Videos and lessons with examples and solutions to help High School students
learn how to rewrite simple rational expressions in different forms; write
*a*(*x*)/*b*(*x*) in the form *q*(*x*)
+ *r*(*x*)/*b*(*x*), where *a*(*x*),
*b*(*x*), *q*(*x*), and *r*(*x*)
are polynomials with the degree of *r*(*x*) less than the degree of
*b*(*x*), using inspection, long division, or, for the more complicated
examples, a computer algebra system.

- Rewrite rational expressions,

*a*(*x*)/*b*(*x*) in the form*q*(*x*) +*r*(*x*)/*b*(*x*), where*a*(*x*),*b*(*x*),*q*(*x*), and*r*(*x*) by using inspection, long division, or synthetic division and comparing coefficients. **Use a computer algebra system for complicated examples to assist with building a broader conceptual understanding**.

Common Core: HSA-APR.D.6

Ti-Nspire CX CAS Polynomial Division Expand function.

Divide x

Rewrite the expression

x

Expanding the right side we get,

(Ax

Matching coefficients of the various powers of x on the left and right hand sides, we get

x

A = 1

(−3A+B) = 1 ⇒ B = 4

(−3B+C ) = 0 ⇒ C =12

−3C + D = -7 ⇒ D = 29

The expression can then be written as

x

Thus, (x

Polynomial Division & Equating Coefficients

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