Directions: Factor each of the following completely
1. 3x² - 48
2. x³ + 125
3. 2x³ - 4x² + 4x - 8
4. a⁴ - a³ - 2a²
5. A rectangular lot whose length is (a - 3) meters has an area of (a² - 9a + 18) square meters. What is the width of the lot?
Answers
Answer:
gud morning dude have a good day ahead
Answer:
have a nice day
Step-by-step explanation:
The polynomial p(x)=x
4
−2x
3
+3x
2
−ax+3a−7 when divided by x+1 leaves the remainder 19.
Find the value of a. Also find the remainder when p(x) is divided by x+2.
MEDIUM
ANSWER
The given polynomial is p(x)=x
4
−2x
3
+3x
2
−ax+3a−7
Given that, the polynomial p(x) when divided by (x+1) leaves remainder 19
Therefore, p(−1)=19 (By Remainder theorem)
=>(−1)
4
−2×(−1)
3
+3(−1)
2
−(−1)a+3a−7=19
=>1+2+3+a+3a−7=19
=>4a−1=19
=>4a=20
=>a=5
The value of a is 5
Now,
p(x)=x
4
−2x
3
+3x
2
−5x+3×5−7
=x
4
−2x
3
+3x
2
−5x+15−7
=x
4
−2x
3
+3x
2
−5x+8
Remainder when the polynomial is divided by (x+2)
=p(−2) (By Remainder Theorem)
=−2
4
−2(−2)
3
+3(−2)
2
−5(−2)+8
=16+16+12+10+8
=62
Thus, the remainder of the polynomial p(x) when divided by (x+2) is 62