Factor completely. If the polynomial cannot be factored say it is prime.
1) 15x^3 + 19x^2 + 6x
A) (3x^2 +2)(5x+3)
B) x(3x+2)(5x+3)
C) x^2(3x+2)(5x+3)
D) x(5x+2)(3x+3)
E) Prime
I chose E) Prime.
2) 2x^2 - 14x - 6x + 42
A) 2(x+7)(x+3)
B) (x+7)(2x-6)
C) 2(x-7)(x-3)
D) (x-7)(x-3)
E) Prime
I know that this is 2x^2 - 20 + 42 when you combine the 14x and 6x so I chose answer E) Prime but I am not sure for this one.
1. Why don't you expand A) and see what you get?
2.
2x^2 - 14x - 6x + 42
= 2x(x-7) - 6(x-7)
= (x-7)(2x-6)
= 2(x-7)(x-3)
Just like what Reiny said, just try and expand it yourself. See what you can find! :)
To factor a polynomial completely, you need to determine if there are any common factors and then apply factoring techniques such as factoring by grouping, factoring trinomials, or using special factoring formulas like the difference of squares or perfect square trinomials.
1) The polynomial 15x^3 + 19x^2 + 6x:
First, check if there are any common factors among the terms. In this case, there is a common factor of x:
x(15x^2 + 19x + 6)
Next, try factoring the remaining quadratic trinomial. In this case, we can use factoring by grouping:
x(5x + 3)(3x + 2)
Therefore, the fully factored form is x(5x + 3)(3x + 2).
Since the polynomial has been factored completely, the correct answer is A) (3x^2 + 2)(5x + 3).
2) The polynomial 2x^2 - 14x - 6x + 42:
Rearrange the terms to group the polynomial:
2x^2 - (14x + 6x) + 42
Combine like terms within the parentheses:
2x^2 - 20x + 42
In this case, the polynomial is a quadratic trinomial. We can try factoring it using various methods such as factoring by grouping, but in this case, none will work. So, we can conclude that the polynomial cannot be factored further and is therefore prime.
Therefore, the correct answer is E) Prime.