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Algebra 1 : Polynomials

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Example Questions

Example Question #4652 : Algebra 1

Factor the following polynomial: $\displaystyle 2x^2-5x-3$.

Possible Answers:

$\displaystyle (2x+1)(x+3)$

$\displaystyle (2x+1)(x-3)$

$\displaystyle (2x-1)(x+3)$

$\displaystyle (2x+3)(x-1)$

$\displaystyle (2x+3)(x+1)$

Correct answer:

$\displaystyle (2x+1)(x-3)$

Explanation:

Because the x^2 $\displaystyle x^2$ term has a coefficient, you begin by multiplying the $\displaystyle a$ and the $\displaystyle c$ terms ($\displaystyle ax^2+bx+c$) together: $2\times-3=-6$ $\displaystyle 2\times-3=-6$.

Find the factors of $\displaystyle -6$ that when added together equal the second coefficient (the $\displaystyle b$ term) of the polynomial: $\displaystyle -5$.

There are four factors of $\displaystyle 6$: $\displaystyle 1, 2, 3, 6$, and only two of those factors, 1, 6 $\displaystyle 1, 6$, can be manipulated to equal $\displaystyle -5$ when added together and manipulated to equal $\displaystyle -6$ when multiplied together: 1, -6 $\displaystyle 1, -6$

$1+-6=-5, 1\times-6=-6$ $\displaystyle 1+-6=-5, 1\times-6=-6$

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Example Question #4653 : Algebra 1

Factor: $\displaystyle x^6+2x^3+2x$

Possible Answers:

$\displaystyle x(x^5+2x^2+2)$

$\frac{1}{x^6}(x^{-6}+2x^{-2}+2x^{-5})$ $\displaystyle \frac{1}{x^6}(x^{-6}+2x^{-2}+2x^{-5})$

$\displaystyle x(6x^5+2x^2+2)$

$\displaystyle x^3(x^3+4)$

$6x(x^5+2x+\frac{1}{3})$ $\displaystyle 6x(x^5+2x+\frac{1}{3})$

Correct answer:

$\displaystyle x(x^5+2x^2+2)$

Explanation:

For each term in this expression, we will notice that each shares a variable of $\displaystyle x$. This can be pulled out as a common factor.

$\displaystyle x^6+2x^3+2x = x(x^5+2x^2+2)$

There are no more common factors, and this is the reduced form.

The answer is: $\displaystyle x(x^5+2x^2+2)$

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Example Question #4654 : Algebra 1

Factor: $\displaystyle x^6+2x^3-3x$

Possible Answers:

$\displaystyle x(x^5+2x^2-3)$

$6x(x^5+2x-\frac{1}{18})$ $\displaystyle 6x(x^5+2x-\frac{1}{18})$

$\displaystyle x(6x^5+2x^2-2)$

$\frac{1}{x^6}(x^{-6}+2x^{-2}-3x^{-5})$ $\displaystyle \frac{1}{x^6}(x^{-6}+2x^{-2}-3x^{-5})$

$\displaystyle x^3(x^3-8)$

Correct answer:

$\displaystyle x(x^5+2x^2-3)$

Explanation:

For each term in this expression, we will notice that each shares a variable of $\displaystyle x$. This can be pulled out as a common factor.

$\displaystyle x^6+2x^3-3x = x(x^5+2x^2-3)$

There are no more common factors, and this is the reduced form.

The answer is: $\displaystyle x(x^5+2x^2-3)$

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Algebra 1 : Polynomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #4652 : Algebra 1

Example Question #4653 : Algebra 1

Example Question #4654 : Algebra 1

All Algebra 1 Resources

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