Question

If (x – 3) is a factor of x2 – kx -+ 12. The find the value of ‘k’. Also find the other factor for this value of ‘k’.

Answer 1

p(x) = x² - kx + 12

x -3 is a factor of p(x)

x - 3 = 0

x = 3

p(3) = 0

p(3) = 3² - 3k + 12

9 - 3k + 12 = 0

21 - 3k = 0

21 = 3k

k = 7

Hope this helps you !

Answer 2

Answer:

The value of k is 7 and the other factor for this value of ‘k’ is (x-4).

Step-by-step explanation:

P(x)=$x^2-kx+12$

(x-3)is a factor of P(x)

So, 3 is the zero of the polynomial

Substitute x = 3 in P(x)

$x^2-kx+12=0$

$3^2-k(3)+12=0$

$9-k(3)+12=0$

$-k(3)+21=0$

$\frac{21}{3}=k$

$7=k$

So, P(x)=$x^2-7x+12$

Now To find other factor

Dividend = $x^2-7x+12$

Divisor = x-3

$Dividend= (Divisor \times quotient)+Remainder$

$x^2-7x+12= ( x-3 \times x-4)+0$

Quotient = x-4

Hence the value of k is 7 and the other factor for this value of ‘k’ is (x-4).