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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
What else can I help you with?
How do you find a degree of a graphed polynomial?
Factors
How do you factor a polynomial if their are more than one factors?
Factor it once, and then factor the factors.
What does factor theorem mean?
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
When you factor with tiles the height and width of the rectangle are the factors of the polynomial?
True
How do you find the remaining factors of this polynomial Find the remaining factors of 3x to the 3rd 11x to the 2nd-27x-35 if x 5 is a factor?
You need to know whether the given factor is x + 5 or x - 5. Then it is a simple problem in long division.
How do you find a degree of a graphed polynomial?
Factors
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - b is a factor?
a
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - a is a factor?
B
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - c is a factor?
a
You can also use of a polynomial to help you find its factors and roots?
graph!
You can use the BLANK of a polynomial to help you find its factors or roots?
Graph factor
You can also use the of a polynomial to help you find its factors?
graph apex xD
When a polynomial is divided by one of its binomial factors what is the quotient called?
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.
What is the relationship between zeros and factors?
Zeros and factors are closely related in polynomial functions. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero, while a factor is a polynomial that divides another polynomial without leaving a remainder. If ( x = r ) is a zero of a polynomial ( P(x) ), then ( (x - r) ) is a factor of ( P(x) ). Thus, finding the zeros of a polynomial is equivalent to identifying its factors.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
How do you know if you have simplified a polynomial correctly?
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
Why might it be useful to know the linear factors of a polynomial function?
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.
