- c. Suppose 2/7*z**4 + 0*z - 4/7*z**3 + 0 + r*z**2 = 0. Calculate z.
0, 1
Let w(j) be the first derivative of -j**5/20 + 5*j**4 - 200*j**3 + 3*j**2/2 + 17*j - 28. Let b(p) be the second derivative of w(p). Solve b(m) = 0.
20
Let r(c) = -8*c**3 - 2*c + 5. Let o(g) = 3*g - 1323 + 9*g**3 + 0*g + 1317. Let z = -15 + 21. Let x(n) = z*r(n) + 5*o(n). Suppose x(j) = 0. What is j?
-1, 0, 1
Factor 23*g - 12*g**2 + 1/3*g**3 - 34/3.
(g - 34)*(g - 1)**2/3
Let i(p) be the first derivative of p**6/8 - 2*p**5 + 133*p**4/16 - 37*p**3/3 + 9*p**2/2 - 4318. Determine k so that i(k) = 0.
0, 1/3, 2, 9
Let d(m) be the third derivative of -2/165*m**5 - 1/1155*m**7 + 0*m**3 - 1/165*m**6 + 3 + 0*m**4 + 4*m**2 + 0*m. Suppose d(n) = 0. Calculate n.
-2, 0
Let y(t) be the first derivative of t**4/2 - 9*t**3 + 24*t**2 - 17*t - 32. Let k(o) = -o**3 + o**2 + o + 1. Let j(l) = -3*k(l) + y(l). Factor j(b).
5*(b - 4)*(b - 1)**2
Let j(f) = -5*f - 123. Let d be j(-25). Suppose -10*c + c = -c. Let 25*i + c + 5/2*i**d = 0. What is i?
-10, 0
Factor 6216/5*u**2 + 2076/5*u**3 + 2/5*u**4 + 414 + 6212/5*u.
2*(u + 1)**3*(u + 1035)/5
Let i(w) = -1659*w**2 + 1662*w**2 - 3 + 0 - 5*w**3 + 2*w. Let f(s) = 36*s**3 - 22*s**2 - 14*s + 22. Let r(p) = -6*f(p) - 44*i(p). Factor r(k).
4*k*(k - 1)*(k + 1)
Suppose -5*m - 6 = 2*s - 7*m, -5*s + m = -5. Let h(d) be the second derivative of -1/6*d**4 - 11/3*d**3 - d - 10*d**s + 0. Let h(l) = 0. Calculate l.
-10, -1
Let y be -1*(-1 - -1)/(-5 - -4). Let u be ((y - 3) + 4)*0/(-1). Suppose u + 1/3*c**2 + c = 0. Calculate c.
-3, 0
Let o(g) = g**2 + 20*g + 37. Let v be o(-18). Let m(r) = -r**3 + r**2 - r. Let t(d) = d**3 + 14*d**2 - 14*d. Let n(w) = v*t(w) + 6*m(w). Factor n(y).
-5*y*(y - 2)**2
Factor 199/4*j + 99/4 + 1/4*j**3 + 101/4*j**2.
(j + 1)**2*(j + 99)/4
Let s = -304 - -310. Let i = s + -3. Suppose -1/5*m**3 - i*m**2 - 15*m - 25 = 0. Calculate m.
-5
Suppose 168 = 2*h + 5*h. Solve 507 - 5*b**2 + 303*b - 69*b + 8*b**2 + h*b**2 = 0.
-13/3
Suppose -52*f + 8*f = -23*f + 50*f. Let g(a) be the second derivative of 15/2*a**2 - 21*a - 1/4*a**5 - 5/4*a**4 + 5/6*a**3 + f. Factor g(s).
-5*(s - 1)*(s + 1)*(s + 3)
Let w = 56 + -36. Suppose w = -6*u + 16*u. Solve -o**u - 3/4*o**3 + 1/2*o**4 + 1/4*o**5 + 0 + o = 0.
-2, 0, 1
Let z(w) = 19*w**3 - 751*w**2 - 185999*w - 15438253. Let v(t) = -5*t**3 + t**2 - t + 1. Let d(m) = -12*v(m) - 3*z(m). Solve d(n) = 0 for n.
-249
Suppose 0 = -9*l + 81 - 63. Find i, given that -2*i**4 + l*i**5 - 10*i**3 + 32*i**2 + 8 + 16*i - 66*i**2 + 36*i**2 = 0.
-1, 2
Let v = 467 + -407. Factor -v*x - 1081 + 564 - 5*x**2 + 582.
-5*(x - 1)*(x + 13)
Let x = 94403 + -94401. Factor 1/2*d**x + 121/2 + 11*d.
