(1) If 4x3 - 7x2 + ax - 9 is exactly divisible by x - 3, find the value of a.
(2) What should br subtracted from x3 + 13x2 + 43x + 40 so that the result is exactly divisible by x + 5 ?
give me the answer of both .
Answers
Answer:
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Step-by-step explanation:
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Answer:
1. Given : Polynomial x
4
+ax
3
−7x
2
−8x+b is exactly divisible
by (x+2) as well (x+3)
⇒x=−2,−3 are the roots of polynomial
∴(−2)
4
+a(−2)
3
−7(−2)
2
−8(−2)+b=0
16−8a−28+16+b=0
−8a+b=−4 ... (I)
(−3)
4
+a(−3)
3
−7(−3)
2
−8(−3)+b=0
81−27a−63+24+b=0
−27+b=−42 .... (II)
(I) - (II)
Ref. Image
a=2
put a=2 in equation (I)
−16+b=−4
b=−4+16
b=12
∴a=2,b=12
2. We divide the polynomial x
3
+13x
2
+35x+25 by x
2
+11x+10 as shown in the above image:
From the above division, we conclude that the quotient is x+2 and the remainder is 3x+5.
Hence, 3x+5 must be subtracted from the polynomial x
3
+13x
2
+35x+25 so that the resulting polynomial is exactly divisible by x
2
+11x+10.
Step-by-step explanation:
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