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PSAT Math : How to subtract trinomials

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Example Questions

Example Question #3 : Simplifying Polynomials

Evaluate the following:

$(2x^2+\frac{3}{4}x-5) - (x^2+x-10)$ $\displaystyle (2x^2+\frac{3}{4}x-5) - (x^2+x-10)$

Possible Answers:

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

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

$x^2-\frac{7}{4}x + 10$ $\displaystyle x^2-\frac{7}{4}x + 10$

$x^2-\frac{1}{4}x -15$ $\displaystyle x^2-\frac{1}{4}x -15$

Correct answer:

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

Explanation:

To subtract these two trinomials, you first need to flip the sign on every term in the second trinomial, since it is being subtrated:

$(2x^2+\frac{3}{4}x-5) - (x^2+x-10)$ $\displaystyle (2x^2+\frac{3}{4}x-5) - (x^2+x-10)$

$2x^2+\frac{3}{4}x-5 - x^2-x+10$ $\displaystyle 2x^2+\frac{3}{4}x-5 - x^2-x+10$

Next you can combine like terms. You have two terms with x^2 $\displaystyle x^2$, two terms with $\displaystyle x$, and two terms with no variable:

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

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Example Question #1 : How To Subtract Trinomials

Find the difference:

$\displaystyle (25a^3+14a^2+9a)-(-6a^3-14a^2+8a)$

Possible Answers:

31a^3+a $\displaystyle 31a^3+a$

19a^3+a $\displaystyle 19a^3+a$

$\displaystyle 31a^3+28a^2+a$

$\displaystyle 19a^3+17a$

$\displaystyle 31a^3+14a^2+a$

Correct answer:

$\displaystyle 31a^3+28a^2+a$

Explanation:

Find the difference:

$\displaystyle (25a^3+14a^2+9a)-(-6a^3-14a^2+8a)$

Distribute the negative to the second trinomial:

$\displaystyle 25a^2+14a^2+9a+6a^3+14a^2-8a$

Combine like terms:

$\displaystyle 31a^3+28a^2+a$

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Example Question #1 : How To Subtract Trinomials

Subtract:

$\displaystyle (x^2+15x-3)-(x^2-5x-3)$

Possible Answers:

$\displaystyle 2x^2+20x+6$

$\displaystyle x^4+20x^2+6$

20x $\displaystyle 20x$

20x+6 $\displaystyle 20x+6$

20x^2 $\displaystyle 20x^2$

Correct answer:

20x $\displaystyle 20x$

Explanation:

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses: $\displaystyle (x^2+15x-3)-(x^2-5x-3)=x^2+15x-3-x^2+5x+3$

Next, identify and group the like terms in order to combine them: $\displaystyle (x^2-x^2)+(15x+5x)+(3-3)=20x$.

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PSAT Math : How to subtract trinomials

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #3 : Simplifying Polynomials

Example Question #1 : How To Subtract Trinomials

Example Question #1 : How To Subtract Trinomials

All PSAT Math Resources

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