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PSAT Math : Trinomials

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Example Question #1 : How To Factor A Trinomial

Factor the following expression completely:

x^4-8x^3+12x^2

Possible Answers:

x^2(x-6)(x-2)

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

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

x^2(x^2-8x+12)

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

Correct answer:

x^2(x-6)(x-2)

Explanation:

We must begin by factoring out x^2 from each term.

x^2(x^2-8x+12)

Next, we must find two numbers that sum to and multiply to .

(-6)+(-2)=-8

-6*-2=12

Thus, our final answer is:

x^2(x-6)(x-2)

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Example Question #1 : How To Factor A Trinomial

Factor the following trinomial:

x^2-x-12

Possible Answers:

(x+3)(x-4)

(x-1)(x-12)

(x+4)(x-3)

(x-6)(x+2)

(x-3)(x-4)

Correct answer:

(x+3)(x-4)

Explanation:

x^2-x-12

To trinomial is in ax+bx+c form

In order to factor, find two numbers whose procuct is , in this case , and whose sum is , in this case

Factors of :

-1, 12; 1, -12; -3,4; 3,-4;-2,6; 2,-6

Which of these pairs has a sum of ?

and

Therefore the factored form of x^2-x-12 is:

(x+3)(x-4)

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Example Question #41 : Algebra

Factor the trinomial.

$x^{2}-5x-14$

Possible Answers:

(x+7)(x-2)

(x-7)(x+2)

(x-3)(x-2)

(x-8)(x+3)

Correct answer:

(x-7)(x+2)

Explanation:

Our factors will need to have a product of (-14) , and a sum of (-5) , so our factors must be (-7) and .

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Example Question #1 : Trinomials

(x^2+y^2+z^2)(x^2+y^2+z^2)

Possible Answers:

x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2

x^2y^2+y^2z^2+x^2z^2

x^4+x^2y^2+y^2z^2+z^4

2x^2y^2+z^4+y^4+2z^2y^2

x^4+y^4+z^4

Correct answer:

x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2

Explanation:

(x^2+y^2+z^2)(x^2+y^2+z^2)

Use the distributive property:

x^2(x^2+y^2+z^2)+y^2(x^2+y^2+z^2)+z^2(x^2+y^2+z^2)

x^4+x^2y^2+x^2z^2 + x^2y^2+y^4+y^2z^2+x^2z^2+y^2z^2+z^4

Combine like terms:

x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2

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Example Question #2 : How To Multiply Trinomials

Find the product:

(x^2+7x+4)(x^2-3x-2)

Possible Answers:

x^4+4x^3-19x^2-26x-8

x^4-10x^3+27x^2-14x-4

x^4-21x-8

2x^2+4x+2

2x^2-4x-2

Correct answer:

x^4+4x^3-19x^2-26x-8

Explanation:

Find the product:

(x^2+7x+4)(x^2-3x-2)

Step 1: Use the Distributive Property

x^2(x^2-3x-2)+7x(x^2-3x-2)+4(x^2-3x-2)

x^4-3x^3-2x^2+7x^3-21x^2-14x+4x^2-12x-8

Step 2: Combine like terms

x^4+4x^3-19x^2-26x-8

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Example Question #3 : How To Multiply Trinomials

Find the product:

(2x^2+3y+6)(7x^2+4y+1)

Possible Answers:

14x^2+8x^2y+12y^2+8

14x^2+29x^2y+44x^2+12y^2+27y+6

21x^2y+12y^2+3y

14x^4+8x^2y+2x^2

42x^2+24y+6

Correct answer:

14x^2+29x^2y+44x^2+12y^2+27y+6

Explanation:

Find the product:

(2x^2+3y+6)(7x^2+4y+1)

Use the distributive property:

2x^2(7x^2+4y+1)+3y(7x^2+4y+1)+6(7x^2+4y+1)

14x^4+8x^2y+2x^2+21x^2y+12y^2+3y+42x^2+24y+6

14x^4+29x^2y+44x^2+12y^2+27y+6

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Example Question #31 : Polynomials

Simplify:

(4x^2+6x+5)+(3x^3+10x+7)

Possible Answers:

3x^3+4x^2+13x+15

7x^2+13x+15

7x^2+16x+12

3x^3+4x^2+16x+12

Correct answer:

3x^3+4x^2+16x+12

Explanation:

All operations are addition, so we can first remove the parentheses:

(4x^2+6x+5)+(3x^3+10x+7)

=4x^2+6x+5+3x^3+10x+7

Now rearrange the terms so that like terms are next to each other:

