hey i can't figure this one out, does anyone know the answer?
Question: Shenika factored the polynomial completely. What is the value of A?
5x3+35x2+6x+42
(5x2+A)(x+B)
A. 1
B. 5
C. 6
D. 7
(if anyone is confused why this question is written weird, i don't know why its like that either)
Nothing at all wrong with this question, nor the way it is written
so you have:
(5x^2+A)(x+B) = 5x^3+35x^2+6x+42 , ..... notice how I wrote the powers.
expand the left side:
5x^3 + 5Bx^2 + Ax + AB
match the terms:
5x^3 <----> 5x^3
5Bx^2 <----> 35x^2 , so 5B = 35, then B = 7
Ax <----> 6x , then A = 6
AB <----> 42 , true since AB = 6*7 = 42
A = 6
B = 7 , so C is your correct choice
check, sub those values into the factored form,
(5x^2+6)(x+7)
= 5x^3 + 35x^2 + 6x + 42 , which is the expanded form given
So, my answer is correct
(and yes, im this bad at math)
Ah thanks so much!
To find the value of A, you need to understand how to factor a polynomial. In this case, Shenika has factored the given polynomial into the form (5x^2+A)(x+B).
To find the value of A, you should compare the coefficient of x in the original polynomial (6x) with the coefficient of x in the factored form [(5x^2 + A)(x + B)].
Since the coefficient of x in the original polynomial is 6, it must be equal to the sum of the coefficients of x in the factored form. This means:
6 = (coefficient of x in the first binomial) + (coefficient of x in the second binomial)
In the factored form, there is only one term involving x, which is (x + B). Therefore, the coefficient of x in the second binomial is 1.
Hence, you can write:
6 = (5x^2) + (1)
Now, solve for A by comparing the coefficients of x^2 in the original polynomial (0) and the factored form (5x^2 + A):
0 = 5x^2
Since the coefficients of x^2 are equal, you can conclude that A must be 0.
Thus, the correct answer is:
A. 0
Note: It seems there was a typo in the answer choices you provided, as none of them indicate this correct answer.