Steps for factoring trinomials:
Example
20x**3-62x**2-28x
1. Factor out GCF from each term
20x**3-62x**2-28x - 2x(10x**2-31x-14)
2. Multiply First and Last term
10*-14=140
3. Find 2 factors of Step 2 (140) whose sum is the second term (-31)
140=2*2*5*7
-140=-2*70, 2*-70
-140=-5*28, 5*-28
-140=-7*20, 7*-20
-140=-4*35, 4*-35
-140=-10*14, 10*-14
4. Rewrite
2x(10x**2-31x-14) = 2x(10x**2+4x-35x-14)
5. Factor pairs of terms
2x(10x**2+4x-35x-14) = 2x(2x(5x+2)-7(5x+2))
6. Factor
2x(2x(5x+2)-7(5x+2)) = 2x((2x-7)(5x+2))
2x(2x-7)(5x+2)
Special cases
A. ax**2-b, where sqrt(a) and sqrt(b) are both whole numbers
ax**2-b = (sqrt(a)x+sqrt(b))(sqrt(a)x-sqrt(b))
4x**2-81 =(2x-9)(2x+9)
B. x**2+ax+b where b=c*d and a=c+d
x**2+ax+b = (x+c)(x+d)
x**2-8x-105
Factors of 105:
105=3*5*7
-105=-3*35, 3*-35
-105=-5*21, 5*-21
-105=-7*15, 7*-15
x**2-8x-105 = (x+7)(x+-15)
C. x**2+ax+b where b=c**2 and a=2c
x**2+ax+b = (x+c)**2
x**2+8x+16 = (x+4)**2
NOTES:
> b=c*d OR b=-c*-d
> -b=-c*d OR -b=c*-d
Factors
Factor it once, and then factor the factors.
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
True
You need to know whether the given factor is x + 5 or x - 5. Then it is a simple problem in long division.
Factors
a
B
a
graph!
graph apex xD
Graph factor
When a polynomial is divided by one of its binomial factors, the quotient is called the "reduced polynomial" or simply the "quotient polynomial." This resulting polynomial represents the original polynomial after removing the factor, and it retains the degree that is one less than the original polynomial.
false
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
It is useful to know the linear factors of a polynomial because they give you the zeros of the polynomial. If (x-c) is one of the linear factors of a polynomial, then p(c)=0. Here the notation p(x) is used to denoted a polynomial function at p(c) means the value of that function when evaluated at c. Conversely, if d is a zero of the polynomial, then (x-d) is a factor.
Completely Factored