 Let h = 321 + -294. Let c be s(h). Factor 3*z**2 + 1/2 + 2*z + 1/2*z**c + 2*z**3.
(z + 1)**4/2
Let f(m) = 68*m**2 - 10171*m + 3235978. Let d(h) = -40*h**2 + 5085*h - 1617990. Let j(r) = -5*d(r) - 3*f(r). Factor j(n).
-4*(n - 636)**2
Determine r so that 18*r**2 + 144*r + 2/3*r**3 + 360 = 0.
-15, -6
Let o(y) be the first derivative of -y**5/55 - 25*y**4/44 + y**3/33 + 25*y**2/22 - 1830. Find p, given that o(p) = 0.
-25, -1, 0, 1
Let s(h) = h**5 + h**4 - h**2 - 3*h - 1. Let r(a) = -194*a**5 - 83*a**4 + 559*a**3 + 617*a**2 + 195*a + 21. Let g(f) = r(f) + 5*s(f). Find z such that g(z) = 0.
-1, -2/9, -4/21, 2
Suppose 84*p + 64*p - 444 = 0. Let m(l) be the first derivative of -20 - 3/35*l**5 - 9/28*l**4 + 6/7*l**2 + 0*l + 0*l**p. Factor m(x).
-3*x*(x - 1)*(x + 2)**2/7
Let z(t) be the second derivative of -t**6/150 + t**5/50 + t**4/60 - t**3/15 - 14*t - 38. Factor z(h).
-h*(h - 2)*(h - 1)*(h + 1)/5
Let o(p) be the second derivative of p**4/48 - 161*p**3/6 - 41*p - 6. Factor o(g).
g*(g - 644)/4
Let l(q) be the first derivative of 153 + 8*q - 4/3*q**3 + 31/2*q**2. Factor l(g).
-(g - 8)*(4*g + 1)
Solve 596/23 - 10/23*i**2 + 1486/23*i = 0.
-2/5, 149
Let c(v) be the third derivative of 1/96*v**8 + 3*v**2 + 0*v**3 - 1/84*v**7 + 25*v - 31/120*v**5 - 37/240*v**6 - 1/8*v**4 + 0. Determine o, given that c(o) = 0.
-1, -2/7, 0, 3
Let u(m) be the second derivative of -m**7/357 + 14*m**6/85 + 22*m**5/85 - 7*m**4/17 - 43*m**3/51 - 551*m. Determine r, given that u(r) = 0.
-1, 0, 1, 43
Let c = -493 - -495. Factor c*x**4 + 2*x**4 - 1161*x**3 + 965*x**3.
4*x**3*(x - 49)
Suppose 10*b = 71438 + 8432. Let 2*n**4 + 0*n**4 - 20*n**3 + 7987 - b + 32*n**2 = 0. What is n?
0, 2, 8
Let w be ((-2)/16)/((-1)/2). Let y = -479081/4 + 119771. Factor w*h**5 - y*h**3 + 0 + h + h**2 - 1/2*h**4.
h*(h - 2)**2*(h + 1)**2/4
Let n = -361 - -376. Factor n*t**2 - 19*t**2 + 4*t**4 - 112*t**3 - 4*t**5 + 116*t**3.
-4*t**2*(t - 1)**2*(t + 1)
Let r(x) = 37*x**2 + 297*x + 11559. Let y(i) = 21*i**2 + 148*i + 5780. Let s(z) = -4*r(z) + 7*y(z). Solve s(b) = 0 for b.
-76
Find v such that 21 + 27/4*v**2 - 3*v**4 + 87/4*v**3 - 87*v = 0.
-2, 1/4, 2, 7
Suppose 2*b - 5*o = 32, -2*b + 0*o + 20 = o. Suppose 3*p - m + 2*m - b = 0, -14 = -2*p - 2*m. Factor -14*d**2 + 4*d**2 + 3*d**3 + 0*d**2 + 3*d + 4*d**p.
3*d*(d - 1)**2
What is g in -200/3 - 290/9*g - 2/9*g**3 - 44/9*g**2 = 0?
-12, -5
Let q(f) be the first derivative of f**7/4620 + f**6/1980 - f**5/330 - 91*f**3/3 - 62. Let h(x) be the third derivative of q(x). Let h(n) = 0. Calculate n.
-2, 0, 1
Let 304/9 + 28/3*b**2 + 104/3*b + 2/9*b**3 = 0. Calculate b.
-38, -2
Suppose -3*a = -5*c - 252 - 53, 0 = -5*a + 3*c + 535. Solve -387*u**2 + 192*u**2 + 190*u**2 - 605 + a*u = 0.
11
Let y(i) be the second derivative of -2*i - 1/9*i**2 - 25/6*i**4 + 10/9*i**3 - 53. Factor y(h).
