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

a) Prove that the set $β = {p_{0} (x) p_{1} (x), \dots, p_{n} (x)}$ of Lagrange polynomials is linearly independent in $P_{n} (b)$ . Deduce that $β$ basis for $P_{n}$

opatovaL 2021-09-05

Subtract $5 y^{2} - 6 y - 11$ from $6 y^{2} + 2 y + 5$

Tolnaio 2021-09-05

Add the given polynomials.
$6 x^{2} + 8 x + 4$ and $- 7 x^{2} - 7 x - 10$

FobelloE 2021-09-05

Applying the theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation
$2 x^{4} - 9 x^{3} - 8 x - 10 - 0$

BolkowN 2021-09-05

The polynomial of degree 4, $P (x)$ has a root of multiplicity 2 at $x = 2$ and roots of multiplicity 1 at $x = 0$ and $x = - 2$ . It goes thgough the point $(5, 157.5)$
Find a formula for $P (x)$ .

Bergen 2021-09-05

Calculate the Taylor polynomials $T_{2} (x)$ and $T_{3} (x)$ centered at $x = 9$ for $x = 9$ for $f (x) = \ln (x + 1)$

allhvasstH 2021-09-05

Consider these Values: $A = 32, B = 15 and C = 17$
The set ot first four Hermite polynomials is
S={ $1, 2 t, - 2 + 4 t^{2}, - 12 t + 8 t^{3}$ }. These polynomials have a wide variety of applications in physics and engineering.
1) Show that the set S of first four Hermite polynomials form a basis for $P_{3}$
2) Find the coordinate vector of the polynomial $p (t) = - 1 + A t + 8 t^{2} + B t^{3}$ relative to S

beljuA 2021-09-05

Use a second degree Taylor polynomial to approximate the two solutions to $\cos (x) = \frac{3}{4}$ in the interval ( $- \frac{π}{2}, \frac{π}{2}$ )

Tyra 2021-09-05

Determine the degree of the given polynomials.
$5 x^{2} - 7 x - 2$

waigaK 2021-09-04

Find (a) , (b) $| | p | |$ , (c) $| | q | |$ , and (d) $d (p, q)$ for the polynomials in $P_{2}$ using the inner product $< p, q \geq a_{0} b_{0} + a_{1} b_{1} + a_{2} b_{2}$ .
$p (x) = 1 - 3 x + x^{2}, q (x) = - x + 2 x^{2}$

glamrockqueen7 2021-09-04

Find values of x, if any, at which f is not continuous: $f (x) = \frac{5}{x} + \frac{2 x}{x + 4}$

Maiclubk 2021-09-04

Subtract the polynomials $(10 x^{3} - 5 x^{2} + 3 x - 4) - (6 x^{3} + 4 x^{2} - 3 x - 1)$

geduiwelh 2021-09-04

If when adding three polynomials, P+Q+R the result is $2 x^{2} y$ and the polynomials P and Q are given by the expressions $P = x^{3} + 5 x y^{2} + y^{3}, Q = y^{3} - 10 x y^{2} - x^{3}$ . What is the expression for the polynomial R?

vazelinahS 2021-09-04

Let $f (x) = \sin (2 x)$
Prove or disprove there are a sequnce of polynomials $P_{n} (x)$ which convenes to $f (x)$ uniformly on $(0, \infty)$ .

texelaare 2021-09-04

Add the polynomials:
$(10 x^{5} - 8 x^{4} - 7 x^{3} - 10) + (- 4 x^{4} + 12 x^{3} + 7 x + 9)$

Yulia 2021-09-03

Test the sets of polynomials for linear independence. For those that are linearly dependent, express one of the polynomials as a linear combination of the others { $1 - 2 x, 3 x + x^{2} - x^{3}, 1 + x^{2} + 2 x^{3}, 3 + 2 x + 3 x^{3}$ } in P3

Tahmid Knox 2021-09-03

Let $P (x) = 8 x^{4} + 6 x^{2} - 3 x + 1$ and $D (x) = 2 x^{2} - x + 2$ . Find polynomials $Q (x)$ and $R (x)$ such that $P (x) = D (x) \cdot Q (x) + R (x)$ .

melodykap 2021-09-03

Add the polynomials:
$(- 10 x^{4} + 8 x^{3} - x^{2} + 10 x) + (- 8 x^{3} - 5 x^{2} - 4)$

sodni3 2021-09-03

To add polynomials, we add ______ terms, So

$(3 x^{2} + 2 x + 4) + (8 x^{2} - x + 1) =$

Emily-Jane Bray 2021-09-03

Find the least common multiple of the following pair of polynomials:
$x {(x - 1)}^{2} (x + 1)$ and $4 (x - 1) {(x + 1)}^{3}$

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