(d + 11)**2/2
Suppose 20 = 2*v - 4*a, -2*v + 3*a + 11 = -4. Let s be (-10 + v)/(2/(-4)*4). What is c in -4*c**3 - 135*c**2 + 8*c**4 + 135*c**2 - 4*c**s = 0?
0, 1
Solve 5783*q + 385*q**2 + 5127*q - 5951405 - 134*q**2 - 125*q**2 - 131*q**2 = 0 for q.
1091
Let x = 126389/128 + -287/384. Let p = -986 + x. Determine r, given that r**2 + 5/3*r + p = 0.
-1, -2/3
Let f be -2*6/4*(-127)/3. Let d = f + 18. Factor 145*c - d*c + 4*c**2 + 4*c**3.
4*c**2*(c + 1)
Let p(t) = 223*t**3 + 49*t**2 + 9294*t + 115509. Let g(s) = -61*s**3 - 13*s**2 - 2324*s - 28877. Let c(z) = 22*g(z) + 6*p(z). Factor c(u).
-4*(u - 40)*(u + 19)**2
Let c(f) be the third derivative of -18*f**2 + 2*f + 25/336*f**8 + 3/4*f**6 + 0 + 0*f**3 - 2/3*f**5 - 8/21*f**7 + 5/24*f**4. Solve c(g) = 0 for g.
0, 1/5, 1
Let x(y) = 4*y. Suppose j - 5*t + 5 = 4*j, -5*t + 5 = 0. Let f be x(j). Determine z, given that f - 2/5*z**2 + 2/5*z**4 - 6/5*z + 6/5*z**3 = 0.
-3, -1, 0, 1
Let z(w) = w**3 + 9*w**2 - 7*w - 3. Let y(u) = u**2 - u. Let x = -314 - -315. Let d(a) = x*z(a) - 6*y(a). Factor d(c).
(c - 1)*(c + 1)*(c + 3)
Let o(z) be the second derivative of -4/27*z**3 + 1/90*z**5 - 8/9*z**2 + 0 + 1/27*z**4 + 34*z. Solve o(h) = 0 for h.
-2, 2
Let v be (-20 - -2)/(2/(-3)). Suppose 7*p = -2*p + v. Suppose -n + n**3 + n + 2*n**2 - p*n = 0. Calculate n.
-3, 0, 1
Let a be (0/(-1) - -5)/((-58170)/(-46536)). Determine k, given that 2/3*k**a - 2*k**3 - 8*k - 32/3*k**2 + 0 = 0.
-2, -1, 0, 6
Let n be (-28)/10 + -2*(-3)/2. Let s = 2/20165 + 4029/40330. Factor s*v**2 + n*v + 0.
v*(v + 2)/10
Let c be (-126)/(-84) + 2/(-4). Let w be 28/(-189)*(3/(-2))/c. Suppose 2/9*i**3 + 2/3 + w*i**2 - 10/9*i = 0. Calculate i.
-3, 1
Let i be 6/(-4)*1/(-6). Let s = 44158 - 44156. Let -1/2 - i*w + 1/4*w**s = 0. Calculate w.
-1, 2
Let j = -114707/20 - -22163/4. Let l = -193 - j. Solve 24/5*m + 2*m**2 + l = 0 for m.
-2, -2/5
Factor 342/7*s + 29241/7 + 1/7*s**2.
(s + 171)**2/7
Let w = -28981 - -172249/6. Let h = 273 + w. Suppose 1/6*d**3 - 1/2*d**2 - h*d + 1/6*d**4 + 1/3 = 0. What is d?
-2, -1, 1
Let z(w) be the first derivative of -w**4/16 - 6*w**3 - 1221*w**2/8 + 1369*w/2 - 1648. Find b, given that z(b) = 0.
-37, 2
Determine q, given that 1440 - 287*q + 136*q**2 - 71*q - 668*q + 4*q**3 + 102*q = 0.
-40, 3
Let k(q) = -2*q**2 - 36*q + 4. Let i(r) = 12*r**2 + 220*r - 26. Let x(c) = 2*i(c) + 13*k(c). What is p in x(p) = 0?
-14, 0
Solve -1458*g - 36*g**2 - 2106 + 2/3*g**5 + 30*g**4 + 156*g**3 = 0 for g.
-39, -3, 3
Let -99*q**2 - 2*q**3 - 15*q**2 + 44*q**2 + 27 + 89 - 126*q + 82 = 0. What is q?
-33, -3, 1
Let s(t) be the third derivative of t**8/448 + 3*t**7/70 + 31*t**6/160 - 3*t**5/20 - t**4 - 10*t**2 - 85*t. Determine q so that s(q) = 0.
-8, -4, -1, 0, 1
Let z(w) be the second derivative of -9*w**6/10 + 9*w**5/4 + 61*w**4/2 + 66*w**3 + 60*w**2 - 424*w. What is m in z(m) = 0?
