4m^4-24m³+33m²+9m-9=0
help me with factor
(8m^2-24m-3+3√17)/4 * (8m^2-24m-3-3√17)/4
4m⁴-24m³+33m²+9m-9=0
re-write the polynomial equation as:
4m⁴-24m³+36m²-3m²+9m-9=0
because: 36m²-3m²=33m²
re-grouping
(4m⁴-24m³+36m²)-(3m²-9m)-9
factor out 4
4(m⁴-6m³+9m²)-(3m²-9m)-9
note:
m⁴-6m³+9m²=(m²-3m)²
therefore,we ve:
4(m²-3m)²-(3m²-9m)-9=0
4(m²-3m)-3(m²-3m)-9=0
so,another form of rewriting 4m⁴-24m³+33m²+9m-9=0, is
4(m²-3m)²-3(m²-3m)-9=0
let
(m²-3m)=a
therefore,we ve:
4a²-3a-9=0
solve for a.
recall:
solving the two equation quadratically will give the root of the polynomial
then u no what to do agn
i think steve is right
To factorize the given polynomial, we need to find the factors that satisfy the equation when multiplied together. Here are the steps to factorize the polynomial:
Step 1: Check for a common factor
First, check if there is a common factor that can be factored out from all the terms. In this case, the only common factor is 1.
Step 2: Find the possible factor pairs for the constant term
The constant term of the polynomial is -9. We need to find pairs of factors of -9 that add up to the coefficient of the linear term, which is 9. The pairs of factors for -9 are (-1, 9) and (1, -9).
Step 3: Check for the rational roots using the factor pairs
To find the possible rational roots, we use the factor pairs found in step 2 in the form of p/q, where p is the factor of the constant term (-9) and q is the factor of the leading coefficient (4 in this case) of the highest degree term. The possible rational roots are: ±1, ±3/2, ±9/2.
Step 4: Apply synthetic division or long division to find the factors
Using synthetic division or long division, divide the polynomial by each possible rational root obtained in step 3. The resulting quotient and remainder will help us determine if the root is a factor.
Step 5: Factorize the polynomial
From step 4, if any of the possible rational roots are found to be factors, we can rewrite the polynomial as a product of factors:
(potential factor) × (remaining quadratic polynomial)
Repeat this process until we have completely factored the polynomial.
Note: If the polynomial cannot be factored using rational roots, it may require more advanced techniques like factoring by grouping, quadratic formula, or completing the square.
By following the steps above, you should be able to factorize the given polynomial.