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Chapter 5: Q. 7 (page 441)

Show that the equation p(x)=q(x)m(x)+R(x)is equivalent to the equation p(x)q(x)=m(x)+R(x)q(x)for all x for which q(x) is nonzero.

Short Answer

Expert verified

The given equation has been proved.

Step by step solution

01

Step 1. Given Information

The given equation isp(x)=q(x)m(x)+R(x)

02

Step 2. Proof

Divide both the sides of the given equation by q(x) after that simplify the equation.

p(x)q(x)=q(x)m(x)+R(x)q(x)p(x)q(x)=q(x)m(x)q(x)+R(x)q(x)p(x)q(x)=m(x)+R(x)q(x)

Thus, the equation is proved.

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