q**2 - 32*q - 1213. Determine n, given that c(n) = 0.
-2/7, -2/9, 1, 2
Let h(f) be the third derivative of -f**7/42 - 49*f**6/24 - 145*f**5/3 - 735*f**4/2 - 1320*f**3 - 7*f**2 - 30*f - 1. Solve h(t) = 0.
-33, -12, -2
Factor -3448/5*m - 1/5*m**2 - 2972176/5.
-(m + 1724)**2/5
Let r(x) be the second derivative of x**6/120 + x**5/30 - x**4/24 - x**3/3 - 51*x**2 - 8*x - 3. Let b(m) be the first derivative of r(m). Factor b(y).
(y - 1)*(y + 1)*(y + 2)
Suppose 3*m + 2*a - 3 = 0, -a - 7 = -1. Let x(g) be the third derivative of 0*g**3 + 0*g + 1/80*g**m + 0 - 1/240*g**6 - 1/96*g**4 - g**2. Factor x(y).
-y*(y - 1)*(2*y - 1)/4
Let k(p) be the second derivative of 11/10*p**3 - 98*p + 0 - 3*p**2 - 1/20*p**4. Determine c so that k(c) = 0.
1, 10
Let x(d) be the first derivative of -58*d**3 - 879*d**2/2 - 45*d - 112. Let x(z) = 0. Calculate z.
-5, -3/58
Determine y so that -815/7*y + 13/7*y**4 + 87*y**2 + 50 - 157/7*y**3 = 0.
1, 14/13, 5
Suppose 0 = 6*u - 24 - 0. Factor -12*z**3 - 13*z - z**5 + 22*z**2 - 5*z**u + 21*z**4 - 9*z**4 - 6*z**3 + 3.
-(z - 3)*(z - 1)**4
Let k(a) be the second derivative of 2/255*a**6 - 8 + 4/51*a**4 + 4*a - 7/170*a**5 + 0*a**2 - 1/17*a**3. Determine r, given that k(r) = 0.
0, 1, 3/2
Let r(k) be the first derivative of -k**5/20 + 141*k**4/16 - 5177*k**3/12 + 14559*k**2/8 - 4761*k/2 + 5380. Determine g, given that r(g) = 0.
1, 2, 69
Let o(u) be the first derivative of -12*u**3 + 2*u**2 - 76/5*u**5 - 35 + 4*u**6 + 0*u + 21*u**4. Solve o(h) = 0 for h.
0, 1/6, 1
Solve -3/7*g**2 + 522/7 + 519/7*g = 0 for g.
-1, 174
Find x, given that -2/11*x**2 + 174*x - 1912/11 = 0.
1, 956
Let m(g) be the second derivative of 2*g**3 - 6*g**2 - g. Let u(x) = -23*x - 76 - x**3 - 96 + 197 - x**2. Let h(f) = -7*m(f) - 3*u(f). Factor h(q).
3*(q - 1)**2*(q + 3)
Suppose 17*w = 5*s + 16*w - 22, 0 = 2*w + 4. Let b(n) be the first derivative of 4/3*n**3 + 0*n**2 - 1 - s*n. Let b(o) = 0. Calculate o.
-1, 1
Suppose -2*h + 3252 = 10*h. Find z such that 134*z**5 - 108*z**2 + 138*z**5 + 90*z**3 - 17*z**4 - h*z**5 - 216*z = 0.
-1, 0, 6
Let z(k) be the third derivative of k**6/30 - 17*k**5/15 + 8*k**4/3 - k**2 + 533. Solve z(t) = 0.
0, 1, 16
Suppose 0 = 5*w - 25, -75 = -4*u + 2*w - 69. Let i(o) be the second derivative of 16/5*o**2 + 8*o + 1/30*o**u - 8/15*o**3 + 0. Factor i(n).
2*(n - 4)**2/5
Suppose -806*a - 229*a = -1835*a - 3319*a + 12357. Determine r so that 1/4*r**a + 25/4*r**2 - 13/2*r + 0 = 0.
-26, 0, 1
Let q be (-310)/15 + (5 - (19 + -36)). Let w = 12 + -10. Factor -2/3*k**2 - w*k - q.
-2*(k + 1)*(k + 2)/3
Let s(g) be the second derivative of g**6/48 + 41*g**5/80 + 11*g**4/8 - 245*g**3/6 - 50*g**2 + 1847*g. Solve s(b) = 0 for b.
-10, -2/5, 4
Let b(m) be the first derivative of -m**3/8 + 135*m**2/8 - 1043. Let b(g) = 0. Calculate g.
