Learning Task 2
A. Determine the factors of the given polynomial.
1. x3 + 2x2 - 5x - 6
2. x3 + x2 - X-1
3. x3 - x2 - 10x - 8
A. Determine the factors of the given polynomial.
1. x3 + 2x2 - 5x - 6
2. x3 + x2 - X-1
3. x3 - x2 - 10x - 8
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Answers & Comments
1.) x³+2x2-5x-6
x³+2x²-5x-6
(x+1)(x²+x-6)
(x+1)(x-2)(x+3)
2.) x3+x2-x-1
x³+x²-x-1
x²(x + 1) - (x+1)
(x+1)(x² - 1²)
(x+1)(x+1)(x-1)
(x+1)² (x-1)
3.) x3 - x2 - 10X-8
x³-x²-10x-8
(x+1)(x²-2x-8)
(x+1)(x-4)(x+2)
Solutions:
P(×)=׳+2ײ-5×-6 ÷ (×-2)
P(×)=׳+2ײ-5×-6; ×= 2
P(2)=(2)³+2(2)²-5(2)-6
P(2)=8 + 8 - 10 - 6
P(2)= 0 ➡️ FACTOR
P(×)=׳+2ײ-5×-6 ÷ (×+1)
P(×)=׳+2ײ-5×-6; ×= -1
P(-1)=(-1)³+2(-1)²-5(-1)-6
P(-1)=1 + 2 - 5 - 6
P(-1)= 0 ➡️ FACTOR
P(×)=׳+2ײ-5×-6 ÷ (×+3)
P(×)=׳+2ײ-5×-6; ×= -3
P(-3)=(-3)³+2(-3)²-5(-3)-6
P(-3)=27 + 18 - 15 - 6
P(-3)= 0 ➡️ FACTOR