Factoring polynomials | Practice Problems, Examples & Solutions

Factoring Binomials and Perfect Square Trinomials

Prealgebra and Introductory Algebra

For Exercises 140 to $143,$ find all integers $k$ such that the trinomial can be factored over the integers.
$$y^{2}+4 y+k$$

Factoring

Factoring Polynomials of the Form $x^{2}+b x+c$

01:12

Prealgebra and Introductory Algebra

State whether the trinomial has a factor of $x+3$
a. $3 x^{2}-3 x-36$
b. $x^{2} y-x y-12 y$

Factoring

Factoring Polynomials of the Form $x^{2}+b x+c$

01:07

Prealgebra and Introductory Algebra

Find all integers $k$ such that the trinomial is a perfect-square trinomial.
$$x^{2}+10 x+k$$

Factoring

Special Factoring

Applications of Quadratic Equations

5 Practice Problems

02:36

Beginning and Intermediate Algebra

A famous comedian will appear at a comedy club for one performance. The equation $R(p)=-5 p^{2}+300 p$ describes the relationship between the price of a ticket,
$p,$ in dollars, and the revenue, $R,$ in dollars, from ticket sales. That is, the revenue is a function of price.
a) Determine the club's revenue from ticket sales if the price of a ticket is $\$ 40$
b) Determine the club's revenue from ticket sales if the price of a ticket is $\$ 25$
c) If the club is expecting its revenue from ticket sales to be $\$ 4500,$ how much should it charge for each ticket?

Factoring Polynomials

Applications of Quadratic Equations

03:27

Beginning and Intermediate Algebra

A wire is attached to the top of a pole. The pole is $2 \mathrm{ft}$ shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 ft less than the length of the wire. Find the length of the wire and the height of the pole.

Factoring Polynomials

Applications of Quadratic Equations

00:48

Beginning and Intermediate Algebra

In your own words, explain the Pythagorean theorem.

Factoring Polynomials

Applications of Quadratic Equations