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 ...

121

You visited us 121 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 $x^{2} - 4 x + 3 ?$