Get Expert Help with Polynomials: Examples, Word Problems, and Practice Questions

Is the function in $f (x) = \frac{x}{29} + \frac{2}{x}$ a rational function? If so, write it in the form $\frac{p (x)}{q (x)}$ , the ratio of polynomials, where p(x) has leading coefficient 1, and p(x) and q(x) share no common factors.

Jerold 2021-09-10

Find the zeros of the following quadratic functions.
$a) f (x) = 4 x^{2} - 4 x + 1$
$b) f (x) = 12 x^{2} - 3 x + 5$

arenceabigns 2021-09-10

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
$\sin x = x^{2} - x, (1, 2)$

Rivka Thorpe 2021-09-10

Multiply the following polynomials:
$(4 x + 4) (4 x + 4)$

Anish Buchanan 2021-09-10

Let $p (t) = t^{5} - 6 t^{4} + 6 t^{3} - 6 t^{2} + 5 t$ .
a) Factorise p(t) as a product of degree 1 polynomials.
b) Give an example of a matrix with characteristic polynomial p(t). That is, find a matrix A such that $P_{a} (t) = p (t)$
c) Give an example of a degree 3 polynomial q(t) with real coefficients that has two imaginary roots. For the polynomial q(t) you find, give a matrix that has characterestic polynomial q(t).

EunoR 2021-09-10

Multiply the polynomials.
$(6 x^{2} + 6 x + 1) (3 x - 1)$

Tyra 2021-09-09

Determine whether the following polynomials u,v, w in P(t) are linearly dependent or independent:
$u = t^{3} - 5 t^{2} - 2 t + 3, v = t^{3} - 4 t^{2} - 3 t + 4, w = 2 t^{3} - 17 t^{2} - 7 t + 9$

Anonym 2021-09-09

Taylor polynomials for $e^{x}$
a. Find the Taylor polynomials of order $n = 0, 1, 2,$ and 3 for $f (x) = e^{x}$ centered at 0.

banganX 2021-09-09

Approximations with Taylor polynomials
a. Approximate the given quantities using Taylor polynomials with n = 3.
b. Compute the absolute error in the approximation, assuming the exact value is given by a calculator.
$e^{0.12}$

sanuluy 2021-09-09

Let $f (x) = x^{3} + x^{2} + x + 1 \in Z_{2} [x]$ . Write f(x) as a product of irreducible polynomials over $Z_{2}$

foass77W 2021-09-09

Subtract the polynomials using the horizontal format. $2 a^{2} - 6 a - 4$ from $- 4 a^{2} + 6 a + 10$

Wotzdorfg 2021-09-09

Add the polynomials.
$(9 t^{2} + 16 t - 14) + (- 2 t^{2} - 13 t + 10)$

Trent Carpenter 2021-09-09

Determine whether each set {p1,p2} is a linearly independent set in $P^{3}$ .
The polynomials $p_{1} (t) = 1 + t^{2}$ and $p_{2} (t) = 1 - t^{2}$ .

Joni Kenny 2021-09-09

Solve the equation:
$(3 x + 1) (x^{2} + 2 x - 10)$

Annette Arroyo 2021-09-09

Find the indicated products. Assume all variables that appear as exponents represent positive integers.
$(x^{2 a} - 7) (x^{2 a} - 3)$

Zoe Oneal 2021-09-09

Add or subtract the following polynomials.
$(2 a^{3} b + 1) + (4 a^{3} b + 2)$

Armorikam 2021-09-08

Add the polynomials.
$(5 x^{4} + 7 x^{3} + 2 x^{2} + 25 x - 9) + (6 x^{4} - 9 x^{3} + 8 x^{2} - 17 x + 5)$

Suman Cole 2021-09-08

Perform the indicated operations, and simplify.
$(x + 2) (x^{2} + 2 x + 3)$

Dillard 2021-09-08

Perform the indicated operation and simplify
Subtract the sum of $x^{3} + 17 x + 36 x - 15$ and $3 x^{3} - 13 x + 33$
From the sum of $79 x - 2 x^{3} - 8 x^{2} + 8$ and $5 x^{3} - 73 x^{2} + 99 x + 67$

Amari Flowers 2021-09-08

Explain the step by step of this factoring polynomials.
$8 x^{3} + 1$
This problem is the sum of 2 perfect cubes.
$8 x^{3} + 1 = {(2 x)}^{3} + {(1)}^{3}$
and so we know that it is the fourth special form from above. Here is the factor for this polynomials.
$8 x^{3} + 1 = (2 x + 1) (4 x^{2} - 2 x + 1)$

When you are looking through polynomials questions as you try to understand what are the expressions with all these indeterminates and coefficients, it is essential to see some polynomials examples. Since there are different types of polynomials, you will have Monomial, Binomial, and Trinomial in most cases. You will require a polynomials solver by taking a look at the answers provided. Always think about polynomials equations type before you start as it is what you have to do with algebraic expressions. The list of extensive and free polynomials questions and answers will help you learn and see the logic.

Precalculus

Get Expert Help with Polynomials: Practice Questions and Examples