Factor and Remainder Theorem
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Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=30$.
polynomials
edited Nov 16 at 13:55
Ernie060
2,520319
asked Nov 16 at 13:43
Lombe Lombe
11
add a comment |
up vote
-2
down vote
favorite
Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=30$.
polynomials
edited Nov 16 at 13:55
Ernie060
2,520319
asked Nov 16 at 13:43
Lombe Lombe
11
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
– GK A
Nov 16 at 13:46
1
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
– trancelocation
Nov 16 at 13:49
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=30$.
polynomials
edited Nov 16 at 13:55
Ernie060
2,520319
asked Nov 16 at 13:43
Lombe Lombe
11
Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=30$.
polynomials
polynomials
edited Nov 16 at 13:55
Ernie060
2,520319
asked Nov 16 at 13:43
Lombe Lombe
11
edited Nov 16 at 13:55
Ernie060
2,520319
asked Nov 16 at 13:43
Lombe Lombe
11
edited Nov 16 at 13:55
Ernie060
2,520319
edited Nov 16 at 13:55
Ernie060
2,520319
edited Nov 16 at 13:55
Ernie060
2,520319
2,520319
asked Nov 16 at 13:43
Lombe Lombe
11
asked Nov 16 at 13:43
Lombe Lombe
11
asked Nov 16 at 13:43
Lombe Lombe
11
11
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
– GK A
Nov 16 at 13:46
1
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
– trancelocation
Nov 16 at 13:49
add a comment |
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
– GK A
Nov 16 at 13:46
1
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
– trancelocation
Nov 16 at 13:49
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
– GK A
Nov 16 at 13:46
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
– GK A
Nov 16 at 13:46
1
1
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
– trancelocation
Nov 16 at 13:49
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
– trancelocation
Nov 16 at 13:49
add a comment |
2 Answers
2
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oldest
votes
up vote
0
down vote
If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
$$Rightarrow 2q = -60$$
answered Nov 16 at 13:52
trancelocation
8,3541520
add a comment |
up vote
0
down vote
You want $P(2)=0$
What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?
Let $x=2$ and solve for $q$
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
$$Rightarrow 2q = -60$$
answered Nov 16 at 13:52
trancelocation
8,3541520
add a comment |
up vote
0
down vote
If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
$$Rightarrow 2q = -60$$
answered Nov 16 at 13:52
trancelocation
8,3541520
add a comment |
up vote
0
down vote
up vote
0
down vote
If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
$$Rightarrow 2q = -60$$
answered Nov 16 at 13:52
trancelocation
8,3541520
If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
$$Rightarrow 2q = -60$$
answered Nov 16 at 13:52
trancelocation
8,3541520
answered Nov 16 at 13:52
trancelocation
8,3541520
answered Nov 16 at 13:52
trancelocation
8,3541520
answered Nov 16 at 13:52
trancelocation
8,3541520
8,3541520
add a comment |
add a comment |
up vote
0
down vote
You want $P(2)=0$
What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?
Let $x=2$ and solve for $q$
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
add a comment |
up vote
0
down vote
You want $P(2)=0$
What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?
Let $x=2$ and solve for $q$
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
add a comment |
up vote
0
down vote
up vote
0
down vote
You want $P(2)=0$
What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?
Let $x=2$ and solve for $q$
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
You want $P(2)=0$
What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?
Let $x=2$ and solve for $q$
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
answered Nov 16 at 13:52
Mohammad Riazi-Kermani
40.3k41958
40.3k41958
add a comment |
add a comment |
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Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
– GK A
Nov 16 at 13:46
1
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
– trancelocation
Nov 16 at 13:49