0, 90
Let w(z) = 8*z**2 - 226*z - 1449. Let d(g) = -2*g**2 + 52*g + 362. Let q(f) = -9*d(f) - 2*w(f). Find u such that q(u) = 0.
-10, 18
Let u(b) be the first derivative of 3/5*b**5 + 9*b**2 + 6*b**4 + 13*b**3 + 0*b + 43. Factor u(a).
3*a*(a + 1)**2*(a + 6)
Suppose 0*j + 22 = 2*j - 5*x, 4*j - x = 26. Let o(d) = d**3 - 6*d**2 + 2. Let c be o(j). Solve 2*z**5 - 2*z - 130*z**3 + c*z**4 + 126*z**3 + 2*z = 0 for z.
-2, 0, 1
Let n(a) be the second derivative of -a**5/5 - 5*a**4/3 + 22*a**3 - 54*a**2 + 23*a - 12. Let n(q) = 0. Calculate q.
-9, 1, 3
Let a(h) be the second derivative of 9*h**5/20 - 25*h**4/12 - h**3 - 9107*h. Factor a(f).
f*(f - 3)*(9*f + 2)
Let k = 3 + 1. Let s = 75 + -72. Find t, given that -65*t**4 + 5*t**s + 127*t**4 - 67*t**k = 0.
0, 1
Suppose -134*u + 133*u + 29 = 0. Let -76*c**2 + 31*c**3 + 4 + 722*c - u*c**3 - 4 = 0. What is c?
0, 19
Let a(g) be the third derivative of g**7/735 - 89*g**6/140 + 3036*g**5/35 - 4356*g**4/7 + g**2 + 1101*g. Factor a(u).
2*u*(u - 132)**2*(u - 3)/7
What is s in -150*s + 3/2*s**3 + 297/2*s**2 + 0 = 0?
-100, 0, 1
Let v(n) = -n**2 - 55*n - 153. Let s be v(-35). Let l = s - 2727/5. Suppose 2/5 - l*u**4 + 2*u**3 - 2*u + 6/5*u**2 = 0. What is u?
-1, 1/4, 1
Let j(w) = w**2 - 1148*w + 60118. Let h be j(55). Let -37/5*d**2 + 4/5*d**5 - 2/5 - 21/5*d**4 + h*d + 41/5*d**3 = 0. What is d?
1/4, 1, 2
Determine o, given that 1/12*o**2 + 89/4*o - 67/3 = 0.
-268, 1
Let j(c) be the first derivative of 4*c**3/9 + 20*c**2 - 256*c/3 - 1760. Let j(z) = 0. What is z?
-32, 2
Find g such that -35*g**3 - 65*g + 5*g**4 - 1076 + 2151 - 11*g**2 - 1055 + 86*g**2 = 0.
1, 4
Factor -139*s**3 + 1625*s**3 - 389*s**3 + 903*s**3 + 1605*s - 40 - 3077*s**2 - 13123*s**2.
5*(s - 8)*(20*s - 1)**2
Let y = -43 - -239. Let b(u) = 3*u**2 - y - 2*u**2 - u**2 - 3*u**2 + 52*u. Let o(q) = -15*q**2 + 261*q - 981. Let w(x) = -21*b(x) + 4*o(x). Factor w(i).
3*(i - 8)**2
Let q(w) be the second derivative of -16*w**6/135 + 436*w**5/3 + 727*w**4/6 + 818*w**3/27 - 2340*w + 1. Factor q(n).
-2*n*(n - 818)*(4*n + 1)**2/9
Let h = 398468 - 6773920/17. Factor h*d - 2 - 2/17*d**2.
-2*(d - 17)*(d - 1)/17
Let r be (576/(-42))/(2/(-14)). Factor 32*a + 2*a**3 + 153 + 39 + 28*a**2 + r*a.
2*(a + 4)**2*(a + 6)
Let f = 243 + -240. Let q = 35 + -32. Find j, given that -6*j**3 + f*j**2 - 5*j**4 + q*j**4 + 5*j**4 = 0.
0, 1
Let l(m) be the first derivative of 1/12*m**4 + 29 + 3/2*m**3 - 5*m + 4*m**2. Let x(t) be the first derivative of l(t). Suppose x(v) = 0. What is v?
-8, -1
Let s(i) be the first derivative of 2*i**6/3 - 28*i**5/5 - 6*i**4 + 96*i**3 + 641. Factor s(k).
4*k**2*(k - 6)*(k - 4)*(k + 3)
Let o(k) be the second derivative of -k**5/160 + k**4/16 + 117*k**3/16 + 243*k**2/2 - 2360*k. Factor o(g).
