Advertisements
Advertisements
Question
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Solution
\[\text{We have to find the value of a if} (x + 2) \text{is a factor of} (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a) . \]
\[\text{Substituting}\ x = - 2\ \text{in}\ 4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a, \text{we get:} \]
\[4( - 2 )^4 + 2( - 2 )^3 - 3( - 2 )^2 + 8( - 2) + 5a = 0\]
\[or, 64 - 16 - 12 - 16 + 5a = 0\]
\[or, 5a = - 20\]
\[or, a = - 4\]
\[ \therefore If (x + 2) \text{is a factor of}\ (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a), a = - 4 . \]
APPEARS IN
RELATED QUESTIONS
Divide 24a3b3 by −8ab.
Divide 5x3 − 15x2 + 25x by 5x.
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Divide 9x4 − 4x2 + 4 by 3x2 − 4x + 2 and find the quotient and remainder.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
Divide 15y4 + 16y3 +\[\frac{10}{3}\]y − 9y2 − 6 by 3y − 2. Write down the coefficients of the terms in the quotient.
Find whether the first polynomial is a factor of the second.
y − 2, 3y3 + 5y2 + 5y + 2
Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
7ab3 ÷ 14ab = 2b2
The denominator of a fraction exceeds Its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get `3/2`. Find the original fraction.
