5. Suppose r(m) = 0. Calculate m.
0, 1, 17
Let x be 55/(-44) + 49/28. Let v(d) be the second derivative of 0 + 1/4*d**5 - 2/3*d**3 + 1/30*d**6 + x*d**4 - 4*d**2 + 28*d. Factor v(q).
(q - 1)*(q + 2)**3
Suppose 3*s - 44 = 1. Suppose -d - s = -4*d + 3*a, 2*a - 2 = -4*d. Find i, given that 6*i**d - 4*i**2 + 4*i**3 - i**3 - 2*i**3 = 0.
-2, 0
Factor -5655*c - 62027*c**3 + 5040 + 599*c + 1276*c**2 + 62023*c**3.
-4*(c - 315)*(c - 2)**2
Let l(a) = a**2 - 25*a - 19. Suppose -4*z + 27 + 13 = 0. Let b(i) = -3*i + z + 15*i - 2 + 2. Let p(y) = -5*b(y) - 2*l(y). Let p(c) = 0. Calculate c.
-3, -2
Let u(q) be the third derivative of q**8/192 - 4*q**7/105 + 3*q**6/160 + 2*q**5/15 - q**4/6 + 80*q**2. Determine t so that u(t) = 0.
-1, 0, 4/7, 1, 4
Let y(u) be the third derivative of u**6/72 - 29*u**5/6 - 5*u**4/72 + 145*u**3/3 - 2*u**2 + 273*u + 1. What is l in y(l) = 0?
-1, 1, 174
Let z be (2/7 + (-22)/77)/4. Suppose z = 120*w - 125*w. Solve 1/4*h**2 - 3/4*h**3 + 3/4*h - 1/4*h**4 + w = 0.
-3, -1, 0, 1
Let n(a) be the second derivative of -a**4/4 + 79*a**3/6 + 28*a**2 - a + 1. Let w be n(27). Factor 5*d + 20 - 5/2*d**w.
-5*(d - 4)*(d + 2)/2
Let h be 12 - 7 - (-2 + 5). Suppose -n**2 + 0*n**h + 189*n - 188*n = 0. What is n?
0, 1
Suppose 0 = 4*v + 4*h, -h = -14*v + 10*v + 20. Let l(u) = -10*u**3 + 12*u**2 - 2*u + 22. Let g(i) = -i**3 + i**2 + 2. Let s(r) = v*l(r) - 44*g(r). Factor s(d).
4*d*(d - 1)*(d + 2)
Let r be (10/15)/((-4)/(-2)). Suppose -h = -11*n - 81, -4*h - 18 = 4*n - 6. Suppose -4/3*c**3 + r*c**h + 0 - 1/3*c**2 + 4/3*c = 0. What is c?
-1, 0, 1, 4
Let y(u) = -75*u + 150*u - 20*u**2 - 70*u + 5. Let d(w) = 5 + 3*w - w**2 - 4*w - 4 + w**3 - 2*w**3. Let b(x) = 5*d(x) - y(x). Factor b(g).
-5*g*(g - 2)*(g - 1)
Let q(g) be the second derivative of -62*g**7/147 - 128*g**6/105 + 24*g**5/7 + 10*g**4/3 - 178*g**3/21 - 12*g**2/7 + 1336*g. Determine m, given that q(m) = 0.
-3, -1, -2/31, 1
Let x be 84/105 - ((-2106)/120)/39. Factor -3/2*w + 1/4*w**2 + x.
(w - 5)*(w - 1)/4
Let t(w) be the first derivative of -2*w**3/39 - 184*w**2/13 - 1790*w/13 - 9713. Factor t(n).
-2*(n + 5)*(n + 179)/13
Let u(m) be the first derivative of -27/16*m**2 + 16*m + 6 - 3/8*m**3 - 1/32*m**4. Let b(q) be the first derivative of u(q). Factor b(f).
-3*(f + 3)**2/8
Let v be (22 - 12)*(-36)/(-10). Suppose 27*l = 9*l + v. Find y such that -8/5*y**l - 12/5*y + 0 + 4/5*y**3 = 0.
-1, 0, 3
Let r = -198 - -234. Factor -r*o**2 - 39*o**2 - 42*o - 37 - 110 + 72*o**2.
-3*(o + 7)**2
Suppose 24 = 81*y - 85*y - 4*k, 0 = -5*y + 4*k + 24. Let o(u) be the second derivative of -15*u + 0 + y*u**3 + 0*u**2 + 1/8*u**5 + 5/24*u**4. Solve o(g) = 0.
-1, 0
Let y = -47/22 + 763/352. Let j(d) be the first derivative of -1/8*d + 1/16*d**2 + 1/24*d**3 - 5 - y*d**4. Find m such that j(m) = 0.