=3x^3+4x^2+(6x+10x)+(5+7)

Combine like terms:

=3x^3+4x^2+16x+12

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Example Question #1 : Trinomials

Add, expressing the result in simplest form:

$\left ( 4x^{2}+ 9y^{2} \right ) + \left ( 2x^{2}- 4xy + 7y\right )$

Possible Answers:

$6x^{2} + 16y^{3} - 4xy$

$6x^{2} + 9y^{2} +3xy^{2}$

$6x^{2} + 16y^{2} - 4xy$

$6x^{2} + 9y^{2} - 4xy + 7y$

$6x^{2} + 9y^{2} +3xy$

Correct answer:

$6x^{2} + 9y^{2} - 4xy + 7y$

Explanation:

$\left ( 4x^{2}+ 9y^{2} \right ) + \left ( 2x^{2}- 4xy + 7y\right )$

$= 4x^{2}+ 2x^{2} + 9y^{2} - 4xy + 7y$

$= 6x^{2} + 9y^{2} - 4xy + 7y$

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Example Question #1 : How To Add Trinomials

Add, expressing the result in simplest form:

$\left ( 4x^{2}+ 2xy + 7y^{2} \right ) + \left ( 2x^{2}+7y\right )$

Possible Answers:

$4x^{2}+ 4xy + 7y^{2} +7y$

$6x^{2} +9xy + 7y^{2}$

$6x^{2} + 2xy + 14y^{2}$

$6x^{2} + 2xy + 14y^{3}$

$6x^{2} + 2xy + 7y^{2} + 7y$

Correct answer:

$6x^{2} + 2xy + 7y^{2} + 7y$

Explanation:

$\left ( 4x^{2}+ 2xy + 7y^{2} \right ) + \left ( 2x^{2}+7y\right )$

$= 4x^{2}+ 2x^{2} + 2xy + 7y^{2} + 7y$

$= 6x^{2} + 2xy + 7y^{2} + 7y$

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Example Question #4 : How To Add Trinomials

Add, expressing the result in simplest form:

$\left ( \frac{1}{2}x^{2} + \frac{2}{3}x - \frac{1}{5}\right ) + \left ( \frac{1}{4}x^{2} - \frac{1}{4}x - \frac{1}{4}\right )$

Possible Answers:

$\frac{1}{6} x^{2} + \frac{5}{12}x + \frac{1}{20}$

$\frac{3}{4} x^{2} + \frac{5}{12}x - \frac{9}{20}$

$\frac{3}{4} x^{2} + \frac{5}{12}x + \frac{1}{20}$

$\frac{1}{6} x^{2} + \frac{11}{12}x - \frac{9}{20}$

$\frac{3}{4} x^{2} + \frac{11}{12}x - \frac{9}{20}$

Correct answer:

$\frac{3}{4} x^{2} + \frac{5}{12}x - \frac{9}{20}$

Explanation:

$\left ( \frac{1}{2}x^{2} + \frac{2}{3}x - \frac{1}{5}\right ) + \left ( \frac{1}{4}x^{2} - \frac{1}{4}x - \frac{1}{4}\right )$

$= \frac{1}{2}x^{2} + \frac{2}{3}x - \frac{1}{5} + \frac{1}{4}x^{2} - \frac{1}{4}x - \frac{1}{4}$

$= \frac{1}{2}x^{2} + \frac{1}{4}x^{2} + \frac{2}{3}x - \frac{1}{4}x- \frac{1}{5} - \frac{1}{4}$

$=\left ( \frac{1}{2} + \frac{1}{4} \right )x^{2} +\left ( \frac{2}{3} - \frac{1}{4} \right )x- \left (\frac{1}{5}+\frac{1}{4} \right )$

$=\left ( \frac{2}{4} + \frac{1}{4} \right )x^{2} +\left ( \frac{8}{12} - \frac{3}{12} \right )x- \left (\frac{4}{20}+\frac{5}{20} \right )$

$= \frac{3}{4} x^{2} + \frac{5}{12}x - \frac{9}{20}$

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PSAT Math : Trinomials

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Factor A Trinomial

Example Question #1 : How To Factor A Trinomial

Example Question #41 : Algebra

Example Question #1 : Trinomials

Example Question #2 : How To Multiply Trinomials

Example Question #3 : How To Multiply Trinomials

Example Question #31 : Polynomials

Example Question #1 : Trinomials

Example Question #1 : How To Add Trinomials

Example Question #4 : How To Add Trinomials

All PSAT Math Resources

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