1
Factor 50915*z - 717602/7 + 1196/7*z**2 + 1/7*z**3.
(z - 2)*(z + 599)**2/7
Factor 330*s**2 + 135 - 54*s - 162*s**2 - 165*s**2.
3*(s - 15)*(s - 3)
Let q be 34/10 - (-4)/(-10). Let o = -2300226 - -2300228. Factor 9/2 - 3/2*h**o - q*h.
-3*(h - 1)*(h + 3)/2
Factor 0 + 10/9*o**3 + 120*o + 1358/9*o**2.
2*o*(o + 135)*(5*o + 4)/9
Let m(b) be the second derivative of 128*b**7/21 + 656*b**6/15 + 929*b**5/20 - 2203*b**4/12 - 95*b**3/2 - 9*b**2/2 - 4*b + 54. Determine u, given that m(u) = 0.
-3, -1/16, 1
Factor 13068/5 + 3/5*i**2 + 396/5*i.
3*(i + 66)**2/5
Let x = 50 + -42. Let m be (x/12)/(6/4545). Factor 0 - 3*y**2 + 0 - 502*y + m*y.
-3*y*(y - 1)
Let d(r) be the second derivative of r**4/12 - 5*r**3/3 + 5*r**2/2 - 36*r. Let h(c) = -c**2 + 12*c - 6. Let g(j) = -6*d(j) - 5*h(j). Factor g(x).
-x**2
Factor 0*f + 0 + 264/7*f**3 - 512/7*f**2 - 4/7*f**4.
-4*f**2*(f - 64)*(f - 2)/7
Factor -4*l**2 + 212*l - 127*l + 87*l + 960.
-4*(l - 48)*(l + 5)
Let c be 1 + 4/(-10) - (-153)/45. Solve 0*m - 6*m - 12*m**4 + 9*m**2 + 3*m**3 - 15*m**4 + 18*m**c + 3*m**5 = 0.
-1, 0, 1, 2
Let j(h) = 7*h**3 - h**2 - h + 4. Let k(u) = -48*u**3 + 561*u**2 - 2880*u + 1281. Let m(d) = 6*j(d) + k(d). Factor m(q).
-3*(q - 87)*(q - 5)*(2*q - 1)
Let b(h) be the second derivative of h**6/2520 - h**5/56 - 43*h**3/6 - h**2 + 28*h. Let q(g) be the second derivative of b(g). Factor q(c).
c*(c - 15)/7
What is m in -18 - 371*m**4 - 96*m**2 + 33*m + 374*m**4 + 87*m**2 - 9*m**3 = 0?
-2, 1, 3
Let f(r) be the first derivative of r**3/7 - 12*r**2 + 165*r/7 - 3312. Suppose f(s) = 0. What is s?
1, 55
Suppose -8 = -5*x - 0*k + 3*k, 0 = -4*x + k + 12. Factor -9*h**2 - 16*h**x + 22*h**4 + 15*h - 3*h**3 - 6 - 3*h**4.
3*(h - 1)**3*(h + 2)
Let g = -10787/3 + 44273/12. Factor 1176 + 21570*x**3 + 5475/2*x**4 + 8988*x + 23316*x**2 + g*x**5.
3*(x + 14)**2*(5*x + 2)**3/4
Let v(c) = 3*c - 5 + 2*c**2 - 1 + 3*c**2. Let l(w) = -11*w**2 + 38*w + 13 - 28*w - 16*w. Let i(q) = 6*l(q) + 13*v(q). Solve i(t) = 0 for t.
0, 3
Suppose -u - 4*u = -17200. Let s be (8/7)/4 - u/(-210). Determine p, given that -32/3 - 368/3*p**2 + 64*p + 80*p**3 - s*p**4 = 0.
2/5, 2
Find v, given that -88/9*v**2 - 170/9*v - 2/9*v**3 - 28/3 = 0.
-42, -1
Suppose -7966*j + 7958*j + 88 = 0. Let s(f) be the third derivative of -1/480*f**6 + 1/96*f**4 - j*f**2 + 0*f**3 + 0 + 0*f + 0*f**5. Factor s(v).
-v*(v - 1)*(v + 1)/4
Let d = 1387825 + -578722748/417. Let q = 1/417 + d. Factor q*r + 0 + 4/3*r**2 + 8/3*r**4 - 14/3*r**3.
2*r*(r - 1)**2*(4*r + 1)/3
Let h(j) = 2*j**2 + 11*j - 3. Let i be h(-5). Let d be ((-4)/i)/(1*4/32). Determine g, given that -14*g**2 + 10*g**3 - 8*g**4 + 14*g**2 + 13*g**d = 0.
