I used synthetic division which is where I ended up with (1x^2+2x-3)
Unfortunately the answer choices are
(x-1)^2(x-3)
(X-1)(x+1)(x-3)
(X-1)^2(x+3)
(X+3)(x+1)^2
I believe I'm suppose to go one step further, if I did I feel like I would get
(x-1)^2(x-3)
Would I be correct ?
What is the factored form of x^3+x^2-5x+3 if (x-1) is a factor ?
2016-07-17 7:55 pm
回答 (3)
2016-07-17 8:27 pm
x³ + x² - 5x + 3
= (x³ - x²) + x² + x² - 5x + 3
= (x³ - x²) + 2x² - 5x + 3
= (x³ - x²) + (2x² - 2x) + 2x - 5x + 3
= (x³ - x²) + (2x² - 2x) - 3x + 3
= (x³ - x²) + (2x² - 2x) - (3x - 3)
= x²(x - 1) + 2x(x - 1) - 3(x - 1)
= (x - 1)(x² + 2x - 3)
= (x - 1)(x - 1)(x + 3)
= (x - 1)²(x + 3)
...... The answer is: (x - 1)²(x + 3)
(The third option)
= (x³ - x²) + x² + x² - 5x + 3
= (x³ - x²) + 2x² - 5x + 3
= (x³ - x²) + (2x² - 2x) + 2x - 5x + 3
= (x³ - x²) + (2x² - 2x) - 3x + 3
= (x³ - x²) + (2x² - 2x) - (3x - 3)
= x²(x - 1) + 2x(x - 1) - 3(x - 1)
= (x - 1)(x² + 2x - 3)
= (x - 1)(x - 1)(x + 3)
= (x - 1)²(x + 3)
...... The answer is: (x - 1)²(x + 3)
(The third option)
2016-07-17 8:04 pm
(x - 1)(x - 3) = x² - 4x + 3 so this is wrong. You should get
x² + 2x - 3 = (x - 1)(x + 3)
Then the factored form is (x - 1)²(x + 3)
x² + 2x - 3 = (x - 1)(x + 3)
Then the factored form is (x - 1)²(x + 3)
2016-07-17 8:27 pm
1 I 1_____1_____-5_____3
_ I ______1_____ 2____ -3
_ I 1_____2_____-3_____0
(x - 1) (x² + 2x - 3) = (x - 1) (x + 3) (x - 1)
_ I ______1_____ 2____ -3
_ I 1_____2_____-3_____0
(x - 1) (x² + 2x - 3) = (x - 1) (x + 3) (x - 1)
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