Factorize -2 x4-x3-14 x2-19 x-6Please provide solution-

2x⁴+x³ 14x² 19x 6 Putting x=3 p(3)=2(3)⁴+(3)³ 14(3)² 19(3) 6 = gt;0 (x 3) is a factor Dividing 2x⁴+x³ 14x² 19x 6 by x 3 x 3) 2x⁴+x³ 14x² 19x 6( 2x³+7x²+7x+2 ...

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Byju's Answer

Standard IX

Mathematics

Identity (x+y)(x-y)

Factorize -2 ...

Question

Factorize -
2x⁴ + x³ - 14x² - 19x - 6.
Please provide solution.

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Solution

2x⁴+x³-14x²-19x-6
Putting x=3
p(3)=2(3)⁴+(3)³-14(3)²-19(3)-6
=>0
(x-3) is a factor

Dividing 2x⁴+x³-14x²-19x-6 by x-3

x-3) 2x⁴+x³-14x²-19x-6( 2x³+7x²+7x+2
-2x⁴+6x³
__
7x³-14x²
-7x³+21x²
_
7x²-19x
-7x²+21x
_
2x-6
-2x+6
___
00
=>2x³+7x²+7x+2
≈≈≈×≈≈≈≈≈×
2x⁴+x³-14x²-19x-6
=>(x-3)(2x³+7x²+7x+2)
=>(x-3){2(x³+1)+7x(x+1)}
=>(x-3)(2+7x)(x³+x+2)

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Similar questions

Q. Factorize :

2 x^{4} + x^{3} - 14 x^{2} - 19 x - 6

Q. Obtain all zeros of the polynomial f(x) = 2x⁴ + x³ − 14x² − 19x − 6, if two of its zeros are −2 and −1.

Q. If the quotient on dividing

2 x^{4} + x^{3} - 14 x^{2} - 19 x + 6

2 x + 1

x^{3} + a x^{2} - b x - 6

.
Find the values of a and b, also the remainder

Q. Find

k

so that

(x^{2} + 2 x + k)

is a factor of

(2 x^{4} + x^{3} + - 14 x^{2} + 5 x + 6)

Q. Find

k

so that

x^{2} + 2 x + k

is a factor of

2 x^{4} + x^{3} - 14 x^{2} + 5 x + 6

. Also, find the zeroes of the two polynomials.

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Factorize - 2x⁴ + x³ - 14x² - 19x - 6. Please provide solution.

Factorize -
2x⁴ + x³ - 14x² - 19x - 6.
Please provide solution.