Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Proposition 12.5.14. Polynomials in R[x] have both right distributivity across addition: (g(x) +r(x))p(x) = g(x)p(x) +r(x)p(x), and left distributivity across addition: p(x) (q(x) +r(x)) = p(x)q(x) + p(x)r(x).

Proposition 12.5.14. Polynomials in R[x] have both right distributivity across addition: (g(x) +r(x))p(x) = g(x)p(x) +r(x)p(x), and left distributivity across addition: p(x) (q(x) +r(x)) = p(x)q(x) + p(x)r(x).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 2E
See similar textbooks
icon
Related questions
Question

Please do Exercise 12.5.15 and please show step by step and explain

PROOF. Το show right distributivity, we have: 71 (q(z) + r(x))p(x) =(Σ+ j=0 - - || - max(n.) Σ j=0 max(n.) m Σ Σ(bya + cal)* j=0 =0 max(n,e) m - Σ Σ(byzana + cjzatz) j=0 t=0 mix(n,e) m max(n.) m Σ Σααρα + Σ Σφα j=0 i=0 j=0 i=0 j=0 max(n.) Σ (0;te)a) Samart Σα j=0 i=0 Gaj max(nl) TTL Σ (bind tead)) Σαγα j=0 i=0 ΤΕ 772 Σαμαρά i=0 j=0 i=0 772 (bind test) Saint) i=0 771 -ΣΣ+ΣΣτα j=0 t=0 ι ΤΟ Τ ΤΙΣ -Στη Σα+Στη Σαμ j=0 j=0 i=0 i=0 =q(x)p(a) + r(x)p(a), which gives us right distributivity. We'll leave left distributivity up to you: Exercise 12.5.15. Provide justification for each of the steps in the calcu- lation in Proposition 12.5.14
Transcribed Image Text:PROOF. Το show right distributivity, we have: 71 (q(z) + r(x))p(x) =(Σ+ j=0 - - || - max(n.) Σ j=0 max(n.) m Σ Σ(bya + cal)* j=0 =0 max(n,e) m - Σ Σ(byzana + cjzatz) j=0 t=0 mix(n,e) m max(n.) m Σ Σααρα + Σ Σφα j=0 i=0 j=0 i=0 j=0 max(n.) Σ (0;te)a) Samart Σα j=0 i=0 Gaj max(nl) TTL Σ (bind tead)) Σαγα j=0 i=0 ΤΕ 772 Σαμαρά i=0 j=0 i=0 772 (bind test) Saint) i=0 771 -ΣΣ+ΣΣτα j=0 t=0 ι ΤΟ Τ ΤΙΣ -Στη Σα+Στη Σαμ j=0 j=0 i=0 i=0 =q(x)p(a) + r(x)p(a), which gives us right distributivity. We'll leave left distributivity up to you: Exercise 12.5.15. Provide justification for each of the steps in the calcu- lation in Proposition 12.5.14
Proposition 12.5.14. Polynomials in R[x] have both right distributivity across addition: (q(x) +r(x))p(x) = q(x)p(x) +r(x)p(x), and left distributivity across addition: p(x) (q(x) +r(x)) = p(x)q(x) + p(x)r(x).
Transcribed Image Text:Proposition 12.5.14. Polynomials in R[x] have both right distributivity across addition: (q(x) +r(x))p(x) = q(x)p(x) +r(x)p(x), and left distributivity across addition: p(x) (q(x) +r(x)) = p(x)q(x) + p(x)r(x).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS