divide p(x) = 2x⁴-7x³-13x²+63x-45 by g(x) = x² - 4x + 3
Answers
Step-by-step explanation:
f(x) = 2x⁴ - 7x³ - 13x² + 63x - 45
x = 1
f(1) = 2(1)⁴ - 7(1)³ - 13(1)² + 63(1) - 45
= 2 - 7 - 13 + 63 - 45
= 0
=> x = 1 is a factor
(x - 1) is a factor
2x³ - 5x² - 18x + 45
x - 1 _| 2x⁴ - 7x³ - 13x² + 63x - 45
2x⁴ - 2x³
___________
-5x³ - 13x² + 63x - 45
-5x³ + 5x²
_______________
-18x² + 63x - 45
-18x² + 18x
______________
45x - 45
45x - 45
_______
0
2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (2x³ - 5x² - 18x + 45)
Similarly
x = 3 => 2x³ - 5x² - 18x + 45 = 0
x - 3 is factor
=> 2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (x - 3) (2x² + x - 15)
(x - 1) (x - 3) (2x² + x - 15)
= (x - 1) (x - 3) (2x² + 6x - 5x - 15)
= (x - 1) (x - 3) (2x(x + 3) - 5(x + 3))
= (x - 1) (x - 3) (2x - 5)(x + 3)
= (x - 1) (x - 3) (x + 3)(2x - 5)
2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (x - 3) (x + 3)(2x - 5)
Answer:
1
Franklin1713
11.03.2020
Math
Secondary School
+15 pts
Answered
Using factor theorem, factorize each of the following polynomial:
2x⁴-7x³-13x²+63x-45
2
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Answers
amitnrw
amitnrw Genius
2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (x - 3) (x + 3)(2x - 5)
Step-by-step explanation:
f(x) = 2x⁴ - 7x³ - 13x² + 63x - 45
x = 1
f(1) = 2(1)⁴ - 7(1)³ - 13(1)² + 63(1) - 45
= 2 - 7 - 13 + 63 - 45
= 0
=> x = 1 is a factor
(x - 1) is a factor
2x³ - 5x² - 18x + 45
x - 1 _| 2x⁴ - 7x³ - 13x² + 63x - 45
2x⁴ - 2x³
___________
-5x³ - 13x² + 63x - 45
-5x³ + 5x²
_______________
-18x² + 63x - 45
-18x² + 18x
______________
45x - 45
45x - 45
_______
0
2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (2x³ - 5x² - 18x + 45)
Similarly
x = 3 => 2x³ - 5x² - 18x + 45 = 0
x - 3 is factor
=> 2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (x - 3) (2x² + x - 15)
(x - 1) (x - 3) (2x² + x - 15)
= (x - 1) (x - 3) (2x² + 6x - 5x - 15)
= (x - 1) (x - 3) (2x(x + 3) - 5(x + 3))
= (x - 1) (x - 3) (2x - 5)(x + 3)
= (x - 1) (x - 3) (x + 3)(2x - 5)
2x⁴ - 7x³ - 13x² + 63x - 45 = (x - 1) (x - 3) (x + 3)(2x - 5)