Determine without actual division whether x+ 1 is a factor of x^3 + x^2
Answers
Step-by-step explanation:
x
2
+2x−3=x
2
+3x−x−3
=x(x+3)−1(x+3)
=(x+3)(x−1)
checking whether (x+3) and (x−1) are the factors or not,
Taking x+3=0 So, x=−3
Putting the value of x in given equation,
x
3
−3x
2
−13x+15=0
(−3)
3
−3(−3)
2
−13(−3)+15=0
−27−3(9)+39+15=0
−27−27+39+15=0
−54+54=0
0=0
Hence, (x+3) is the factor,
checking for (x−1) , x=1
Putting the value of x in given equation,
x
3
−3x
2
−13x+15=0
(1)
3
−3(1)
2
−13(1)+15=0
1−3−13+15=0
−15+15=0
0=0
Hence, (x−1) is also a factor.
Then, x
2
+2x−3 is the factor of given equation
Answer:
Step-by-step explanation:
→ So we already know that , if x + 1 is a factor of x³ + x² , then
→ x + 1 =0
→ x = -1
→ By putting the value of x = -1 , in x³ + x² = 0
→ If by putting x = -1 in x³ + x² = 0 , then x + 1 is a factor of x³ + x².
→ (-1)³ + (-1)² = 0
→ -1 + 1 = 0
→ 0=0
→ Hence , it is correct that x + 1 is a factor of x³ + x²