What is the remainder when 6x2 – 11x + 15 is divided by 2x – 5?a)15b)25c)35d)– 25Correct answer is option 'B'. Can you explain this answer?

Question

What is the remainder when 6x2 &ndash; 11x + 15 is divided by 2x &ndash; 5?a)15b)25c)35d)&ndash; 25Correct answer is option 'B'. Can you explain this answer?

Answer

Answer

Answer

Understanding Polynomial Division
To find the remainder when $6x^2 - 11x + 15$ is divided by $2x - 5$, we can use the Remainder Theorem. The theorem states that the remainder of a polynomial $f(x)$ divided by $ax - b$ is $f\left(\frac{b}{a}\right)$.
Step 1: Identify the Polynomial and Divisor
- Let $f(x) = 6x^2 - 11x + 15$
- Divisor: $2x - 5$
Step 2: Find the Value to Substitute
- Set $2x - 5 = 0$ to find $x$:
$2x = 5$
$x = \frac{5}{2}$
Step 3: Substitute into the Polynomial
Now, substitute $x = \frac{5}{2}$ into $f(x)$:
- Calculate $f\left(\frac{5}{2}\right)$:
$$
f\left(\frac{5}{2}\right) = 6\left(\frac{5}{2}\right)^2 - 11\left(\frac{5}{2}\right) + 15
$$
$$
= 6 \cdot \frac{25}{4} - \frac{55}{2} + 15
$$
$$
= \frac{150}{4} - \frac{110}{4} + \frac{60}{4}
$$
$$
= \frac{150 - 110 + 60}{4} = \frac{100}{4} = 25
$$
Final Answer
The remainder when $6x^2 - 11x + 15$ is divided by $2x - 5$ is $25$.
Thus, the correct option is b) 25.

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