/2
Let r(i) be the second derivative of -i**5/45 + 19*i**4/27 + 40*i**3/27 + 362*i. Factor r(z).
-4*z*(z - 20)*(z + 1)/9
Let m be ((-21 - -42)/21 - 0/(-1) - 5)*-52. Factor -100/13*a**2 + 88*a + 2/13*a**3 + m.
2*(a - 26)**2*(a + 2)/13
Suppose -3*t = -5*c - 18 - 99, -4*t + 2*c + 156 = 0. Let b = 1602 - 1598. Factor -18*j + 2*j**2 + t*j - 6*j**2 - 4*j**3 + b - 17*j.
-4*(j - 1)*(j + 1)**2
Let g(p) be the first derivative of -p**8/1960 - p**7/5880 + 3*p**3 + p**2 - 12. Let l(v) be the third derivative of g(v). Determine z, given that l(z) = 0.
-1/6, 0
Let z(m) be the second derivative of -m**5/20 - m**4/4 + 9*m**3 - 3445*m. Factor z(j).
-j*(j - 6)*(j + 9)
Let b(l) be the third derivative of -112*l**5/15 + 22*l**4/3 - 121*l**3/42 - 441*l**2 - 1. Suppose b(q) = 0. What is q?
11/56
Let s = -850 + 853. Determine q, given that 11*q + 9*q + 2*q**2 + 2*q**2 + 24*q**2 - s*q**2 = 0.
-4/5, 0
Let d(h) be the first derivative of 0*h - 1/7*h**3 + 9/14*h**2 + 26. Factor d(t).
-3*t*(t - 3)/7
Determine p so that 7 - 3*p + 37 - 13*p - 6*p**2 + 12 - 16*p**2 = 0.
-2, 14/11
Let n be (-16)/(64/6) + (-595)/(-400). Let i = 323/240 + n. Solve 0*h + i*h**3 + 1/3*h**4 + 0 + 4/3*h**2 = 0.
-2, 0
Let f(v) be the third derivative of -2*v**7/315 - 13*v**6/90 - 2*v**5/3 + 1730*v**2. Find j such that f(j) = 0.
-10, -3, 0
Let k(p) be the first derivative of p**5/5 + 19*p**4/4 - 14*p**3 - 1093. Factor k(q).
q**2*(q - 2)*(q + 21)
Let z(g) be the first derivative of 42 - 9/2*g**2 + 27*g - 5*g**3 - 3/4*g**4. Find u, given that z(u) = 0.
-3, 1
What is w in -4*w**2 - 12*w**2 - 2*w**3 + w**2 + w**2 + 4*w**3 = 0?
0, 7
Let d(b) be the first derivative of -23/6*b**3 + 43/4*b**2 - 15 - 21/2*b + 1/8*b**4. Factor d(y).
(y - 21)*(y - 1)**2/2
Let h = -18 + 21. Suppose -v**3 - v**h + 2*v - 2 + 16*v**2 - 14*v**2 = 0. Calculate v.
-1, 1
Let c = -247 - -249. Factor 3*a**2 + 17*a**c + 2*a**3 - 71*a + 111*a - 62*a.
2*a*(a - 1)*(a + 11)
Let h be 2 + 2/(6/9*(-3)/2). Let j(z) be the third derivative of -1/60*z**5 + 9*z**2 + 5/96*z**4 + h*z + 0 - 1/24*z**3. Suppose j(o) = 0. Calculate o.
1/4, 1
Let k be 1 - 1 - (-3 - 1)/2. Suppose 48 = k*p - 32. Find v, given that -4*v**2 - p*v + 0*v**2 - 2*v**2 - 80 + v**2 = 0.
-4
Let x(k) be the third derivative of 0 + 1/36*k**5 + 0*k - 5/24*k**4 + 0*k**3 + 82*k**2. Factor x(a).
5*a*(a - 3)/3
Let u = -858 + 855. Let d be -5 - (1 - 5) - u. Solve 1 + 55/8*t**3 - 7/4*t**5 - 35/4*t**d + 1/2*t + 17/8*t**4 = 0 for t.
-2, -2/7, 1/2, 1, 2
Let o(c) be the second derivative of 3*c**4/4 + 1387*c**3/2 - 1389*c**2 - 912*c. Determine g so that o(g) = 0.
-463, 2/3
Determine d so that 0 - 6/5*d**3 + 1/5*d**5 + 9/5*d**4 + 168/5*d - 116/5*d**2 = 0.
-7, -6, 0, 2
Let -12 + 11*a**2 + 36*a**2 - 13*a**2 - 6*a**3 - 3*a**3 - 13*a**2 = 0. What is a?
