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High School Math : Factoring Polynomials

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Example Question #21 : Intermediate Single Variable Algebra

Factor the following polynomial:

(3a-4b)^2-(a+3b)^2

Possible Answers:

(4a-2b)(2a-7b)

(4a-b)(2a+7b)

(4a+b)(2a+7b)

(4a+b)(2a-7b)

(4a-b)(2a-7b)

Correct answer:

(4a-b)(2a-7b)

Explanation:

To begin, distribute the squares:

(3a-4b)^2-(a+3b)^2

[(3a-4b)+(a+3b)][(3a-4b)-(a+3b)]

Now, combine like terms:

(4a-b)(2a-7b)

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Example Question #22 : Intermediate Single Variable Algebra

Factor the following polynomial:

5x^3y+40y^4

Possible Answers:

y(x+2y)(x^2-2xy+4y^2)

2y(x+2y)(x^2-2xy+4y^2)

4y(x+2y)(x^2-2xy+4y^2)

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

5y(x+2y)(x^2-2xy+4y^2)

Correct answer:

5y(x+2y)(x^2-2xy+4y^2)

Explanation:

Begin by extracting from the polynomial:

5x^3y+40y^4

5y(x^3+8y^3)

Now, distribute the cubic polynomial:

5y(x+2y)(x^2-2xy+4y^2)

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Example Question #23 : Intermediate Single Variable Algebra

Factor the following polynomial:

x^5-x^3y^2+27y^5-27x^2y^3

Possible Answers:

(x+y)(x+y)(x-3y)(x^2+3xy+9y^2)

(x+y)(x-y)(x+3y)(x^2+3xy+9y^2)

(x-y)(x-y)(x-3y)(x^2+3xy+9y^2)

(x+y)(x-y)(x-3y)(x^2-3xy+9y^2)

(x+y)(x-y)(x-3y)(x^2+3xy+9y^2)

Correct answer:

(x+y)(x-y)(x-3y)(x^2+3xy+9y^2)

Explanation:

Begin by extracting like terms:

x^5-x^3y^2+27y^5-27x^2y^3

x^3(x^2-y^2)+27y^3(y^2-x^2)

Now, rearrange the right side of the polynomial by reversing the signs:

x^3(x^2-y^2)-27y^3(x^2-y^2)

Combine like terms:

(x^2-y^2)(x^3-27y^3)

Factor the square and cubic polynomial:

(x+y)(x-y)(x-3y)(x^2+3xy+9y^2)

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Example Question #1571 : High School Math

Factor the following polynomial:

x^2-9-6xy+9y^2

Possible Answers:

(x-3y-3)(x-3y-3)

(x-3y+3)(x-3y-3)

(x-3y+3)(x+3y-3)

(x+3y+3)(x-3y-3)

(x+3y+3)(x+3y+3)

Correct answer:

(x-3y+3)(x-3y-3)

Explanation:

Begin by rearranging the terms to group together the quadratic:

x^2-9-6xy+9y^2

(x^2-6xy+9y^2)-9

Now, convert the quadratic into a square:

(x-3y)^2-9

Finally, distribute the :

(x-3y+3)(x-3y-3)

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Example Question #1572 : High School Math

Factor the following polynomial:

m^4n+m^2n-mn^4-mn^2

Possible Answers:

mn(m-n)(m^2+mn-n^2+1)

mn(m-n)(m^2+mn+n^2-1)

mn(m+n)(m^2+mn+n^2+1)

mn(m-n)(m^2-mn+n^2+1)

mn(m-n)(m^2+mn+n^2+1)

Correct answer:

mn(m-n)(m^2+mn+n^2+1)

Explanation:

Begin by extracting from the polynomial:

m^4n+m^2n-mn^4-mn^2

mn(m^3+m-n^3-n)

Now, rearrange to combine like terms:

mn(m^3-n^3+m-n)

Extract the like terms and factor the cubic:

mn[(m-n)(m^2+mn+n^2)+1(m-n)]

Simplify by combining like terms:

mn(m-n)(m^2+mn+n^2+1)

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Example Question #1573 : High School Math

Factor the following polynomial:

3x^3+9x^2+9x+3

Possible Answers:

3(x-1)^2(x+1)

3(x+1)^2(x-1)

3(x-1)^3

3(x+1)^3

Correct answer:

3(x+1)^3

Explanation:

Begin by extracting from the polynomial:

3x^3+9x^2+9x+3

3(x^3+3x^2+3x+1)

Now, rearrange to combine like terms:

3(x^3+1+3x^2+3x)

Extract the like terms and factor the cubic:

3[(x+1)(x^2-x+1)+3x(x+1)]

Simplify by combining like terms:

3[(x+1)(x^2-x+1+3x)]

3(x+1)(x^2+2x+1)

3(x+1)(x+1)(x+1)

3(x+1)^3

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High School Math : Factoring Polynomials

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : Intermediate Single Variable Algebra

Example Question #22 : Intermediate Single Variable Algebra

Example Question #23 : Intermediate Single Variable Algebra

Example Question #1571 : High School Math

Example Question #1572 : High School Math

Example Question #1573 : High School Math

All High School Math Resources

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