-2, -2/3, 5
Let v(z) = z**3 - 10*z**2 + 16*z + 4. Let u be v(8). Let -i**4 + u*i**3 + 0*i**3 + 18*i**2 - 13*i**2 = 0. Calculate i.
-1, 0, 5
Let g(k) be the first derivative of 8*k + 148 + 19/5*k**2 - 2/15*k**3. Factor g(h).
-2*(h - 20)*(h + 1)/5
Let r(a) be the first derivative of -3*a**4/32 + 15*a**3 - 357*a**2/16 - 108. Factor r(f).
-3*f*(f - 119)*(f - 1)/8
Let k be (-12 - (-560)/49)/(20/(-154)). Let t = -144/35 + k. Factor -1/7*m**4 - 1/7*m**3 + 0*m + t*m**2 + 0.
-m**2*(m - 1)*(m + 2)/7
Suppose -292 + 844 = 6*b. Suppose b = -126*v + 344. Factor -1/5*g + 1/5*g**3 + 1 - g**v.
(g - 5)*(g - 1)*(g + 1)/5
Let m(x) be the second derivative of 1/150*x**6 + 0 + 1/100*x**5 + 0*x**2 - 103*x - 1/30*x**4 + 0*x**3. Suppose m(z) = 0. Calculate z.
-2, 0, 1
Let p(b) = -7*b**2 - 15*b + 20. Let j(u) = -2*u**2 + u - 7. Let z(s) = 12*j(s) - 3*p(s). Factor z(m).
-3*(m - 16)*(m - 3)
Let c = -7657554/7 + 1093938. Factor 2/7*x**2 + 18/7 + c*x.
2*(x + 3)**2/7
Factor 1024/5*v + 2056/5 - 2/5*v**2.
-2*(v - 514)*(v + 2)/5
Let s be -2 - (-10)/(-6)*(1 - 4). Let u = -3/64 - -137/192. Factor 1/3*y**s - u*y - 1/3*y**2 + 0.
y*(y - 2)*(y + 1)/3
Suppose 4*k + 35*u - 83*u = -43*u - 37, 0 = 3*u - 27. Let m = 24 + -102/5. Factor 3*h + m + 3/5*h**k.
3*(h + 2)*(h + 3)/5
Suppose -4 + 18 - 20*l + 2*l**2 + 32*l - 28*l = 0. Calculate l.
1, 7
Let g = -3675 + 3677. Let o(w) be the third derivative of 0 + 0*w + 0*w**3 - 1/540*w**6 - 1/27*w**4 + 1/54*w**5 + 9*w**g. Factor o(j).
-2*j*(j - 4)*(j - 1)/9
Let x(c) be the second derivative of c**3/2 - 18*c**2 + 35*c. Let w be x(13). Find n such that -14*n**2 - 85 - 2*n**w + 31 + 38 - 28*n = 0.
-4, -2, -1
Let n(c) be the first derivative of 4/3*c**3 - 168*c - 38*c**2 + 25. Let n(x) = 0. What is x?
-2, 21
Let v(h) be the second derivative of -h**7/5040 + h**5/240 - 7*h**4/12 + 2*h**2 - 145*h. Let b(a) be the third derivative of v(a). Factor b(f).
-(f - 1)*(f + 1)/2
Let w be (-1)/(-2)*((-42)/7 + -28). Let r be 0 + (3 - 1) + w/(-17). Factor -6*v**r + 4*v**3 - 31*v + 71*v - 38*v.
-2*v*(v - 1)*(v + 1)
Let g = 122 + -120. What is s in -11*s**2 + s - 16*s - 3*s - 20 + 13*s**g = 0?
-1, 10
Let p(n) be the third derivative of n**6/60 + 13*n**5/10 + 30*n**4 - 400*n**3/3 + 1296*n**2. Determine m so that p(m) = 0.
-20, 1
Let t(c) be the second derivative of 9*c**6/40 - 17199*c**5/40 - 5739*c**4/4 - 5741*c**3/3 - 1276*c**2 + 2657*c. Factor t(d).
(d - 1276)*(3*d + 2)**3/4
Let m = 60957/71386 - -33/10198. Let d = -518 - -3632/7. Factor 2/7*y**3 - 2/7 + d*y - m*y**2.
2*(y - 1)**3/7
Let c(q) be the first derivative of 0*q**2 + 45 - 4/3*q**3 + 0*q**4 + 8*q + 1/10*q**5. Factor c(r).
(r - 2)**2*(r + 2)**2/2
Let c(s) be the second derivative of -19/2*s**2 - 5/2*s**3 + 0 - 40*s - 1/12*s**5 - 5/6*s**4