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Algebra 1 : Variables

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Example Questions

Example Question #4652 : Algebra 1

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

Possible Answers:

(2x+1)(x+3)

(2x+1)(x-3)

(2x-1)(x+3)

(2x+3)(x-1)

(2x+3)(x+1)

Correct answer:

(2x+1)(x-3)

Explanation:

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

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

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

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

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Example Question #4653 : Algebra 1

Factor: x^6+2x^3+2x

Possible Answers:

x(x^5+2x^2+2)

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

x(6x^5+2x^2+2)

x^3(x^3+4)

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

Correct answer:

x(x^5+2x^2+2)

Explanation:

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

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: x(x^5+2x^2+2)

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Example Question #4654 : Algebra 1

Factor: x^6+2x^3-3x

Possible Answers:

x(x^5+2x^2-3)

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

x(6x^5+2x^2-2)

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

x^3(x^3-8)

Correct answer:

x(x^5+2x^2-3)

Explanation:

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

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: x(x^5+2x^2-3)

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Example Question #421 : Variables

$Expand \;x(x-2)$

Possible Answers:

$x^{2}-2x$

$x^{2}$

$x^{2}+2x$

2x -2

Correct answer:

$x^{2}-2x$

Explanation:

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Example Question #422 : Variables

Evaluate.

$ab(ab^{2}+4a-b)$

Possible Answers:

$a^{2}b^{3}+4a^{2}b-ab^{2}$

$a^{2}b^{2}+4a-b$

2ab+4a-b

$4a^{3}b^{2}$

Correct answer:

$a^{2}b^{3}+4a^{2}b-ab^{2}$

Explanation:

$ab(ab^{2}+4a-b)$

Using the distributive property you are simply going to share the term , with every term in the poynomial

$ab\cdot ab^{2}+ ab\cdot 4a- ab\cdot b$

Now because we are multiplying like variables we can add the exponents, to simplify each expression

$a^{2}b^{3}+4a^{2}b-ab^{2}$

This will be our final answer because we can not add terms unless they are 'like' meaning they contain the same elements and degrees.

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Example Question #1 : How To Multiply A Monomial By A Polynomial

Multiply:

$-3t ^{2} ( 2t ^{2} - 5t + 7)$

Possible Answers:

$-6 t ^{4} - 15t ^{3} +21t ^{2}$

$-6 t ^{4} + 5t ^{3} -7t ^{2}$

$-6 t ^{4} - 5t ^{3} +7t ^{2}$

$-6 t ^{4} + 15t ^{3} -21t ^{2}$

$-6 t ^{4} - 15t ^{3} -21t ^{2}$

Correct answer:

$-6 t ^{4} + 15t ^{3} -21t ^{2}$

Explanation:

$-3t ^{2} ( 2t ^{2} - 5t + 7)$

$= -3t ^{2} \cdot 2t ^{2} - \left (-3t ^{2} \right )\cdot 5t +\left (-3t ^{2} \right )\cdot 7$

$= -3t ^{2} \cdot 2t ^{2} + 3t ^{2} \cdot 5t -3t ^{2}\cdot 7$

$= -3\cdot 2 \cdot t ^{2} \cdot t ^{2} + 3\cdot 5 \cdot t ^{2} \cdot t -3\cdot 7 \cdot t ^{2}$

$= -6 \cdot t ^{2+2} + 15\cdot t ^{2+1} -21 \cdot t ^{2}$

$= -6 t ^{4} + 15t ^{3} -21t ^{2}$

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Example Question #3 : Monomials

Simplify the following:

$(2p^{2})(4x+p)$

Possible Answers:

$(8xp)^{2}+2p^{3}$

$6xp^{2}+3p^{3}$

$8xp^{2}+2p^{2}$

$8xp^{2}+2p^{3}$

None of the other answers

Correct answer:

$8xp^{2}+2p^{3}$

Explanation:

Distribute the $2p^{2}$ to each term in the parentheses in the other polynomial.

$2p^{2}(4x)=8xp^{2}$

$2p^{2}(p)=2p^{3}$

Putting the results back together

$(2p^{2})(4x+p)=8xp^{2}+2p^{3}$

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Example Question #4 : Monomials

Multiply:

-4x(3x^2-2x+4)

Possible Answers:

12x^3-8x^2+16x

-12x^3+8x^2-16x

-12x^3-8x^2-16x

-12x^3-8x^2+16x

Correct answer:

-12x^3+8x^2-16x

Explanation:

Multiply each term of the polynomial by -4x . Be careful to distribute the negative sign.

(-4x)(3x^2)=-12x^3

(-4x)(-2x)=8x^2

(-4x)(4)=-16x

Add the individual terms together:

-12x^3+8x^2+(-16x)=12x^3+8x^2-16x

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Example Question #3 : Monomials

Simplify the following

$(7y)(7t-3y^{3} + 2)$

Possible Answers:

$49yt-21y^{2} +14y$

$14yt-21y^{4} +14y$

$14yt-10y^{4} +14y$

$49yt-21y^{4} +14y$

$28y-21y^{4} +14t$

Correct answer:

$49yt-21y^{4} +14y$

Explanation:

Distribute to each term in the parentheses in the polynomial

7y(7t)=49yt

$7y(-3y^{3})=-21y^{4}$

7y(2)=14y

Combine the results

$(7y)(7t-3y^{3} + 2)=49yt-21y^{4} +14y$

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Example Question #2 : Monomials

Expand the expression by multiplying the terms.

$\small (x-4)(x+2)(2x-5)$

Possible Answers:

$\small 2x^3+9x^2-6x+40$

$\small 2x^3+x^2-26x+40$

$\small 2x^3-9x^2-6x+40$

$\small 2x^3-x^2-26x+40$

Correct answer:

$\small 2x^3-9x^2-6x+40$

Explanation:

$\small (x-4)(x+2)(2x-5)$

When multiplying, the order in which you multiply does not matter. Let's start with the first two monomials.

(x-4)(x+2)

Use FOIL to expand.

x^2+2x-4x-8=x^2-2x-8

Now we need to multiply the third monomial.

$\small (x-4)(x+2)(2x-5)=(x^2-2x-8)(2x-5)$

Similar to FOIL, we need to multiply each combination of terms.

2x(x^2-2x-8)+(-5)(x^2-2x-8)

2x^3-4x^2-16x-5x^2+10x+40

Combine like terms.

2x^3-9x^2-6x+40

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Algebra 1 : Variables

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

Example Question #421 : Variables

Example Question #422 : Variables

Example Question #1 : How To Multiply A Monomial By A Polynomial

Example Question #3 : Monomials

Example Question #4 : Monomials

Example Question #3 : Monomials

Example Question #2 : Monomials

All Algebra 1 Resources

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