Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

sir
   show that (x+1) 8(2x-3)are factors of 2x^3-9x^2+x+12
Asked by seeni2005 | 14 May, 2016, 11:51: AM
answered-by-expert Expert Answer
C o n s i d e r space t h e space g i v e n space p o l y n o m i a l
2 x cubed minus 9 x squared plus x plus 12
W e space n e e d space t o space p r o v e space t h a t comma space x plus 1 comma space x minus 4 space a n d space 2 x minus 3 space a r e space f a c t o r s space o f space t h e space a b o v e space p o l y n o m i a l.
L e t space f open parentheses x close parentheses equals 2 x cubed minus 9 x squared plus x plus 12
C o n s i d e r space t h e space f a c t o r space left parenthesis x plus 1 right parenthesis
I f space left parenthesis x plus 1 right parenthesis space i s space a space f a c t o r comma space t h e n space b y space f a c t o r space t h e o r e m comma space x equals negative 1 space i s space a space z e r o space o f space t h e space p o l y n o m i a l.

L e t space u s space c o n s i d e r comma
f open parentheses negative 1 close parentheses equals 2 cross times open parentheses negative 1 close parentheses cubed minus 9 open parentheses negative 1 close parentheses squared plus open parentheses negative 1 close parentheses plus 12
space space space space space space space equals negative 2 minus 9 minus 1 plus 12
space space space space space space space equals 0
S i n c e space f open parentheses negative 1 close parentheses equals 0 comma space t h e n space open parentheses x plus 1 close parentheses space i s space a space f a c t o r space o f space t h e space g i v e n space p o l y n o m i a l.

S i m i l a r l y comma space l e t space u s space f i n d space f open parentheses 3 over 2 close parentheses colon
L e t space u s space c o n s i d e r comma
f open parentheses 3 over 2 close parentheses equals 2 cross times open parentheses 3 over 2 close parentheses cubed minus 9 open parentheses 3 over 2 close parentheses squared plus open parentheses 3 over 2 close parentheses plus 12
space space space space space space space equals 27 over 4 minus 81 over 4 plus open parentheses 3 over 2 close parentheses plus 12
space space space space space space space equals 27 over 4 minus 81 over 4 plus 6 over 4 plus 48 over 4
space space space space space space space equals fraction numerator 27 minus 81 plus 6 plus 48 over denominator 4 end fraction
space space space space space space space equals 0
S i n c e space f open parentheses 3 over 2 close parentheses equals 0 comma space t h e n space open parentheses 2 x minus 3 close parentheses space i s space a space f a c t o r space o f space t h e space g i v e n space p o l y n o m i a l.

S i m i l a r l y comma space l e t space u s space f i n d space f open parentheses 4 close parentheses colon
L e t space u s space c o n s i d e r comma
f open parentheses 4 close parentheses equals 2 cross times open parentheses 4 close parentheses cubed minus 9 open parentheses 4 close parentheses squared plus open parentheses 4 close parentheses plus 12
space space space space space space space equals 128 minus 144 plus 4 plus 12
space space space space space space equals 0
S i n c e space f open parentheses 4 close parentheses equals 0 comma space t h e n space open parentheses x minus 4 close parentheses space i s space a space f a c t o r space o f space t h e space g i v e n space p o l y n o m i a l.
T h u s comma space space open parentheses x plus 1 close parentheses comma space open parentheses 2 x minus 3 close parentheses comma space open parentheses x minus 4 close parentheses space a r e space t h e space f a c t o r s space o f space t h e space g i v e n space p o l y n o m i a l.
Answered by Vimala | 14 May, 2016, 02:48: PM

Application Videos

CBSE 10 - Maths
Asked by anubhutiupadhaya | 14 Mar, 2024, 11:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by reetudetha | 08 Jan, 2024, 04:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by mysticsurya201 | 04 Jan, 2024, 08:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by fatehbahadurtiwari3 | 30 Dec, 2023, 06:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by dhaneswarnimal80 | 11 Nov, 2023, 06:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by skandachiranjeevin | 01 Nov, 2023, 08:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by sazimkhan178 | 16 Sep, 2023, 11:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pranavtamboli65 | 09 Jul, 2023, 09:13: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by rekhapreetham | 15 Jun, 2023, 08:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by dimpaldihingia2 | 24 May, 2023, 06:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×