Match each polynomial in standard form to its equivalent factored form.
Standard forms:
8x^3+1
2x^4+16x
x^3+8
the equivalent equation that would match with it
(x+2)(x2−2x+4)
The polynomial cannot be factored over the integers using the sum of cubes method.
(2x+16)(4x^2−32x+64)
(x+1)(4x^2−2x+1)
2x(x+2)(x^2−2x+4)
(x+8)(x^2−16x+64)
(2x+1)(4x^2−2x+1)
For equation 1) 8x^3+1 I believe the matching product is (x+8)(x^2−16x+64)
For equation 2) (2x+16)I believe the matching product is (4x^2−32x+64)
For equation 3) x^3+8 I believe the matching product is (x+1)(4x^2−2x+1)
I am not really sure at all I am struggling with this subject
your factoring is correct.
sum and difference of cubes can always be factored.
8x^3+1 = (2x)^3 + 1^3 = ((2x)+1)((2x)^2 - (2x)(1) + 1^2)
= (2x+1)(4x^2-2x+1)
2x^4+16x = 2x(x^3+1) = 2x(x+1)(x^2-x+1)
x^3+8 = x^3 + 2^3 = ...
would the third one be (x+2)(x2−2x+4)
or The polynomial cannot be factored over the integers using the sum of cubes method.
2x^4+16x = 2x(x^3+1) = 2x(x+1)(x^2-x+1)
Is not a choice I am confused.
Yeah I was looking at that and was wondering of I messed up some where
To match each polynomial in standard form to its equivalent factored form, we need to factor each polynomial. Let's go through the process for each polynomial:
1) 8x^3 + 1:
To factor this polynomial, we can use the sum of cubes formula, which states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2). In this case, let's rewrite 8x^3 as (2x)^3 and 1 as 1^3. Applying the sum of cubes formula, we have:
8x^3 + 1 = (2x)^3 + 1^3
= (2x + 1)(4x^2 - 2x + 1)
So, the factored form of 8x^3 + 1 is (2x + 1)(4x^2 - 2x + 1).
2) 2x^4 + 16x:
To factor this polynomial, we can factor out the greatest common factor, which is 2x. Dividing each term by 2x, we get:
2x^4 + 16x = 2x(x^3 + 8)
Therefore, the factored form of 2x^4 + 16x is 2x(x + 2)(x^2 - 2x + 4).
3) x^3 + 8:
Similar to the first polynomial, we can apply the sum of cubes formula:
x^3 + 8 = x^3 + 2^3
= (x + 2)(x^2 - 2x + 4)
Hence, the factored form of x^3 + 8 is (x + 2)(x^2 - 2x + 4).
Now, let's match each factored form with its equivalent polynomial in standard form:
1) The polynomial (x + 2)(x^2 - 2x + 4) matches with the standard form 8x^3 + 1.
2) The polynomial 2x(x + 2)(x^2 - 2x + 4) matches with the standard form 2x^4 + 16x.
3) The polynomial (x + 1)(4x^2 - 2x + 1) matches with the standard form x^3 + 8.
I hope this explanation clarifies how to match each polynomial to its factored form and vice versa.