Question

Given that x+1 is a factor of 3x³-14x²-7x+d, show that d= 10

Answer 1

3x³ - 14x² - 7x + d = (x + 1)(ax² + bx + c)

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(x + 1)(ax² + bx + c)

= ax³ + bx² + cx + ax² + bx + c

= ax³ + (a + b)x² + (b + c)x + c

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ax³ + (a + b)x² + (b + c)x + c = 3x³ - 14x² - 7x + d

=> a = 3

a + b = -14

b + c = -7

c = d

=> a = 3, b = -17, c = 10, d = 10