Find the value of m if $x^{3} - 6 x^{2} + m x + 60$ leaves the remainder 2 when divided by $(x + 2)$ .

Open in App

Solution

According to remainder theorem, when $f (x)$ is divided by $(x + 2)$ ,Remanider $= f (- 2) = 2$ (given).
$f (x) = x^{3} - 6 x^{2} + m x + 60$
$f (- 2) = (- 2)^{3} - 6 (- 2)^{2} + (- 2) m + 60$
$⟹ 2 = - 8 - 24 - 2 m + 60$
$⟹ 2 m = 28 - 2 = 26$
$⟹ m = \frac{26}{2} = 13$

Suggest Corrections

Similar questions

When $x^{3} + 3 x^{2} - m x + 4$ is divided by x- 2, the remainder is m + 3 find the value of m.

If the polynomials $x^{3} + 3 x^{2} - m$ and $2 x^{3} - m x + 9$ leave the same remainder when they are divided by $(x - 2)$ , find the value of $m$ . Also find the remainder.

If $x^{3} + m x^{2} + n x + 6$ has $(x - 2)$ as factor and leaves a remainder $3$ when divided by $(x - 3)$ find the values of $m, n$

Find the value of 'm', if $m x^{3} + 2 x^{2} - 3$ and $x^{2} - m x + 4$ leave the same remainder when each is divided by x - 2.

Q. If (x³ + mx² − x + 6) has (x − 2) as a factor and leaves a remainder r when divided by (x − 3), find the values of m and r.

Join BYJU'S Learning Program

Find the value of m if x3−6x2+mx+60 leaves the remainder 2 when divided by (x+2).

According to remainder theorem, when f(x) is divided by (x+2),Remanider =f(−2)=2(given).f(x)=x3−6x2+mx+60f(−2)=(−2)3−6(−2)2+(−2)m+60⟹2=−8−24−2m+60⟹2m=28−2=26⟹m=262=13

Find the value of m if $x^{3} - 6 x^{2} + m x + 60$ leaves the remainder 2 when divided by $(x + 2)$ .

According to remainder theorem, when $f (x)$ is divided by $(x + 2)$ ,Remanider $= f (- 2) = 2$ (given).
$f (x) = x^{3} - 6 x^{2} + m x + 60$
$f (- 2) = (- 2)^{3} - 6 (- 2)^{2} + (- 2) m + 60$
$⟹ 2 = - 8 - 24 - 2 m + 60$
$⟹ 2 m = 28 - 2 = 26$
$⟹ m = \frac{26}{2} = 13$