-2/3, 1, 2
Suppose 9 = 3*i + 2*z, 5*z = 4*i - 162 + 150. Suppose 4*g - 12 = -5*m, -6*g + 4 = i*m - 2*g. Factor d**3 + 0 - 4*d - 2*d**2 + 1/2*d**m.
d*(d - 2)*(d + 2)**2/2
Let s(r) = 187*r - 3734. Let j be s(20). Let b(a) be the third derivative of 9/20*a**5 + 0*a**3 + 0*a + 0 + j*a**2 - 7/40*a**6 - 1/4*a**4. Factor b(c).
-3*c*(c - 1)*(7*c - 2)
Suppose 0 = s + 34 - 62. Suppose 7*x = 497 + s. Factor 35*i**2 + x*i - 2*i**3 + 7*i**3 + 22 + 23.
5*(i + 1)*(i + 3)**2
Let i = 62/737 + 551/2211. Let d(g) be the first derivative of -1/9*g**3 - i*g + 2 - 1/3*g**2. Determine v, given that d(v) = 0.
-1
Let v(d) be the third derivative of 1/40*d**5 + 1/80*d**6 + 0*d**4 + 139*d**2 + 0*d**3 - 1/140*d**7 - 1/224*d**8 + 0 + 0*d. Find w, given that v(w) = 0.
-1, 0, 1
Let b(p) be the second derivative of -3*p**5/40 - 3*p**4/2 - 397*p - 1. Solve b(l) = 0.
-12, 0
Suppose 57 = 2*z + 3*y + 72, 4*z + 4*y + 20 = 0. Let h(w) be the second derivative of -5/12*w**4 - 55/3*w**3 + 44*w + z - 605/2*w**2. Factor h(b).
-5*(b + 11)**2
Let y(i) be the first derivative of -i**6/4 - 44*i**5/5 - 579*i**4/8 - 189*i**3 + 8*i**2 + 336*i - 339. Determine p so that y(p) = 0.
-21, -4, -1, 2/3
Suppose -934*w + 1788 = -80. Factor -2/9*y**w - 2/9 + 4/9*y.
-2*(y - 1)**2/9
Let 21695780372/5*o**3 - 32/5 + 84336/5*o - 74089176/5*o**2 = 0. What is o?
2/1757
Let l(d) be the second derivative of -d**4/12 - d**3/2 + 11*d**2 + 10*d. Let i be l(-5). Factor 20*t**4 - 23*t**2 + 11*t**5 - 7*t**5 - 13*t**2 + i*t**3.
4*t**2*(t - 1)*(t + 3)**2
Suppose 156/7*b - 153/7 - 3/7*b**2 = 0. Calculate b.
1, 51
Let j = -11239 - -11244. Let a(s) be the first derivative of -21 - 7/10*s**2 - 1/4*s**4 - 1/25*s**j - 3/5*s**3 - 2/5*s. Factor a(o).
-(o + 1)**3*(o + 2)/5
Let j(b) = -8*b**5 + 10*b**4 - 18*b**3 - 265*b**2 + 17*b + 12. Let h(m) = -m**5 + m**4 - m**3 - 28*m**2 + m. Let k(p) = 18*h(p) - 2*j(p). Solve k(f) = 0 for f.
-2, -1, 1, 3
Let s = 3028 + -3028. Let u(m) be the second derivative of 0*m**4 + 1/18*m**6 + 0 - 1/126*m**7 + 0*m**2 + s*m**3 + 14*m + 0*m**5. Factor u(p).
-p**4*(p - 5)/3
Let u be (-48018)/(-27) - (-24)/(-18). Let p = u - 1770. Determine g, given that 16/9 - 44/9*g**2 + p*g - 4*g**3 = 0.
-2, -2/9, 1
Let 43*r**3 + 100*r**3 + 420 - 165*r**2 - 1181*r + 55*r**4 + 67*r**3 + 661*r = 0. What is r?
-42/11, -2, 1
Let y(d) = -d**3 + d. Let p be y(1). Let n be (336/(-36) - -8)*(636/96 - 7). Suppose p*q - 2 + n*q**2 = 0. Calculate q.
-2, 2
Let v be (75/90)/(20/(-12))*(-4)/8. Let c(u) be the second derivative of u**3 + 0*u**2 + v*u**4 + 0 + 7*u. Factor c(x).
3*x*(x + 2)
Let f(j) be the first derivative of -1/90*j**5 + 2/63*j**3 - 3*j**2 + 0*j + 8 + 5/252*j**4. Let x(q) be the second derivative of f(q). Factor x(u).
