first derivative of -g**4 - 424*g**3/3 + 430*g**2 - 432*g + 735. Suppose x(n) = 0. What is n?
-108, 1
Let r(a) = a + 1. Suppose -2*t - 3*t - 30 = 0. Let n(m) = m**4 - 6*m**3 + 8*m**2 + 8*m - 7. Let x(j) = t*r(j) + 3*n(j). Factor x(v).
3*(v - 3)**2*(v - 1)*(v + 1)
Determine o, given that -38*o + 156 + 21 - 60*o**2 - 9 + 281*o**3 - 68*o - 283*o**3 = 0.
-28, -3, 1
Let v = -7794/11 + 38981/55. Factor -3/5 + 4/5*k**2 + v*k.
(k + 1)*(4*k - 3)/5
Factor -305 - 796*z + 2785*z**2 - 632*z - 1007*z - 45*z**3.
-5*(z - 61)*(z - 1)*(9*z + 1)
Let c(g) be the first derivative of -g**7/168 - g**6/72 + g**5/24 + 5*g**4/24 - 35*g**3/3 + 81. Let f(l) be the third derivative of c(l). Factor f(m).
-5*(m - 1)*(m + 1)**2
Factor -82/5*a + 2/5*a**2 - 84/5.
2*(a - 42)*(a + 1)/5
Let g(u) be the first derivative of 2/15*u**6 - 58/5*u**2 + 23/5*u - 61 + 74/15*u**3 + 28/5*u**4 - 97/25*u**5. Determine y, given that g(y) = 0.
-1, 1/4, 1, 23
Determine r, given that -6/17*r**4 - 126/17*r**2 + 90/17*r - 58/17*r**3 + 100/17 = 0.
-5, -2/3, 1
Let r(o) be the third derivative of -o**8/4032 + o**7/336 - o**6/72 + o**5/60 - 10*o**3/3 - 88*o**2. Let d(v) be the third derivative of r(v). Factor d(u).
-5*(u - 2)*(u - 1)
Let y(s) = -s**2 - 30*s - 40. Let f be y(-23). Find z such that -40*z**3 + z - f*z + 110*z**2 + 45 + 34*z**4 - 29*z**4 = 0.
1, 3
Suppose 252*k - 37*k - 806 = -188*k. Suppose 2*w = 3 + 1. Suppose -1/2*i**k + w*i - 3/2 = 0. Calculate i.
1, 3
Suppose 5*m - 4*l - 34 = 0, 2 = 2*m - 2*l - 12. Suppose m - 18 = -4*s. Find w such that -5*w**4 + 11*w**2 + 10*w + w**2 + 3*w**s - 7*w**2 - 13*w**3 = 0.
-2, -1, 0, 1
Solve -140/13*j + 142/13 - 2/13*j**2 = 0 for j.
-71, 1
Let k(m) be the first derivative of -m**5/10 + m**4/4 + m**3/2 - 420. Let k(f) = 0. What is f?
-1, 0, 3
Let s = 19 + -17. Suppose 20 + 28 = s*z. Factor 15*p + 11*p - 10*p - z*p**2 - p**4 + 9*p**3.
-p*(p - 4)**2*(p - 1)
Let s(j) be the third derivative of j**6/180 + j**5/60 - 17*j**3/3 - 14*j**2 + j. Let r(k) be the first derivative of s(k). Factor r(i).
2*i*(i + 1)
Let t(s) be the second derivative of -s**4/12 - s**3/6 + 2*s. Let y(w) = 2*w**2 + 2*w + 12. Let g(j) = 3*t(j) + y(j). Factor g(q).
-(q - 3)*(q + 4)
Let r(a) be the first derivative of -a**8/2520 + a**7/420 + a**6/135 + 214*a**3/3 - 90. Let h(z) be the third derivative of r(z). Solve h(q) = 0 for q.
-1, 0, 4
Solve -3/2*g**2 + 1770*g - 522150 = 0 for g.
590
Suppose 2*n = -5*k + 3*n + 871, -k - n = -179. Let c be 3*k/126*(-20)/(-25). Suppose 5/3*g**2 + c*g + 0 = 0. Calculate g.
-2, 0
What is t in -10/23*t**5 + 12/23*t**3 + 0 - 16/23*t - 26/23*t**4 + 40/23*t**2 = 0?
-2, 0, 2/5, 1
Let d(o) be the third derivative of -o**5/570 + 237*o**4/19 - 674028*o**3/19 - 2*o**2 + 573*o. Solve d(c) = 0.
1422
Let f be 41/(-246)*((-24)/(-40))/((-2)/5). Factor -f*u - 1/4*u**3 - 1/2*u**2 + 0.
