David Troyer
2021-12-17
Answered

Express as a polynomial. $({t}^{2}+2t-5)(3{t}^{2}-t+2)$

You can still ask an expert for help

Alex Sheppard

Answered 2021-12-18
Author has **36** answers

Step 1

Given:

$({t}^{2}+2t-5)(3{t}^{2}-t+2)$

For the polynomial, we solve the parenthesis,

$\Rightarrow {t}^{2}(3{t}^{2}-t+2)+2t(3{t}^{2}-t+2)-5(3{t}^{2}-t+2)$

$\Rightarrow 3{t}^{4}-{t}^{3}+2{t}^{2}+6{t}^{3}-2{t}^{2}+4t-15{t}^{2}+5t-10$

$\Rightarrow 3{t}^{4}-5{t}^{3}-15{t}^{2}+9t-10$

Step 2

Hence,

The polynomial is,

$\Rightarrow 3{t}^{4}-5{t}^{3}-15{t}^{2}+9t-10$

Given:

For the polynomial, we solve the parenthesis,

Step 2

Hence,

The polynomial is,

Bertha Jordan

Answered 2021-12-19
Author has **37** answers

Consider $({t}^{2}+2t-5)(3{t}^{2}-t+2)$

Treating the polynomial$(3{t}^{2}-t+2)$ as a single real term, and then multiplying, we get

$({t}^{2}+2t-5)(3{t}^{2}-t+2)$

$=({t}^{2}+2t+(-5))(3{t}^{2}+(-t)+2)$

$={t}^{2}(3{t}^{2}+(-t)+2)+2t(3{t}^{2}+(-t)+2)+(-5)(3{t}^{2}+(-t)+2)$

[using distributive property]

Again, using distributive property three times, and simplifying the result, we get

$=3{t}^{4}-{t}^{3}+2{t}^{2}+6{t}^{3}-2{t}^{2}+4t-15{t}^{2}+5t-10$

[adding the powers of same base]

$=3{t}^{4}+(-1+6){t}^{3}+(2-2-15){t}^{2}+(4+5)t-10$

[adding the coefficient of like powers of x]

$=3{t}^{4}+5{t}^{3}-15{t}^{2}+9t-10$ [simplifying]

The three monomials in the first polynomial were multiplied by each of the three monomials in the second polynomial, giving us a total of nine terms, whose sum is the required polynomial, is

$3{t}^{4}+5{t}^{3}-15{t}^{2}+9t-10$

Treating the polynomial

[using distributive property]

Again, using distributive property three times, and simplifying the result, we get

[adding the powers of same base]

[adding the coefficient of like powers of x]

The three monomials in the first polynomial were multiplied by each of the three monomials in the second polynomial, giving us a total of nine terms, whose sum is the required polynomial, is

asked 2021-06-03

Is the following function a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

$g(x)=3-\frac{{x}^{2}}{4}$

asked 2022-02-02

What is the standard form of $y=(-\frac{1}{9}x+\frac{2}{49}{x}^{2})(7x-18)$ ?

asked 2021-12-16

Subtract. $(5{x}^{2}-5x+2)-(-x+6x+5)$

asked 2022-01-17

Is the function in f(x)=x/29+2/x a rational function? If so, write it in the form 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.

asked 2021-12-10

Factor the polynomial. $12{x}^{2}-x-6$

asked 2022-01-31

The standard form of $y=6{(x-1)}^{3}-8{(x-3)}^{2}$ ?

asked 2021-12-02

Factor each polynomial completely.

1.3x+15

2.4x-20

3.${x}^{2}-7x+10$

1.3x+15

2.4x-20

3.