-2*(15*h - 1)**2/9
Let q(y) = 12*y - 2. Let u(j) = j**2 + 711*j - 632. Let g(f) = 40*q(f) - 5*u(f). Factor g(s).
-5*(s - 1)*(s + 616)
Let j(s) be the second derivative of -11/14*s**3 + 0 - 249*s - 1/140*s**5 + 3/14*s**4 + 8/7*s**2. Solve j(m) = 0.
1, 16
Suppose 0 = p - p - 6*p. Let z be (-3)/(p - 9/12) + -2. Factor -4*g**3 - 3*g + 5*g**2 - 3*g**3 - 5*g**z + 2 - 12*g**2.
-(g + 1)**2*(7*g - 2)
Suppose 546*t**2 + 62*t + 36*t**3 - 22*t + 32*t + 36*t**4 + 432 + 24*t - 4*t**5 - 886*t**2 = 0. What is t?
-3, -1, 2, 9
Let i(t) = 5*t**2 - 16*t + 8*t**3 + 0*t**3 - 2*t**2 - 4*t**3 - 9*t**3. Let m(l) = -l**3 - l**2 - l. Let q(x) = i(x) - 6*m(x). Factor q(k).
k*(k - 1)*(k + 10)
Solve 4031 - 6652*c**3 - 17275 - 56300*c**2 + 246*c**4 - 10414 - 18592 - 2*c**5 - 91650*c = 0.
-5, -1, 65
Let t(c) be the third derivative of -38*c**2 + 1/60*c**5 + 11/12*c**4 + 0 + 0*c**3 + 0*c. Factor t(g).
g*(g + 22)
Let m = 55 + -55. Suppose 2*v = -m + 8. What is k in 5*k**2 - v*k**2 + 20*k + 12 - 8*k + 2*k**2 = 0?
-2
Let b(d) be the second derivative of -d**7/70 + 3*d**5/20 - d**4/4 - 65*d**2/2 - 58*d. Let o(c) be the first derivative of b(c). Factor o(w).
-3*w*(w - 1)**2*(w + 2)
Factor 16/13*f**2 + 8/13*f - 2/13*f**3 - 64/13.
-2*(f - 8)*(f - 2)*(f + 2)/13
Let n be (7 + (-7 - 1))/((-13)/((-65)/(-30))). Let m(r) be the first derivative of r**2 + n*r**3 + 3 + 2*r. What is i in m(i) = 0?
-2
Let i(b) be the first derivative of -14/15*b**5 - 8/3*b**4 + 16/3*b**2 - 1/9*b**6 + 32/3*b - 170 - 16/9*b**3. Solve i(d) = 0 for d.
-2, 1
Let z(q) be the first derivative of -41 - 25/2*q**2 - 45/2*q - 5/6*q**3. Suppose z(r) = 0. Calculate r.
-9, -1
Let i(g) be the second derivative of 0*g**2 + 0 + 202*g + 1/2*g**3 + 1/48*g**4. What is h in i(h) = 0?
-12, 0
Solve -1262/9*s**2 - 1258/9*s + 4/9 = 0 for s.
-1, 2/631
Factor 5*i**3 + 495 - 143*i - 22*i**2 - 595 - 13*i**2 + 3*i + 0*i**3.
5*(i - 10)*(i + 1)*(i + 2)
Let m(d) = -10*d**2 - 114*d + 6. Let b(a) = 8*a**2 + 116*a - 5. Suppose 0 = -4*q - 191 + 211. Let y(v) = q*m(v) + 6*b(v). Factor y(t).
-2*t*(t - 63)
Let b(x) = 2*x**5 + 29*x**4 - 109*x**3 + 113*x**2 - 35*x. Let r(k) = -k**5 - 14*k**4 + 54*k**3 - 56*k**2 + 17*k. Let g(d) = -6*b(d) - 10*r(d). Solve g(f) = 0.
-20, 0, 1
Let r(k) = 473*k - 66*k**3 - 876*k + 51*k**2 - 78 + 469*k. Let w(s) = 5*s**3 - 4*s**2 - 5*s + 6. Let t(b) = -2*r(b) - 27*w(b). Factor t(h).
-3*(h - 2)*(h - 1)*(h + 1)
Suppose -10724 = 404*a - 11936. Factor 26/3*l**2 - 26/3 + 2/3*l**a - 2/3*l.
2*(l - 1)*(l + 1)*(l + 13)/3
Let s = -10079/14 + 720. Let r(i) be the third derivative of 4/21*i**3 + 4*i**2 + 1/105*i**5 + s*i**4 + 0 + 0*i. Factor r(b).
4*(b + 1)*(b + 2)/7
Find t such that -t**4 - 56/3 + 149/3*t**2 - 32/3*t**3 + 122/3*t = 0.
