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Polynomials Test - 36

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Polynomials Test - 36
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  • Question 1
    1 / -0
    The _________ power of the variable in a polynomial is called its degree.
    Solution
    The polynomial $$x^2+x+a$$ is in the standard form.

    The power is simply the number in the exponent. 
    In the polynomial, $$x^2+x+a$$, the power of the first term is $$2$$. Since the polynomial has the largest exponent of the variable $$x$$ as $$2$$, it is the degree of the polynomial.

    Hence, the highest power of the variable in a polynomial is called its degree.
  • Question 2
    1 / -0
    $$p(y) = 5y^3 - 2y^2 + y + 10$$ is a polynomial in $$y$$ of degree
    Solution
    in $$5y^3-2y^2+y+10$$ we see the power of the first term is $$3$$, the power of the second term is $$2$$ and the power of the third term is $$1$$. Since the polynomial has the largest exponent, that is $$3$$ which is the degree of the polynomial.

    Hence, the degree of the polynomial is $$3$$.

  • Question 3
    1 / -0
    If $$p(-2) = 24 $$, then $$p(x) = $$
    Solution
    Let $$p(x)=3x^2-5x+2$$ and substitute $$x=-2$$ as shown below:

    $$p(-2)=3(-2)^{ 2 }-\left( 5\times -2 \right) +2=\left( 3\times 4 \right) +10+2=12+10+2=24$$

    Hence, $$p(x)=3x^2-5x+2$$.
  • Question 4
    1 / -0
    If $$p(-3) = 27$$, then $$p(x) =$$
    Solution
    Consider option A
    let $$p(x)=4x^2-3x$$. Then $$p(-3)=4(9)+9=45$$ Hence $$p(-3)\neq 27$$.

    Consider option B
    let $$p(x)=4x-3x=x$$. Then $$p(-3)=-3$$ Hence $$p(-3)\neq 27$$.

    Consider option C
    let $$p(x)=4x^2+3x$$. Then $$p(-3)=4(9)-9=27$$ Hence $$p(-3)=27$$.

    Consider option D
    let $$p(x)=4x^2+3$$. Then $$p(-3)=4(9)+3=39$$ Hence $$p(-3)\neq 27$$.

    Hence the correct option is option C.
  • Question 5
    1 / -0
    If $$p(1) = 8$$, then $$ p(x) = $$
    Solution
    Let $$p(x)=3x+5$$ and substitute $$x=1$$ as shown below:

    $$p(1)=\left( 3\times 1 \right) +5\\=3+5\\=8$$

    Hence, $$p(x)=3x+5$$.
  • Question 6
    1 / -0
    $$p(x) = 6x^2 - 2x^6 $$ is a polynomial in $$x$$ of degree
    Solution
    $$p(x) = 6x^2 - 2x^6$$. 
    Here, the highest degree of the variable $$x$$ is $$6$$.
    $$\therefore p(x)$$ is a polynomial of degree $$6$$
  • Question 7
    1 / -0
    The highest power of the variable in a polynomial is called its _______.
    Solution
    The polynomial $$x^2+x+a$$ is in the standard form.

    The power is simply number in the exponent. In the polynomial, $$x^2+x+a$$, the power of the first term is $$2$$. Since the polynomial has the largest exponent that is $$2$$, which is the degree of the polynomial.

    Hence, the highest power of the variable in a polynomial is called its degree.

  • Question 8
    1 / -0
    $$5x + 3$$ is a polynomial in $$x$$ of degree
    Solution
    The given polynomial is $$5x+3$$ 

    The power of $$x$$ in the first term is $$1$$,and the power of $$x$$ in the second term is $$0$$
     Since in the polynomial the largest exponent of $$x$$ is $$1$$, it is the degree of the polynomial.

    Hence, the degree of the polynomial is $$1$$
  • Question 9
    1 / -0
    If $$p(x) = x^3 - 8x^2 + 4$$, then $$p(4) =$$
    Solution
    The polynomial is $$p(x)=x^3-8x^2+4$$ and substitute $$x=4$$ in the polynomial:
    $$p(4)=(4)^3-8(4)^2+4=64-(8\times 16)+4=64-128+4=68-128=-60$$
    Hence, $$p(4)=-60$$.
  • Question 10
    1 / -0
    Which of the following is NOT a constant polynomial?
    Solution
    $$\textbf{Step-1: Apply the concept of polynomial.}$$
                     $$\text{Since}$$ $$p(x)=x$$ $$\text{is a polynomial with variable}$$ $$x$$ $$\text{and there is no constant term in it.}$$
                     $$\text{In the other given options,  we can see that the polynomials have}$$ 
                     $$\text{constant terms, none of them has any variable term.}$$
                     $$\text{So,}$$ $$p(x)=x$$ $$\text{is not a constant polynomial.}$$
    $$\textbf{Hence, correct option is C}$$
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