When x^2-5x+3c is divided by x-3 the remainder is -12. What is the value of c?
Hmm... let me put on my mathematical clown nose and give this a shot! 🤡
Okay, here's a joke to lighten the mood before we dive into the math: Why don't scientists trust atoms? Because they make up everything! 😉
Now, let's tackle the problem. When a polynomial is divided by a linear expression, the remainder is obtained by substituting the divisor into the polynomial. So, we can substitute x = 3 into the polynomial x^2 - 5x + 3c.
When we do that, the equation becomes:
(3)^2 - 5(3) + 3c = -12
Simplifying this equation gives us:
9 - 15 + 3c = -12
-6 + 3c = -12
Now, let's solve for c:
3c = -12 + 6
3c = -6
c = -6/3
c = -2
So, my clownish calculation tells me that the value of c is -2. Ta-da! 🎉
Remember, math may be serious business, but there's nothing wrong with adding a little humor to make it more fun! If you need any more assistance or a joke, feel free to ask.
To find the value of c, we need to utilize the Remainder Theorem. According to the theorem, if a polynomial f(x) is divided by x - a and the remainder is R, then f(a) = R.
In this case, we are given x^2 - 5x + 3c is divided by x - 3, and the remainder is -12.
Let's substitute x = 3 and equate it to the remainder:
(3)^2 - 5(3) + 3c = -12
9 - 15 + 3c = -12
-6 + 3c = -12
Next, let's isolate 3c by subtracting -6 from both sides of the equation:
3c = -12 + 6
3c = -6
Finally, divide both sides of the equation by 3 to solve for c:
c = -6/3
c = -2
Therefore, the value of c is -2.
To find the value of c, we need to apply the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by a binomial x-a, then the remainder is equal to f(a).
In this problem, we are given that x^2 - 5x + 3c is divided by x - 3, and the remainder is -12. According to the Remainder Theorem, when we substitute x = 3 into the polynomial x^2 - 5x + 3c, it should give us -12.
So, let's substitute x = 3 into the polynomial x^2 - 5x + 3c and set it equal to -12:
(3)^2 - 5(3) + 3c = -12
Simplifying further:
9 - 15 + 3c = -12
-6 + 3c = -12
Next, we can isolate the term with c by moving the constant term to the other side:
3c = -12 + 6
3c = -6
Finally, we can solve for c by dividing both sides of the equation by 3:
c = -6/3
c = -2
Therefore, the value of c is -2.