-1, 1
Suppose 9 - 54 = -5*j - 4*a, 0 = -2*j + a + 5. Suppose 4*o - j*o = -117. Factor 117*h - o*h + 10*h**2 + 5*h**3.
5*h**2*(h + 2)
Let x(v) be the second derivative of 3*v**7/14 + 131*v**6/10 + 25*v**5/2 - 175*v**4/6 - 259*v**3/6 - 43*v**2/2 - 144*v. Suppose x(s) = 0. Calculate s.
-43, -1, -1/3, 1
Let s(t) = -4*t**2 - 79*t + 17. Let d be s(-20). Let p be (d - -1)*(-5 - -2)/30. Factor -1/5*a**2 + 2/5 - p*a.
-(a - 1)*(a + 2)/5
Suppose -106*t + 183*t + 372 - 330 = 91*t. Factor 0 - 3/7*m**2 - 9/7*m**4 + 0*m - 12/7*m**t.
-3*m**2*(m + 1)*(3*m + 1)/7
Let u(y) = -y**3 + 810*y**2 - 18872*y + 195. Let s be u(24). Find n such that 28/5*n**s + 9/5*n**2 - 6/5*n**5 - 44/5*n - 7/5*n**4 + 4 = 0.
-2, 5/6, 1
Solve -135470455*y - 31422*y**2 - 14314613*y - 176396881748 + y**3 - 19167*y**2 + 8193*y**2 - 5*y**3 = 0.
-3533
Let y(f) be the third derivative of 5/9*f**5 + 61*f**2 + 1/540*f**6 + 125000/27*f**3 + 0*f + 625/9*f**4 + 0. Factor y(l).
2*(l + 50)**3/9
Let r(c) be the third derivative of 89*c**2 + 1/12*c**5 - 155/12*c**4 + 0 + 4805/6*c**3 + 0*c. Factor r(l).
5*(l - 31)**2
Suppose 55 = 8*n - 41*n + 154. Suppose 11664/17 + 108/17*k**2 + 2/17*k**n + 1944/17*k = 0. Calculate k.
-18
Let a(c) be the first derivative of -c**5/240 + 13*c**4/48 - 169*c**3/24 - 24*c**2 - 63. Let y(g) be the second derivative of a(g). Factor y(n).
-(n - 13)**2/4
Suppose 2/3*j**5 + 0 - 14/3*j**4 - 26/3*j**3 + 206/3*j**2 - 56*j = 0. What is j?
-4, 0, 1, 3, 7
Find z such that 2160 - 58*z**3 - 52*z**3 - 1830*z - 135*z**2 - 200*z**2 + 115*z**3 = 0.
-6, 1, 72
Let l(m) be the first derivative of 2*m**3/57 + 202*m**2/19 - 406*m/19 - 1428. Factor l(k).
2*(k - 1)*(k + 203)/19
Let p be (124/(-558))/(32/(-180)). Let j(i) be the first derivative of -2 + 0*i**2 - p*i**4 + 4/5*i**5 + 1/6*i**6 + 0*i + 0*i**3. Let j(k) = 0. Calculate k.
-5, 0, 1
Factor -2/7*h**2 - 1868/7*h - 436178/7.
-2*(h + 467)**2/7
Let v(x) = -x**2 + 5*x + 7. Let p be v(6). Let t be (p - -2)/(-3) + 11. Let t - 8 + 6*k**2 - 1 + 2*k**3 - 9 = 0. What is k?
-2, 1
Suppose -271/3*s**2 + 91*s + 5*s**3 - 17/3 = 0. Calculate s.
1/15, 1, 17
Let z be (3/(-39) - 516/52) + 784*(-12)/(-912). Solve 0*m + 0 - 2/19*m**2 + z*m**5 + 2/19*m**4 - 6/19*m**3 = 0.
-1, -1/3, 0, 1
Let y(x) be the first derivative of x**3/12 - 4223*x**2/4 + 17833729*x/4 + 15209. Factor y(t).
(t - 4223)**2/4
Let w(a) be the first derivative of -17*a**5/5 + 25*a**4/2 - 31*a**3/3 - a**2 + 1741. Determine z so that w(z) = 0.
-1/17, 0, 1, 2
Let q = -1 + -47. Let t = 53 + q. Determine x so that 93*x + 1 - 46*x - 4*x**3 + 4*x**2 - 43*x - t = 0.
-1, 1
Suppose 63/2*x**3 + 0 - 10*x**4 + 1/2*x**5 + 10*x**2 - 32*x = 0. Calculate x.
-1, 0, 1, 4, 16
Suppose -324*p + 306*p**2 - 5041/2*p**5 + 0 - 4899/4*p**4 + 7703/4*p**3 = 0. Calculate p.
