Answer:
Therefore, the value of 'a' is -9.
Explanation:
To find the value of 'a', we need to use the Remainder Theorem. According to the theorem, if a polynomial f(x) is divided by (x - p), the remainder is equal to f(p).
In this case, we have the polynomial 5x² - 2x + a divided by (x - 2), and the remainder is given as 7. So, we can set up the equation:
5(2)² - 2(2) + a = 7
Simplifying the equation, we get:
20 - 4 + a = 7
Combining like terms, we have:
16 + a = 7
To find 'a', we can subtract 16 from both sides of the equation:
a = 7 - 16
Simplifying further, we get:
a = -9
Therefore, the value of 'a' is -9.