-2, 0
Let o(k) be the second derivative of -1/6*k**4 + 18 - 6/35*k**5 + 2/7*k**2 - 2*k + 1/3*k**3. Suppose o(u) = 0. Calculate u.
-1, -1/4, 2/3
Let t = -10601 - -10601. Let f(x) be the second derivative of 1/36*x**4 - 1/6*x**2 - 16*x + t - 1/60*x**5 + 1/18*x**3. Factor f(y).
-(y - 1)**2*(y + 1)/3
Let c be (-10)/(-6) + ((-28)/(-6))/14. Factor -v**2 + 7*v**c + 15*v - 2*v**2 - 3*v + 104*v.
4*v*(v + 29)
Suppose -4*k + k = 5*z + 9127, 7308 = -4*z - 4*k. Let o = z + 1833. Suppose 85/2*n**3 + 0 + 50*n**2 + 10*n**4 + o*n = 0. What is n?
-2, -1/4, 0
Let x(h) be the first derivative of h**5/2 + 60*h**4 - 85*h**3 - 610*h**2 - 1455*h/2 + 4067. Let x(y) = 0. Calculate y.
-97, -1, 3
Let k(p) be the third derivative of -p**6/16 - 1043*p**5/60 - 553*p**4/12 - 46*p**3 - 1481*p**2. Let k(y) = 0. What is y?
-138, -2/3, -2/5
Factor 199*d**2 - 203*d**2 + 1225*d + 5*d**3 - 156*d**2 - 2750.
5*(d - 22)*(d - 5)**2
Suppose -3*w + 0*v = -v - 26, 0 = 2*w - 2*v - 24. Suppose -3*o + w = -a, -a = -3*o + o + 4. Let -14*q + 4 + 6 + 9*q - 10*q + 5*q**a = 0. Calculate q.
1, 2
Let c be 4*2*(-11)/(-1056). Let d(n) be the first derivative of c*n**4 + 0*n + 21 - 5/9*n**3 + 2/3*n**2. Factor d(x).
x*(x - 4)*(x - 1)/3
Let l(u) be the second derivative of -43*u - 1/5*u**5 + 0 + 2/15*u**6 + 2/3*u**3 - 1/3*u**4 + 0*u**2. Find g, given that l(g) = 0.
-1, 0, 1
Suppose -4*f = -4*q - 5*f + 15, 0 = 3*q + 4*f - 21. Let k(c) be the first derivative of -q - 14/19*c + 6/19*c**2 + 2/57*c**3. Factor k(m).
2*(m - 1)*(m + 7)/19
Suppose 0 = 4*u + 4*u. Suppose 21 = 3*g - 3*z, 4*g + z - 13 = -u*z. Factor 8*a + 3*a + 0*a**2 + 25*a - 20 - g*a**3 - 12*a**2.
-4*(a - 1)**2*(a + 5)
Suppose n = 2*w + 3*n + 546, -5*w - 1362 = 4*n. Let f = -97 - w. Factor -209 - 217 - 81 + f*s - 3*s**2 - 251*s.
-3*(s + 13)**2
Suppose 177*l**2 + 165*l**2 + 5*l**3 + 7*l**3 - 12*l**5 + 40*l**4 - 382*l**2 = 0. What is l?
-1, 0, 1, 10/3
Let r(l) be the second derivative of -l**7/315 - 7*l**6/75 + 31*l**5/15 + 129*l + 4. Factor r(c).
-2*c**3*(c - 10)*(c + 31)/15
Suppose 0 = 2*w + 2*a, -2*w - 1 - 3 = 3*a. Suppose w*q + 7*q = 44. Factor -s + 1473 - 1473 + s**3 + s**2 - s**q.
-s*(s - 1)**2*(s + 1)
Suppose 379/3*s - 509*s**2 + 254/3 + 901/3*s**3 - 7/3*s**4 = 0. What is s?
-2/7, 1, 127
Let h(w) = -29*w**2 - 340*w - 1382. Let g(i) = 80*i**2 + 935*i + 3800. Let c(y) = 9*g(y) + 25*h(y). Suppose c(b) = 0. What is b?
-10, -7
Let k = 6217/183810 - 3/6127. Let j(i) be the second derivative of -7/20*i**5 - 5*i + k*i**6 + 3*i**2 + 17/12*i**4 + 2 - 17/6*i**3. Let j(w) = 0. What is w?
1, 2, 3
Let y(m) be the second derivative of m**10/30240 + m**9/3780 + m**8/2240 - 4*m**4/3 - m**2/2 + 180*m. Let n(x) be the third derivative of y(x). Factor n(b).
b**3*(b + 1)*(b + 3)
Suppose 2*k = -3*k + 2*d + 60, -k = -3*d + 1. Find h such that 24 + k*h + 0 - 9*h**3 + 64*h + 15*h**2 = 0.
