, and 3 is not a factor of 14. It is therefore the correct answer.

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