Question

if ( x +1 ) is a factor of ax cube + 2x square -x + 3a -7 then find the value of A

Answer 1

Answer:

value of a will be 2

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Answer 2

GIVEN :-

(x + 1) is a factor of ax³ + 2x² - x + 3a - 7

TO FIND :-

Value of a = ?

SOLUTION :-

By using factor theorem,

(x + 1) = 0

➝ x = 0 - 1

➝ x = -1

p(x) = ax³ + 2x² - x + 3a - 7 = 0

Now, substitute the value of x in the given equation.

p(-1) = a(-1)³ + 2(-1)² - (-1) + 3a - 7 =  0

➥ p(-1) = -1a + 2 + 1 + 3a - 7 = 0

➟ p(-1) = -1a + 3 + 3a - 7 = 0

↦ p(-1) = -1a + 3a - 4 = 0

⇢ p(-1) = 2a - 4 = 0

➳ p(-1) = 2a = 4

⇒ p(-1) = a = 2

So, the value of a = 2

Know more:

• Factor theorem states that a polynomial f(x) has a factor (x - a) if and only if f(a) = 0
• Remainder theorem states that when a polynomial p(x) is divided by any binomial (x - a), then the remainder so obtained is p(a)