Finding the GCF of a Polynomial
For the partially complete factorization, find the other binomial which will complete the factorization.
\[
a^{2}+7 a-18=(a+9)(
\]
Factoring Out Greatest Common Factor (GCF)
Factor the given polynomial by finding the greatest common monomial factor (or the negative of the greatest common monomial factor) and rewrite the expression.
\[
33+3 x^{3}
\]
Identifying the Common Factors
Factorize the polynomial \(36x^3y^2 - 48x^2y^3 + 60x^4y\)
Finding the LCM using GCF
Find the least common multiple (LCM) of the polynomials \(4x^2-9\) and \(2x-3\).
Finding the GCF
Find the greatest common factor (GCF) of the polynomials \(12x^3y^2 - 18x^2y^3 + 24x^4y\)
Factoring Trinomials
Question 4 (2 points)
Factor:
\[
x^{2}+7 x+12
\]
Trinomial Squares
Factor the trinomial square \(x^2 - 10x + 25\).
Factoring Using Any Method
Short Fall 2023
Question 10, 4.3.39
Part 1 of 2
HW Score: $75 \%, 7.5$ of 10 points
Points: 0 of 1
Factor the polynomial function $f(x)$. Then solve the equation $f(x)=0$.
\[
f(x)=x^{3}+6 x^{2}+3 x-10
\]
The factored polynomial function is $f(x)=$ (Factor completely)
Factoring a Difference of Squares
Factorize the following expression: \(x^{4} - 256\)
Factoring a Sum of Cubes
Factor the expression \(x^3 + 27\).
Factoring by Grouping
Factor by grouping (sometimes called the ac-method).
\[
28 x^{2}-x-2
\]
First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization.
Form:
\[
28 x^{2}+\square x+\square x-2
\]
$28 x^{2}+\square x-\square x-2$
$28 x^{2}-\square x+\square x-2$
$28 x^{2}-\square x-\square x-2$
Factorization:
Factoring a Difference of Cubes
Factor the expression \(x^3 - y^3\).
Determine if an Expression is a Factor
1 point
Which expression is a factor of \( x^{2}+3 x-40 ? \)
A. \( (x-4) \)
B. \( (x-5) \)
C. \( (x-8) \)
D. \( (x-10) \)
Determining if Factor Using Synthetic Division
Use synthetic division to find the quotient and remainder when $9 x^{6}-5 x^{4}+5 x^{2}+6$ is divided by $x-2$.
The quotient is The remainder is
Find the Factors Using the Factor Theorem
Given $f(x)=6 x^{3}+5 x^{2}-12 x+4$, answer the following.
Part: 0 / 2
Part 1 of 2
Factor $f(x)$, given that $\frac{1}{2}$ is a zero.
\[
f(x)=
\]
Determining if the Expression is a Polynomial
Given the expression \(5x^3+2x^2-3x+4\), is it a polynomial? If yes, factorize it.
Determining if Polynomial is Prime
Exercise 6. Show that the following polynomials are irreducible over \( \mathbb{Q} \)
1) \( A=x^{4}-4 x^{3}+6 \)
2) \( B=4 x^{3}-15 x^{2}+60 x+180 \)
3) \( C=8 x^{3}+6 x^{2}-9 x+24 \)
Determining if the Polynomial is a Perfect Square
Is the polynomial \(x^4 - 2x^2 + 1\) a perfect square? If yes, factorize it.
Expand using the Binomial Theorem
A.Convert from factored form to standard form
b. $A(x)=(x-4)(x+1)$
Factoring over the Complex Numbers
Factorize the polynomial \(x^3 - 8\) over the complex numbers.
Finding All Integers k Such That the Trinomial Can Be Factored
Form a polynomial whose real zeros and degree are given.
Zeros: $-2,0,5$; degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1.
$f(x)=\square$ (Simplify your answer. $)$