Question

16 X square + a x + 7 is divided by x minus 2 the remainder is 13 what is the value of a

Answer 1

Hello student :)

Given, 16x² + ax + 7 is divided by ( x - 2 ) to obtain a remainder 13 .

Let the polynomial be f(x) ,

According to the remainder theorem which states that if a polynomial p(x) is divided by (x-a) it leaves a remainder p(a)

Here, f(2) is the remainder .

f(2) = 16(2²) + a(2)+ 7

= 16(4) + 2a + 7

= 71 + 2a

According to the question,
71 + 2a = 13
2a = 13 - 71
2a = -58
a = -29 .

Therefore, The value of a is -29 .

Answer 2

$given: \\ \\ p(x) = 16 {x}^{2} + ax + 7. \\ \\ it \: is \: divided \: by \: x - 2. \\ \\ so \: according \: to \: remainder \: \\ theorem \: the \: remainder \: will \: be \: \\ p(2).$


$p(2) = 16 \times {(2)}^{2} + a \times (2) + 7. \\ = 16 \times 4 + 2a + 7. \\ = 64 + 2a + 7. \\ = 71 + 2a.$


$it \: is \: also \: given \: that \: the \: remainder \: is \: 13$


$therefore \: 71 + 2a = 13. \\ 2a = 13 - 71 \\ 2a = - 58 \\ a = \frac{ - 58}{2} \\ a = - 29.$


Therefore, a = -29.