Question

Please answer both these questions​

Answer 1

According to Remainder Theorem, the remainder obtained on dividing a polynomial $p(x)$ by $(x-a)$ is $p(a).$

Here the polynomial is,

$\longrightarrow p(x)=3x^4-4x^3-3x-1$

The polynomial is divided by $(x-1).$

$\longrightarrow x-a=x-1$

$\longrightarrow a=1$

So the remainder is equal to $p(1).$

$\longrightarrow p(1)=3(1)^4-4(1)^3-3(1)-1$

$\longrightarrow p(1)=3-4-3-1$

$\longrightarrow\underline{\underline{p(1)=-5}}$

Hence -5 is the answer.

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We know that,

• $(a+b)^3=a^3+3a^2b+3ab^2+b^3$

Here the term containing $a$ (first power of $a$) is $3ab^2.$

Let $a=x$ and $b=3.$

Then this term becomes $3x(3)^2=27x.$

This implies coefficient of $x$ is 27.

Hence 27 is the answer.