Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write a polynomial of least degree with roots $-1$ and $5$ . $\newline$ Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $\newline$ ______

View step-by-step help

View step-by-step help

Write a polynomial from its roots

Full solution

Q. Write a polynomial of least degree with roots

-1

and

5

.

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

\newline

______

Identify root $-1$ factor: The factor for the root $-1$ is $(x - (-1))$ which simplifies to $(x + 1)$ .
Identify root $5$ factor: The factor for the root $5$ is $(x - 5)$ .
Multiply factors: Now, we multiply the factors $(x + 1)$ and $(x - 5)$ to get the polynomial.
Combine factors to get polynomial: $x + 1)(x - 5) = x^2 - 5x + x - 5$ which simplifies to $x^2 - 4x - 5$ .

More problems from Write a polynomial from its roots

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 2 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 1 month ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 2 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 2 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 2 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 2 months ago