-1, -1/2, 0, 36/71
Let n(b) = -3*b**2 - 81*b - 73. Let h(v) = v**2 + 28*v + 24. Let y(f) = -11*h(f) - 4*n(f). Suppose y(o) = 0. Calculate o.
-14, -2
Let f = -2260 - -3551. Factor -2400*p + 160 - 30*p**2 - 35*p**3 + f*p + 1269*p - 5*p**4.
-5*(p - 2)*(p + 1)*(p + 4)**2
Let j be ((-41)/1558 - (-16)/(-114))/(4/(-15)). What is f in -j*f**3 + 0 + 1/8*f**4 + f**2 - 1/2*f = 0?
0, 1, 2
Let p(q) be the second derivative of 0*q**5 + 4/15*q**6 + 0*q**2 + 90 - 1/84*q**7 - q + 0*q**3 + 0*q**4. What is x in p(x) = 0?
0, 16
Suppose -3306 + 5694*y**2 + 1404*y + 3769*y**3 + 3090 - 630*y**4 + 1507*y**3 - 815*y**3 - 513*y**5 = 0. Calculate y.
-3, -2/3, 2/19, 3
Let t(k) be the second derivative of -2/7*k**2 + 81/140*k**5 + 51*k + 20/21*k**3 - 1 - 39/28*k**4. Factor t(z).
(z - 1)*(9*z - 2)**2/7
Suppose 3*g = -i + 4*i - 9, 2*i - 2 = 4*g. Let n = 138296 - 138294. Determine s so that 0 + 0*s + n*s**5 - g*s**3 + 4/7*s**4 - 4/7*s**2 = 0.
-1, -2/7, 0, 1
Let f = -21 - -23. Suppose f + 4 = -3*i, -i - 27 = 5*k. Let d(o) = -o**2 + o - 1. Let h(n) = 3*n**2 - 13*n - 3. Let m(a) = k*d(a) - h(a). Factor m(u).
2*(u + 2)**2
Find n such that -334535*n**2 + 334545*n**2 + 125*n - 631 + 680*n - 184 = 0.
-163/2, 1
Suppose 5*f = 2*t + 176, 0 = -5*f + 3*f - 2*t + 76. Suppose 5*x + 7*x - f = 0. Find q such that -16*q - 8*q - 3*q**2 - 25*q**2 + 11*q**x + q**3 = 0.
-2/3, 0, 3
Find p such that -1856066*p**2 + 4*p**4 + 324*p - 2 + 1856510*p**2 + 2 + 124*p**3 = 0.
-27, -3, -1, 0
Suppose -3*p + 16 = 2*o + 2, 0 = -5*o + 20. Let b(r) be the second derivative of 15*r + 1/60*r**4 + 5/2*r**p + 1/3*r**3 + 0. Find k such that b(k) = 0.
-5
Factor -60*w - 18*w**3 - 21*w**3 + 14*w**4 + 45*w**2 + 3*w**3 - 225 - 11*w**4 + 81*w**2.
3*(w - 5)**2*(w - 3)*(w + 1)
Let y(k) be the third derivative of -6*k**2 - 1/1008*k**8 + 0*k**4 + 0*k + 1/45*k**5 + 1/126*k**7 - 1/45*k**6 + 0*k**3 + 1. Find u such that y(u) = 0.
0, 1, 2
Let v = 95318 + -95316. Factor -12/11 - 3/11*t**3 + 20/11*t - 1/11*t**v.
-(t - 2)*(t + 3)*(3*t - 2)/11
Let u(j) be the second derivative of -j**5/120 - 7*j**4/6 - 196*j**3/3 + 92*j**2 - 35*j + 1. Let s(q) be the first derivative of u(q). Factor s(a).
-(a + 28)**2/2
Let a(r) = 9*r**2 + 905*r - 1783. Let i(v) = 5*v**2 + 452*v - 888. Let c(d) = -4*a(d) + 7*i(d). Factor c(q).
-(q - 2)*(q + 458)
Let z(v) be the third derivative of -137*v**2 + 0 + 0*v + 0*v**5 - 5/336*v**8 + 1/12*v**6 + 1/42*v**7 + 0*v**4 + 0*v**3. What is a in z(a) = 0?
-1, 0, 2
Let y = 349 + -344. Let s(h) be the third derivative of 0*h + 14*h**2 + 0 - 1/6*h**4 + 1/6*h**y - h**3. Suppose s(r) = 0. Calculate r.
-3/5, 1
Let m(o) be the third derivative of o**6/540 - o**5/54 + o**4/27 + 1130*o**2. Factor m(t).
2*t*(t - 4)*(t - 1)/9
Let