-2, -1/3, 4
Let v be -7 + 7/24*28. Let m(j) be the second derivative of 0 - 10*j - 2*j**2 - v*j**3 - 1/6*j**4 + 1/20*j**5. Factor m(a).
(a - 4)*(a + 1)**2
Let q(i) be the second derivative of 5*i**4/102 - 24*i**3/17 - 77*i**2/17 - 165*i. Solve q(d) = 0.
-1, 77/5
Suppose 57*z = 59*z + 2. Let j be (210/20 + -11)*z/3. Let 1/6 + j*v**2 - 1/3*v = 0. What is v?
1
Suppose 83*d = 84*d - 12. Suppose -d*c = -41 + 5. Find m, given that 4*m**5 + 66*m - 11*m**3 + 3*m**c - 62*m = 0.
-1, 0, 1
Let z(s) be the first derivative of 2*s**6/3 - 12*s**5/5 - 3*s**4 + 28*s**3/3 + 12*s**2 - 942. Let z(j) = 0. Calculate j.
-1, 0, 2, 3
Let j be 9/(0 + 1 + (-13080)/13185). Let l = j + -1130. Factor -12/7*g + 1/7*g**5 - l*g**3 + 4/7 + 11/7*g**2 - 3/7*g**4.
(g - 2)*(g - 1)**3*(g + 2)/7
Let q be (96/112)/(8/(-84)). Let u be (q/(-6))/(9 + (-12 - -7)). Factor 0 + u*i - 3/8*i**2 - 3/8*i**3 + 3/8*i**4.
3*i*(i - 1)**2*(i + 1)/8
Let w(u) be the first derivative of -3*u**4/4 + 318*u**3 - 1899*u**2/2 + 948*u + 9774. Factor w(a).
-3*(a - 316)*(a - 1)**2
Let u = 4021102/3 + -1337959. Suppose -u - 1/3*a**2 - 170/3*a = 0. What is a?
-85
Suppose f + 3 - 15 = -3*v, 3*f - 21 = -4*v. Suppose -f*q + 0*q + 4*d + 9 = 0, -4*q = -3*d - 12. Factor -5*k**2 - 14*k + 7*k**2 + 2*k**q + 8*k**2 + 6 - 4*k**3.
-2*(k - 3)*(k - 1)**2
Factor 7/3*b**3 + 8/3 - 62/3*b**2 + 47/3*b.
(b - 8)*(b - 1)*(7*b + 1)/3
Let z(y) be the second derivative of -y**4/32 - 105*y**3/16 - 309*y**2/8 - 2*y - 756. Let z(b) = 0. What is b?
-103, -2
Let a(b) = 23*b**3 - 11*b**2 - 30*b - 5. Let h(l) = 56*l**3 - 28*l**2 - 72*l - 12. Let t(f) = -12*a(f) + 5*h(f). Let t(y) = 0. Calculate y.
0, 2
Let g(u) be the third derivative of -u**6/2520 - u**5/840 + u**4/14 - 139*u**3/6 + 155*u**2. Let h(o) be the first derivative of g(o). Factor h(y).
-(y - 3)*(y + 4)/7
Let n(z) be the third derivative of 1/1440*z**6 + 0*z + 0 - 1/48*z**4 + 1/480*z**5 - 13/3*z**3 - 28*z**2. Let i(b) be the first derivative of n(b). Factor i(c).
(c - 1)*(c + 2)/4
Let p = -80 + 83. What is l in 23 + 17 + 33 + p*l**2 - 36*l - 23 + 10 = 0?
2, 10
Let i(g) be the first derivative of 132*g**5/5 + 105*g**4/8 - 85*g**3/2 - 105*g**2/4 - 9*g/2 - 722. Let i(f) = 0. Calculate f.
-1, -3/11, -1/8, 1
Let s(w) be the third derivative of w**5/360 + 7*w**4/18 + 55*w**3/36 - 6328*w**2. What is c in s(c) = 0?
-55, -1
Let g(j) be the second derivative of -7/5*j**2 + 3/10*j**3 - 1/60*j**4 - 1 + 2*j. Factor g(k).
-(k - 7)*(k - 2)/5
Let a(m) = -3*m**4 - 5*m**3 - 5*m**2 - m - 1. Let z(t) = 17*t + 3. Let b be z(0). Let o(i) = -2*i**4 - i**3 + i - 1. Let y(q) = b*a(q) - 3*o(q). Factor y(r).
-3*r*(r + 1)**2*(r + 2)
Let w = -704 - -714. Let -8 - v**2 + 4*v - v**2 - w + 6 - 14*v = 0. What is v?
-3, -2
Determine d, given that -282 - 6*d**2 + 6*d**2