Question

Find the quotient Q(x) and remainder R(x) when the polynomial P(x) is divided by the polynomial D(x).

P(x) = 4x⁵ + 9x⁴ − 5x³ + x² + x − 25;    D(x) = x⁴ + x³ − 4x − 5

Q(x) =

R(x) =

Use the Factor Theorem to show that x − c is a factor of P(x) for the given values of c.

P(x) = 2x⁴ − 13x³ − 3x² + 117x − 135; c = −3, c = 3

Since

P(−3) = and P(3) = , x + 3 and x − 3

are factors of P(x) by the Factor Theorem.

Factor P(x) completely.

11. -12 POINTS FDPRECALC5 3.3.006. MY NOTES Find the quotient Q(x) and remainder R(x) when the polynomial P(x) is divided by the polynomial D(x). P(x) = 4x5 + 9x4 – 5x3 + x2 + x - 25; D(x) = x4 + x2 - 4x - 5 R(x) = Need Help? Read It Watch It Talk to a Tutor 12. -/3 POINTS FDPRECALC5 3.3.010. MY NOTES MY NOTES Use the Factor Theorem to show that x-c is a factor of P(x) for the given values of c. P(x) = 2x4 – 13x3 - 3x2 + 117x - 135; c= -3, C = 3 Since P(-3) = and P(3) = ,x+3 and x-3 are factors of P(x) by the Factor Theorem. Factor P(x) completely. P(x) = Need Help? Read It Watch It Talk to a Tutor

Answer 1

* ② Given P(x) = 485, 94425x ex ex-5 play = xPfx²ya-5 when P(x) divided by olxs, weget xf+x²_yx-5) 4x849x45x²+x²4x-25(ex 75 4/15f4x4 16x²_20x t o (fl Cf I 529-sx?f172*+21X-257 544f5x3 20x-75 fi cj 1 cf1 -lox+17x2+41 x auchent = 4x5 Remainder = -102' +17% +41%- (12 Given plx) = 2x9=131313x?P117x -435 P(-3) = 26-3)-131-313-36-31241176-3)=35 = 2181) -136–27) =3(9) – 351-135 = 162 +851-27 -31-135 = 135-13530 and P13) = 2(3)4-1313)-3(3) FUF3)-135 = 2(81) -13(274 -27 +357-135 = 162 -801-27 £351-135 E 135-135 = 0. since P1-3) = 0, P(3) = 0 XP3, x-3 are faches of Poks by fache Theolem

w using synthetic dursson, 12 213 - uz -35 57 -162 135 312 19 on us Lo lo. 6 -39 245 2 13 is le 1 : 2x4-1333-34? 41174-137 = 673)(x-3) (222_134+15), 2x²_13x +15 = 2x?-10x -3x+15 = 2x (2-5)-3(x-5) = (2x-3)(x-51 - 284-1343-3x + 117*-135 6273) (x-3) (2x-3) (-5) bera .