Answer:
see explanation
Step-by-step explanation:
Expand the factored form and compare coefficients of like terms with the original polynomial
a(x + 1)(x - 2)² + b(x + 2) + c
= a(x + 1)(x² - 4x + 4) + b(x + 2) + c
= a(x³ - 4x² + 4x + x² - 4x + 4) + b(x + 2) + c
= a(x³ - 3x² + 4) + b(x + 2) + c ← distribute parenthesis
= ax³ - 3ax² + 4a + bx + 2b + c
Compare x³ terms
ax³ with 2x³ , then a = 2
Compare x terms
bx = - 3x , then b = - 3
Compare constant terms
4a + 2b + c = 6
4(2) + 2(- 3) + c = 6
8 - 6 + c = 6
2 + c = 6 ( subtract 2 from both sides )
c = 4
Thus a = 2, b = - 3, c = 4
