Question

Using factor theorem show that x + 3 is factor of 6x3 + 7x2 – 29x + 12​

Answer 1

Answer:

therefore it is proved.

Answer 2

Let us assume

(x + 3) is a factor of 6x³ + 7x² - 29x + 12

Since (x + 3) is a factor,

x + 3 = 0

⇒ x = -3

By Factor theorem,

Substitute value of x in the given equation.

p(x) = 6x³ + 7x² - 29x + 12

p(-3) = 6(-3)³ + 7(-3)² - 29(-3) + 12

⇒ p(-3) = 6(-27) + 7(9) - (-87) + 12

⇒ p(-3) = -162 + 63 + 87 + 12

⇒ p(-3) = -162 + 162

⇒ p(-3) = 0

By Factor theorem,

(x + 3) is a factor of 6x³ + 7x² - 29x + 12

Additional Information:

• Factor theorem states that (x - a) is a factor of the polynomial p(x), if p(a) = 0.
• It's Converse: Also, if (x - a) is a factor of p(x), then p(a) = 0, where a is any real number.