-u*(u + 1)**2/4
Let o = 127 + -125. Let t be (-247)/52 + o + 3. Find a such that t*a**2 - 1/4*a**3 + 0*a + 0 = 0.
0, 1
Let s(q) be the first derivative of -2*q**3/9 - 36*q**2 - 559. Suppose s(v) = 0. What is v?
-108, 0
Let h(k) be the second derivative of 4/5*k**2 + 1/20*k**4 + 7/15*k**3 + 59*k - 1/150*k**6 - 1/25*k**5 - 2. Find u, given that h(u) = 0.
-4, -1, 2
Let t(k) be the first derivative of k**4/2 - 14*k**3 - 34*k**2 + 528*k - 1352. Solve t(h) = 0 for h.
-4, 3, 22
Suppose 0 = 5*y - 20 - 0. Factor 8 - 4*z + z**2 - y - 1.
(z - 3)*(z - 1)
Let y(t) be the first derivative of -t**5/40 + 6*t**4 - 2079*t**3/4 + 35721*t**2/2 - 750141*t/8 - 788. Factor y(h).
-(h - 63)**3*(h - 3)/8
Let t = 19214 + -19212. Factor -4/3 - 5/3*h**t + 1/3*h**3 + 8/3*h.
(h - 2)**2*(h - 1)/3
Let v(j) be the second derivative of -j**4/3 - 14*j**3 - 160*j**2 + 993*j. Solve v(f) = 0.
-16, -5
Suppose 0 = -4*k + 3*c + 77, 3*k - 25*c - 48 = -26*c. Let a be k/4 - 6/24. Factor 0 - 11*m**3 + 14*m**2 + 5/2*m**4 - a*m.
m*(m - 2)**2*(5*m - 2)/2
Let h = 1162 - 1162. Let p(o) be the third derivative of 7/144*o**4 + h*o + 0 + 0*o**3 - o**2 - 1/360*o**5. Find c, given that p(c) = 0.
0, 7
Suppose -4*b + 11 = -17. Let x be (b/3)/7 + (-22)/(-6). Determine c, given that 7*c**5 + 30*c**2 + 70*c**x + 85*c**3 + 3*c**5 + 6*c**5 - c**5 = 0.
-3, -1, -2/3, 0
What is f in 0 - 39/2*f**4 + 1/4*f**5 + 0*f**2 + 0*f + 365/4*f**3 = 0?
0, 5, 73
Let q(p) = p**3 + 2*p - 1810*p**2 + 1810*p**2. Let f(h) = 18*h**3 + 6*h**2 + 33*h. Let v(i) = -f(i) + 15*q(i). Find b such that v(b) = 0.
-1, 0
Let y(w) = w**3 + 14*w**2 + 11*w - 5. Let d be y(-13). Find j such that -3*j**5 - 60*j**2 - 72*j - 54*j**3 + 48*j + 0*j**5 - d*j**4 = 0.
-2, -1, 0
Solve 62*w**2 - 20*w**3 + 89*w**5 - 24*w**4 + 83*w + 106*w**2 - 126*w**5 + 41*w**5 + 77*w = 0 for w.
-2, -1, 0, 4, 5
Factor 13*n**3 + 12*n**3 - 23*n**3 - 167962 + 597*n**2 - 54827 - 27501*n - 5*n**3.
-3*(n - 103)**2*(n + 7)
Let y(j) = j**2 - 30*j - 59. Let a(q) = q**2 - 14*q - 29. Let s = -572 + 569. Let c(w) = s*y(w) + 5*a(w). Factor c(u).
2*(u + 2)*(u + 8)
Let q(i) = -20*i**4 - 180*i**3 + 28. Let o = -47 - -19. Let b(v) = 2*v**4 + 20*v**3 - 3. Let a(m) = o*b(m) - 3*q(m). Suppose a(w) = 0. Calculate w.
0, 5
Let t = -447444/53 - -8442. Let i = t + 268/477. Let 8/9*v**5 + 2/3*v**2 + i*v - 2/3*v**4 + 0 - 10/9*v**3 = 0. What is v?
-1, -1/4, 0, 1
Let v(n) be the third derivative of -1/720*n**6 + 0*n - 25/48*n**4 + 0 + 1/24*n**5 - n**2 - 17/6*n**3. Let a(j) be the first derivative of v(j). Factor a(m).
-(m - 5)**2/2
Factor 136*k**3 - 63*k**3 - 36328 - 522*k**2 - 8048 - 23220*k - 76*k**3.
-3*(k + 2)*(k + 86)**2
Let t(q) = -q**3 + 24*q**2 - 4*q + 96. Let m be t(24). Let r(w) be the first derivative of -w**4 - 12*w**2 + 28/3*w**3 + 30 + m*w. Factor r(d).