-2*(u - 1)*(7*u + 2)/21
Let v(r) be the first derivative of -5*r**4/12 + 5*r**3/3 - 23*r + 76. Let p(z) be the first derivative of v(z). Let p(x) = 0. What is x?
0, 2
Let g(w) = -w**2 - 1. Let z(h) be the second derivative of -5*h**4/6 + 75*h**2/2 + 48*h. Let s(f) = -5*g(f) + z(f). Factor s(m).
-5*(m - 4)*(m + 4)
Factor -10/3*a**2 + 32/3 + 76/3*a.
-2*(a - 8)*(5*a + 2)/3
Let h be 119/(-34)*(-12)/2. Suppose -4*w**3 + 3*w**3 - h*w**2 - 10*w**2 - 18*w**2 + 55*w**2 + 7*w = 0. Calculate w.
-1, 0, 7
Let g = -149542/99 + 16650/11. Factor 4/9*s**2 + g + 32/9*s.
4*(s + 1)*(s + 7)/9
Let t(s) be the third derivative of -s**5/15 - 8*s**4/3 + 938*s**2. Let t(l) = 0. What is l?
-16, 0
Let p be 4/(-15) - 3/(60/(-8)). Suppose 0 = -2*y + 9*s - 6*s - 6, -20 = -5*s. Determine q, given that -4/5*q**y - p*q**4 - 8/15 - 8/5*q - 26/15*q**2 = 0.
-2, -1
Let y(i) be the second derivative of -3*i**3/2 - 161*i**2 + 41*i. Let u be y(-36). Find r such that -2/5*r**4 + 24/5*r - 8/5 - 26/5*r**u + 12/5*r**3 = 0.
1, 2
Factor 5*q**3 + 8808*q**2 - 23*q**3 + 229155 - 2*q**3 + 158045 - 1375905*q + 404385*q.
-4*(q - 220)**2*(5*q - 2)
What is s in 192/5*s**2 - 794/5*s + 2/5*s**3 + 120 = 0?
-100, 1, 3
Let a(r) = -15*r - 103. Let t be a(-7). Factor 17*v + 2*v**2 - t*v - 6 - 19*v.
2*(v - 3)*(v + 1)
Let -44*b**3 - 60*b**2 + 0*b - 1/4*b**5 + 63/4*b**4 + 0 = 0. Calculate b.
-1, 0, 4, 60
Solve -1623*z**3 - 316*z**2 - 10563*z - 14401*z + 1622*z**3 = 0 for z.
-158, 0
Let y(x) be the first derivative of -2197*x**5 - 14365*x**4/2 - 9100*x**3 - 5635*x**2 - 1715*x + 141. Let y(m) = 0. What is m?
-1, -7/13
Let t(w) be the first derivative of 12*w**3 - 3136*w**2 + 1392*w + 5924. Factor t(n).
4*(n - 174)*(9*n - 2)
Let -3576*y**2 + 810*y**4 - 513*y**3 - 567/4*y**5 + 1536 + 4416*y = 0. What is y?
-2, -2/7, 8/3
Let x(v) be the first derivative of 9*v**3 + 27*v**2/2 - 15*v - 2. Let b = -70 - -55. Let t(a) = 7*a**2 + 7*a - 4. Let j(g) = b*t(g) + 4*x(g). Factor j(c).
3*c*(c + 1)
Let y(u) = u**3 + 7*u**2 - 8*u - 7. Suppose -6 - 50 = 8*m. Let n(l) = 4*l**2 - 4*l - 4. Let a(f) = m*n(f) + 4*y(f). Let a(h) = 0. What is h?
-1, 0, 1
Let b = -1429 + 1432. Let y(j) be the second derivative of 0 + 1/3*j**b + 0*j**2 - 1/20*j**5 - j - 1/12*j**4. Factor y(q).
-q*(q - 1)*(q + 2)
Factor 52*m**3 + 0*m - 160*m**2 - 37/8*m**4 + 0 + 1/8*m**5.
m**2*(m - 16)**2*(m - 5)/8
Let p(o) be the second derivative of -5/9*o**3 + 1/90*o**5 + 7/27*o**4 + 0 - 69*o + 0*o**2. Let p(u) = 0. Calculate u.
-15, 0, 1
Solve -96*a - 186 - 3/2*a**2 = 0.
-62, -2
Let r(j) = -3*j**2 - 1250*j - 78117. Let b(v) = 80*v**2 + 33750*v + 2109155. Let i(k) = 2*b(k) + 55*r(k). Solve i(x) = 0 for x.
-125
Suppose 6*t - 11*t + 1445 = 5*u, -2*t - 570 = -2*u. Let j = u - 285. Let 60/7*n + 2/7*n**j + 450/7 = 0. Calculate n.
-15