Multiply these polynomials: 12ab(5/6a + 1/4ab^2)

Multiply these polynomials: 12ab(5/6a + 1/4ab^2)

Question
Polynomials
asked 2021-02-24
Multiply these polynomials: 12ab(5/6a + 1/4ab^2)

Answers (1)

2021-02-25
12ab(5/6a + 1/4ab^2) = = 12ab xx 5/6a + 12ab xx 1/4ab^2 = = (12 xx 5/6)(a xx a)(b) + (12 xx 1/4)(a xx a)(b xx b^2) = = 10a^2b + 3a^2b^3
0

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Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same \(\displaystyle{P}{\left({x}\right)}={3}{x}^{{4}}-{5}{x}^{{3}}+{x}^{{2}}-{3}{x}+{5}\ {Q}{\left({x}\right)}={\left({\left({\left({3}{x}-{5}\right)}{x}+{1}\right)}{x}-{3}\right)}{x}+{5}\) Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial \(\displaystyle{R}{\left({x}\right)}={x}^{{5}}—{2}{x}^{{4}}+{3}{x}^{{3}}—{2}{x}^{{3}}+{3}{x}+{4}\) in “nested” form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value ofa polynomial using synthetic division?

asked 2021-01-13
write the polynomial \(\displaystyle{P}{\left({x}\right)}={x}^{{{2}}},\) if possible as a linear combination of the polynomials \(\displaystyle{1}+{x},{2}+{x}^{{{2}}},−{x}.\)
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