Question

show that x+3 is a factor of 69 + 11x - x2 +x3​

Answer 1

Answer:

${x}^{3} - {x}^{2} + 11x + 69$

$x + 3 = 0 \\ x = - 3$

Trying to prove using factor theorem

$( -3)^{3} -({ - 3})^{2} + 11( - 3)+ 69 = 0$

$- 27 - 9 - 33 + 69 = 0$

$- 69 + 69 = 0$

$0 = 0$

Hence, proved

Answer 2

Answer:

True.

Step-by-step explanation:

Let $P(x)=x^3-x^2+11x+69$.

When x+3 is a factor and $f(x)$ is the quotient.

$P(x)=(x+3)f(x)$

If we let x=-3, the term x+3 will become 0.

$P(3)=0f(3)=0$

$P(3)=-27-9-33+69=69-69=0$

Hence, x+3 is a factor.

This is called factor theorem.