-4*d*(d - 6)*(d - 1)
Factor -204/7*r - 400/7 - 2/7*r**2.
-2*(r + 2)*(r + 100)/7
Suppose -146*q + 156*q = -2*c + 240, -4*c + 4*q = -144. Factor c*d**3 + 0 + 125/3*d**4 + 8/3*d + 20*d**2.
d*(5*d + 2)**3/3
Let n be (4218/(-495))/(-2) + 26/7293*-17. Factor -n*j**2 + 18/5 - 3*j**3 + 3/5*j**4 + 3*j.
3*(j - 6)*(j - 1)*(j + 1)**2/5
Let s be (1252/(-8138))/(12/(-13)). Let z(p) be the second derivative of 1/2*p**2 + s*p**4 - 1/2*p**3 + 24*p + 0. Factor z(k).
(k - 1)*(2*k - 1)
Let x(m) be the first derivative of -4*m**3/3 - 146*m**2 + 600*m + 464. Factor x(n).
-4*(n - 2)*(n + 75)
Suppose 2339*n - 3*o = 2344*n - 37, 3*n - 2*o + 12 = 0. Suppose -2/3*d**2 - n*d - 4/3 = 0. Calculate d.
-2, -1
Factor -6/5*n**2 - 44 + 334/5*n.
-2*(n - 55)*(3*n - 2)/5
Let x be (-1)/(-2)*(0/13 + 4). Suppose -r + 3 = x*a, -5*r = -8*a + 5*a + 11. Factor -1/2 - 5/8*g**3 + g + 7/8*g**a.
-(g - 2)*(g + 1)*(5*g - 2)/8
Find i, given that 56/11*i - 2/11*i**2 + 120/11 = 0.
-2, 30
Let d be (-8)/15*(-78)/195*(-45)/(-12). Factor -4/5*n**2 + d*n + 24/5.
-4*(n - 3)*(n + 2)/5
Suppose 46*h - 14*h = 0. Let b(r) be the third derivative of -1/420*r**7 + 5/48*r**4 + 13/720*r**6 - 1/9*r**3 + 0 - 7/120*r**5 + 30*r**2 + h*r. Factor b(n).
-(n - 1)**3*(3*n - 4)/6
Let k be ((-33)/22)/(11/770). Let d be (343/k - -3)/(4/(-10)). Let 0 + 1/3*z**3 + z**2 + d*z = 0. Calculate z.
-2, -1, 0
Suppose -3*a - p = -22, 0*a + 3*a - 4*p - 32 = 0. Suppose 0 = -a*j + 92 + 36. Determine c so that 56*c - j*c - 23 + 5*c**3 + 3 - 25*c**2 = 0.
1, 2
Let v(a) = -16*a**4 - 472*a**3 + 3888*a**2 + 20*a. Let g(u) = -7*u**4 - 210*u**3 + 1728*u**2 + 9*u. Let q(p) = -20*g(p) + 9*v(p). Solve q(b) = 0 for b.
-18, 0, 6
Let a(g) be the first derivative of 3*g**4/4 - 29*g**3 - 198*g**2 + 4492. Determine m so that a(m) = 0.
-4, 0, 33
Let o(i) = i**3 + 25*i**2 + 44*i + 34. Let l be o(-23). Let b = l - 73. Factor -24*y - 2*y**2 + 4 + 29*y**2 - b*y**2.
4*(y - 1)*(5*y - 1)
Let i(a) = 3*a**3 - 13*a**2 + 58*a + 76. Let l(z) = 7*z**3 - 24*z**2 + 114*z + 150. Let x(s) = 5*i(s) - 2*l(s). Factor x(b).
(b - 10)*(b - 8)*(b + 1)
Let b(t) be the third derivative of 4/315*t**7 + 29/45*t**5 - 1/6*t**6 + t**2 - 7/6*t**4 + 0*t - 8 + 10/9*t**3. Solve b(j) = 0.
1/2, 1, 5
Let m(b) be the first derivative of b**4/20 - 74*b**3/5 + 438*b**2/5 - 872*b/5 - 3217. Determine d so that m(d) = 0.
2, 218
Let c(h) = 2*h**2 + 14*h + 22. Let l(a) = 11. Let p(y) = 2. Let f(b) = -l(b) + 5*p(b). Let i(t) = -c(t) + 2*f(t). Factor i(u).
-2*(u + 3)*(u + 4)
Find m such that -245/2*m**2 - 415/2*m**4 + 18*m**5 - 13*m - 335*m**3 + 0 = 0.
-1, -1/4, -2/9, 0, 13
Find x such that -44 - 9*x**3 - 30693*x + 28794*x - 523 - 597*x**2