-(g - 24)*(g + 9)**2/8
Suppose -2*g - 9 = -3*j, 2*g + 3*j + 0 = -3. Let r be (-40)/(-68)*(-6)/(-9 - g). Let r*d**3 - 2/17*d**4 - 18/17*d - 6/17*d**2 + 0 = 0. Calculate d.
-1, 0, 3
Let c = -6443 - -12889/2. Let o(n) be the second derivative of -9/20*n**5 - 2*n**4 - 15*n + 3*n**2 - c*n**3 + 0. Solve o(g) = 0 for g.
-2, -1, 1/3
Suppose -790 = -350*i + 610. Suppose -i - g + 1/2*g**2 = 0. What is g?
-2, 4
Let o = 1204 - 1178. Suppose o = 392*u - 379*u. Factor 2/3*k + 0 + 2/3*k**3 - 4/3*k**u.
2*k*(k - 1)**2/3
Factor -999/7*w**2 + 250000/7 + 249000/7*w + 1/7*w**3.
(w - 500)**2*(w + 1)/7
Let i(p) = -p**3 + 33*p**2 - 23*p + 3. Let m(k) = -65*k**2 + 50*k - 5. Let l(q) = 5*i(q) + 3*m(q). Let l(v) = 0. What is v?
-7, 0, 1
Let -17*o**2 + 0*o**4 - o**2 - 15*o**3 - 30*o**2 + 4*o**4 - 5*o**3 + 144*o = 0. What is o?
-3, 0, 2, 6
Let s(p) = -23*p**4 + 149*p**3 + 257*p**2 - 145*p. Let n(r) = 12*r**4 - 75*r**3 - 129*r**2 + 72*r. Let m(b) = 11*n(b) + 6*s(b). Determine c so that m(c) = 0.
-2, 0, 1/2, 13
Determine y, given that 0 - 122/21*y + 2/21*y**2 = 0.
0, 61
Suppose 4*i + 8 = 2*n, 7 = -5*n + 2*i + 35. Let z(u) = u**3 - 6*u**2 - u + 8. Let k be z(n). Find q such that -5*q**3 - 3*q**3 + 23*q**2 - 9*q**k - 6*q = 0.
0, 3/4, 1
Let t = -270 + 179. Let p be (-3)/(63/12)*t/65. What is f in p + 32/5*f**4 + 12*f**2 - 6/5*f**5 - 26/5*f - 64/5*f**3 = 0?
1/3, 1, 2
Let v(p) be the first derivative of 7/12*p**3 - 1 + 6*p - 43/4*p**2. Factor v(a).
(a - 12)*(7*a - 2)/4
Let s(z) be the first derivative of -2*z**5/15 - 4*z**4/3 + 22*z**3/3 - 1045. Solve s(b) = 0.
-11, 0, 3
Let a(q) be the second derivative of q**4/24 + 152*q**3 + 207936*q**2 + q + 246. Factor a(i).
(i + 912)**2/2
Suppose -3*l - 6 = 9*v - 13*v, l - 8 = -2*v. Let h(w) be the first derivative of -1/2*w**4 + 0*w - 16/3*w**3 - 23 - 12*w**l. Factor h(o).
-2*o*(o + 2)*(o + 6)
Suppose -8 = 4*f, -37 = -5*w + f - 20. Find b, given that -23/7*b**w + 23/7*b + 6/7 - b**4 + 1/7*b**2 = 0.
-3, -1, -2/7, 1
Let n = 2085 - 3350. Let j be -15 + n/(-85) + (-4)/(-34). Factor k**2 + j + 1/6*k**3 + 5/6*k.
k*(k + 1)*(k + 5)/6
Let i(k) be the second derivative of k**4/54 - 32*k**3/27 + 220*k**2/9 - 1197*k + 2. Solve i(a) = 0 for a.
10, 22
Let f(s) be the second derivative of 2*s**6/15 - 7*s**5 + 128*s**4 - 2360*s**3/3 - 3200*s**2 - 30*s - 4. Let f(t) = 0. Calculate t.
-1, 10, 16
Let u(t) be the first derivative of -2*t**3/3 + 520*t**2/3 + 232*t + 1521. Factor u(r).
-2*(r - 174)*(3*r + 2)/3
Let n(q) be the first derivative of 4/5*q**5 - 149 + 1/3*q**6 + q**2 + 4*q - 8/3*q**3 - q**4. What is t in n(t) = 0?
-2, -1, 1
Let t(o) = -o**3 + 8*o**2 + 8*o + 8. Let q be t(9). Let d be (6 + -3)/(-4*q/4). Factor -d*f + 981 + 2*f - 978 - 3*f**2 + f**3.
(f - 3)*(f - 1)*(