Find the value of k, if x + 3 is a factor of 3x² + kx + 6. *

Given:

Polynomial = P(x) = 3x² + kx + 6

Factor of the ablove polynomial = (x+3)

To Find:

Value of K, for which (x+3) become the factor of P(x) = 3x² + kx + 6

Solution :

Now,

x + 3 = 0

⇒x = (-3)

So,

As (x+3) is a factor so x = (-3) is one root of the polynomial.

Therefore,

P(-3) = 0

→ P(-3) = 3(-3)² + k(-3) + 6 = 0

→ 3(9) - 3k + 6 = 0

→ 27 - 3k + 6 = 0

→ 27 + 6 - 3k = 0

→ 33 - 3k = 0

→ - 3k = -33

→ k = -33 ÷ -3

→ k = 11

3x²+ kx + 6, by putting the value of k = 11 and taking -3 as root the remainder should be zero

→ 3x²+ 11x + 6

→ 3(-3)² + 11(-3) + 6

→ 3(9) - 33 + 6

→ 27 - 33 + 6

→ 27 + 6 - 33

→ 33 - 33

→ 0

Hence verified !

check the picture below.

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13