Trinomials

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PSAT Math › Trinomials

Questions 1 - 10

Add, expressing the result in simplest form:

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

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

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

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

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

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

Explanation

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

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

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

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

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

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

Add, expressing the result in simplest form:

$(0.4x^{2}-0.0006x+ 1)+ (0.03x^{2}+ x - 0.005)$

$0.4 3x^{2} + 0.9994x+ 0.995$

$0.7x^{2} + 0.9994x+ 0.9995$

$0.4 3x^{2} + 0.994x+ 0.9995$

$0.7x^{2} + 0.994x+ 0.9995$

$0.7x^{2} -1.006x+ 0.995$

Explanation

$(0.4x^{2}-0.0006x+ 1)+ (0.03x^{2}+ x - 0.005)$

$= 0.4x^{2}+ 0.03x^{2}+ 1x -0.0006x + 1 - 0.005$

$= 0.4 3x^{2} + 0.9994x+ 0.995$

Add, expressing the result in simplest form:

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

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

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

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

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

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

Explanation

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

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

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

Add, expressing the result in simplest form:

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

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

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

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

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

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

Explanation

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

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

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

Add, expressing the result in simplest form:

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

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

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

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

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

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

Explanation

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

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

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

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

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

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

Add, expressing the result in simplest form:

$(0.4x^{2}-0.0006x+ 1)+ (0.03x^{2}+ x - 0.005)$

$0.4 3x^{2} + 0.9994x+ 0.995$

$0.7x^{2} + 0.9994x+ 0.9995$

$0.4 3x^{2} + 0.994x+ 0.9995$

$0.7x^{2} + 0.994x+ 0.9995$

$0.7x^{2} -1.006x+ 0.995$

Explanation

$(0.4x^{2}-0.0006x+ 1)+ (0.03x^{2}+ x - 0.005)$

$= 0.4x^{2}+ 0.03x^{2}+ 1x -0.0006x + 1 - 0.005$

$= 0.4 3x^{2} + 0.9994x+ 0.995$

Subtract:

Explanation

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses:

Next, identify and group the like terms in order to combine them: .

Subtract:

Explanation

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses:

Next, identify and group the like terms in order to combine them: .

Find the difference:

Explanation

Find the difference:

Distribute the negative to the second trinomial:

Combine like terms:

Factor the following trinomial:

Explanation

To trinomial is in form

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

Factors of :

Which of these pairs has a sum of ?

and

Therefore the factored form of is:

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