Question

if the polynomial ay^3 +4y^2 + 3y-4
and y^3 - 4y +a leaves the same
remainder when clividlecl by y-3
find a

Answer 1

Answer:

-1

Step-by-step explanation:

divide the given polynomials by y-3 and equate your reminders in both cases to get the suitable answer

I hope this would help you.

Answer 2

Value of a is -1.

Given:

• Two polynomial.
• $a {y}^{3} + 4 {y}^{2} + 3y - 4$ and ${y}^{3} - 4y + a$.
• When divide by (y-3) leaves same remainder.

To find:

• Find value of a.

Solution:

Concept to be used:

• Apply remainder theorem.
• Remainder Theorem: It states that if polynomial p(x) is divided by (x-a) then remainder will be p(a).

Step 1:

Let first polynomial is p(y).

$p(y) = a {y}^{3} + 4 {y}^{2} + 3y - 4$

put y=3 in p(y).

$p(3) = a {(3)}^{3} + 4 {(3)}^{2} + 3(3) - 4$

or

$p(3) =27 a + 36 + 9 - 4$

or

$\bf \red{p(3) = 27a + 41...eq1}$

Step 2:

Let the second polynomial is g(y).

$g(y) = {y}^{3} - 4y + a$

put y= 3 in g(y).

$g(3) = {(3)}^{3} - 4(3) + a$

or

$\bf \red{g(3) = 15 + a \: ...eq2}$

Step 3:

Equate both remainders.

$p(3) = g(3)$

or

$27 a + 41 = 15 + a$

or

$26a = - 26$

or

$\bf a = - 1$

Thus,

Value of a is -1.

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