What must be subtracted from the polynomial p-x4-2x3-13x2-12x-21 so that the resulting polynomial is exactly divisible by x2-4x-3-

Step 1: DivisionLet0ex0exx^2 4x+3 x^2 +6x + 8)x^4+ 2x^3 13x^2 12x + 21)x^4 4x^3+3x^2/)6x^3 16x^2 12x)6x^3 24x^2+18x/) 8x^2 30x+21)8x^2 32x+24/2x 30ex0e ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Division of Decimals

What must be ...

Question

What must be subtracted from the polynomial $p (x) = x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21$ so that the resulting polynomial is exactly divisible by $x^{2} - 4 x + 3 ?$

Open in App

Solution

Step 1: Division
$Let x^{2} - 4 x + 3 x^{2} + 6 x + 8 x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21$
$\frac{x^{4} - 4 x^{3} + 3 x^{2}}{6 x^{3} - 16 x^{2} - 12 x}$
$\frac{6 x^{3} - 24 x^{2} + 18 x}{8 x^{2} - 30 x + 21}$
$\frac{8 x^{2} - 32 x + 24}{2 x - 3} \frac{}{}$
Step 2: Subtracting the remainder
$In order to divide the p (x) by x^{2} - 4 x + 3 we subtract the remainder r (x) = 2 x - 3 to p (x) i . e ., (x^{4} + 2 x^{3} - 13 x^{2} - 12 x - 21) - (2 x - 3) = x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24 Now for Verification :$
$x^{2} - 4 x + 3 x^{2} + 6 x + 8 x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24$
$\frac{x^{4} - 4 x^{3} + 3 x^{2}}{6 x^{3} - 16 x^{2} - 14 x}$
$\frac{6 x^{3} - 24 x^{2} + 18 x}{8 x^{2} - 32 x + 24}$
$\frac{8 x^{2} - 32 x + 24}{0} \frac{}{}$
Hence verified
Therefore, the subtracted polynomial is $2 x - 3$

Suggest Corrections

Similar questions

Write the face value and place value of the digits shown in colour.

$340671$

Write the face value and place value of the digits shown in colour.

b) $257208$

What must be subtracted from polynomial $f (x) = x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21$ so that the resulting polynomial is exactly divisible by $x^{2} - 4 x + 3$ ?

Divide $3 x^{3} + 5 x^{2} + 2 x + 7 by x^{2} + 2 x + 3,$ find the quotient and remainder and verify the division algorithm.

Find all the zeroes of $2 x^{4} - 3 x^{3} - 3 x^{2} + 6 x - 2$ , if two of its zeroes are $\sqrt{2}$ and $- \sqrt{2} .$

Join BYJU'S Learning Program

What must be subtracted from the polynomial p(x)=x4+2x3-13x2-12x+21 so that the resulting polynomial is exactly divisible by x2-4x+3?

What must be subtracted from the polynomial $p (x) = x^{4} + 2 x^{3} - 13 x^{2} - 12 x + 21$ so that the resulting polynomial is exactly divisible by $x^{2} - 4 x + 3 ?$