-14, -1, 1/3, 4
Let h = 908 - 852. Suppose 0 = -h*z + 6 + 274. Let 3/7*u**z + 3/7*u + 0*u**4 + 0*u**2 + 0 - 6/7*u**3 = 0. What is u?
-1, 0, 1
Suppose 0*x - 5*x - 10 = 0, x = -4*w + 14. Let p be 2/((1/(-3))/(w/(-8))). Factor 6*r + 3*r**4 + 67*r**p - 67*r**3 - 9*r**2.
3*r*(r - 1)**2*(r + 2)
Suppose 30 = -a + 30. Suppose -2*j - 128 = -66*j. Factor -2/13*h + 0*h**j + 2/13*h**3 + a.
2*h*(h - 1)*(h + 1)/13
Let q be 39985/1078*(-4)/520*2. Let i = 1/1274 - q. Determine r, given that 1/7*r**2 - i - 1/7*r**3 + 4/7*r = 0.
-2, 1, 2
Determine f so that 940/3*f - 156*f**2 - 4/9*f**3 - 1412/9 = 0.
-353, 1
Suppose 2*t - 6*o = -o + 101, -5*t + 269 = 4*o. Suppose 62 + 44 = t*w. Suppose -36/5*h - 18/5*h**w - 3/5*h**3 - 24/5 = 0. What is h?
-2
Factor 12*y**2 + 5 + 22 + 1405*y + 2*y**3 - 15 - 1383*y.
2*(y + 1)*(y + 2)*(y + 3)
Suppose -6*n - 2*m + 378 = -2*n, 4*m - 105 = -n. Factor 125*v + 4*v**2 - 40*v + 54*v + 3364 + n*v.
4*(v + 29)**2
Suppose 4*o + 3*c = 27, o = 236*c - 239*c + 27. Factor 0*n + o + 2/3*n**4 + n**5 + 0*n**3 + 0*n**2.
n**4*(3*n + 2)/3
Factor -83*k**4 - 8*k**2 + 4 + 187*k**4 - 100*k**4.
4*(k - 1)**2*(k + 1)**2
Let q(x) be the third derivative of x**8/16800 + x**7/105 - x**6/1800 - x**5/5 - 157*x**4/12 + 289*x**2. Let d(k) be the second derivative of q(k). Factor d(r).
2*(r - 1)*(r + 1)*(r + 60)/5
Let f(h) be the first derivative of 2*h**5/65 + 25*h**4/26 + 108*h**3/13 - 1728*h/13 + 472. Find n such that f(n) = 0.
-12, -3, 2
Let d(m) be the second derivative of -10/3*m**3 + 0 - 19/6*m**4 - 1/5*m**6 + 0*m**2 - 56*m + 16/5*m**5. Let d(w) = 0. Calculate w.
-1/3, 0, 1, 10
What is j in 89/3*j + 1/3*j**3 - 68/3 - 22/3*j**2 = 0?
1, 4, 17
Let g(z) be the first derivative of -z**3/3 + 61*z**2/2 - 550*z + 10835. Factor g(s).
-(s - 50)*(s - 11)
Suppose 6*o - 8*o = 0. Suppose m + 1 - 6 = o. Let -15*c - 1 + 1 - m*c**2 + 0*c = 0. Calculate c.
-3, 0
Let g(y) = -y**2 + 9*y + 24. Let m be g(0). Let q(n) = -15*n**2 - 5*n - 4. Let j(z) = 2*z**2 + 2*z - 1. Let r(k) = m*j(k) + 3*q(k). Factor r(a).
3*(a - 1)*(a + 12)
Suppose 0 = j + 34 - 36. What is b in -1 + 147 + 3*b**j + 16*b + 13*b + 25*b - 11 = 0?
-15, -3
Let t = -266 - -272. Factor -t - 16*q**2 + 8*q**2 - 9*q + 7*q**2 + 2*q.
-(q + 1)*(q + 6)
Let s(n) be the second derivative of -n**5/4 + 10*n**4/3 + 935*n**3/6 - 4235*n**2 - 1480*n. Factor s(y).
-5*(y - 11)**2*(y + 14)
Let n(s) be the first derivative of 5*s**3/3 - 25*s**2/2 - 120*s + 2641. Factor n(v).
5*(v - 8)*(v + 3)
Let m = 266501/2 - 133247. Suppose 0*q + m*q**3 + 1/8*q**5 + 0 - 3*q**2 - 5/4*q**4 = 0. What is q?
0, 2, 6
Let m(a) be the first derivative of -a**9/27216 + a**8/1260 - 4*a**7/945 - 50*a**3 + 214. Let g(n) be the third derivative of m(n). Find p such that 