, 1
Let i = 23380 + -23378. Let 1/4*b**i + 225/4 - 15/2*b = 0. What is b?
15
Suppose 0 = 22*d - 18*d - 8. Determine g, given that -8*g - 6*g**d - 5 + g**2 + 3*g - 5*g = 0.
-1
Let w(v) be the first derivative of 5*v**6/6 - 5*v**4 + 10*v**3/3 + 15*v**2/2 - 10*v + 78. Factor w(x).
5*(x - 1)**3*(x + 1)*(x + 2)
Let r(f) = f**2 - 13*f + 39. Let k be r(10). Let -k*t**2 - 9*t**2 + 30*t + 13*t**2 = 0. Calculate t.
0, 6
Let r(t) = -5*t**2 + 105*t - 2. Let o(k) = 2*k**2 - 4*k + 1. Let f(a) = 4*o(a) + 2*r(a). What is i in f(i) = 0?
0, 97
Let h = 4635/14 + -331. Let l(b) be the second derivative of -h*b**4 + 3/28*b**5 + 0 + 0*b**3 - 4*b + 9/98*b**7 + 8/35*b**6 + 0*b**2. Factor l(n).
3*n**2*(n + 1)**2*(9*n - 2)/7
Suppose -8/13 + 8/13*c + 2/13*c**2 - 2/13*c**3 = 0. Calculate c.
-2, 1, 2
Let x be (-1 + 0)/((-22)/33). Suppose -10 = -3*s - r, -4*s + 0*r + 17 = 5*r. Factor 3/2*g**s - x - 3/2*g + 3/2*g**2.
3*(g - 1)*(g + 1)**2/2
Let c(w) = -8*w - 8. Suppose 0 = 4*v + 135 - 91. Let h(d) = -3*d**2 + 3*d**2 + 23*d - d**3 + 23 - d**2. Let o(a) = v*c(a) - 4*h(a). Factor o(y).
4*(y - 1)*(y + 1)**2
Let u(j) = j - 16. Let q be u(18). Let g be (-8 + 8)*1/q. Factor g - 4*b + 4/3*b**2.
4*b*(b - 3)/3
Suppose 3*i + 5 = 4*i. Let o be 190/(-204) + 1 + 143/858. Let 0*s**2 - 2/17*s**3 + 0*s - 2/17*s**i + 0 + o*s**4 = 0. Calculate s.
0, 1
Let n(a) = -3*a**3 + 5*a**2 + 20*a - 22. Let d(j) = -2*j**3 + 5*j**2 + 20*j - 23. Let w(i) = -2*d(i) + 3*n(i). Suppose w(t) = 0. What is t?
-2, 1, 2
Let g(l) be the first derivative of -5*l**6/6 + 6*l**5 - 55*l**4/4 + 10*l**3/3 + 30*l**2 - 40*l + 187. Solve g(d) = 0 for d.
-1, 1, 2
Let y(m) = -8*m - 27. Let d be y(-9). Let k be -4*1/1 - (-210)/d. Determine f, given that 2/3*f + 2/3*f**4 - 2/3*f**3 + 0 - k*f**2 = 0.
-1, 0, 1
Let u be 52/507*9/(-30)*-5. Factor -4/13*b**4 + 0*b**2 - u*b**5 + 0*b - 2/13*b**3 + 0.
-2*b**3*(b + 1)**2/13
Suppose 0 = -4*p - 3*v + 78, -2*v + 101 = -10*p + 15*p. Suppose p*n + 2*n - 207 = 0. Factor 0 + 27/2*z + 3/2*z**3 + n*z**2.
3*z*(z + 3)**2/2
Let u(v) = -15*v - 5. Let f(s) = 16*s - 2*s**2 - 2581 + s**2 + 2586. Let b(m) = -5*f(m) - 6*u(m). Find w, given that b(w) = 0.
-1
Let h(l) = 2*l**2 + 4*l + 2. Let j be h(-2). Let -k**j - 8*k**3 - 2*k**5 + 3*k**2 - 5*k**4 + 10*k**5 + 3*k**4 = 0. What is k?
-1, 0, 1/4, 1
Find t, given that 147*t - 605*t**2 - 157*t - 27 - 320*t - 18 = 0.
-3/11
Let b(x) be the second derivative of x**4/24 - 5*x**3/3 - 21*x**2/4 - 163*x. Factor b(r).
(r - 21)*(r + 1)/2
Let f(w) be the first derivative of 15/2*w**4 + 20 + 15*w**3 + 0*w + 0*w**2 + w**5. Factor f(t).
5*t**2*(t + 3)**2
Let r(v) be the third derivative of v**5/30 + 11*v**4/108 + 2*v**3/27 - 70*v**2. Factor r(f).
2*(f + 1)*(9*f + 2)/9
Let g(c) be the third derivative of -c**7/840 + c**6/96 - c**5/60 - 2*c**2 + 84*c. What is w in g(w) = 0?
0, 1, 4
Factor 1/7*y**2 - 1/7 + 0*y.
(y - 1)*(y + 1)/7
Suppose -3*c - 4 + 34 = 0. Suppose -6*t + t = -c. Factor 0 - k**3 + 2*k**t - 3 + k + 1.
-(k - 2)*(k - 1)*(k + 1)
Let c = -9572 + 9577. Factor -1/10*n**c + 0 - 1/5*n**4 + 1/10*n + 1/5*n**2 + 0*n**3.
-n*(n - 1)*(n + 1)**3/10
Let c(d) be the third derivative of -d**5/15 - d**4/3 - 2*d**3/3 - 130*d**2. Factor c(y).
-4*(y + 1)**2
Let t(u) be the second derivative of -6*u**3 - 27*u**2 - 3/40*u**5 + 0 + 11/8*u**4 - 17*u. Factor t(l).
-3*(l - 6)**2*(l + 1)/2
Let j(y) be the second derivative of y**8/120 + 3*y**7/140 + y**6/90 - 17*y**3/6 - 14*y. Let n(b) be the second derivative of j(b). Suppose n(r) = 0. What is r?
-1, -2/7, 0
Let s(i) be the first derivative of -i**3 - 12*i**2 + 27*i + 72. Find j such that s(j) = 0.
-9, 1
Let n be 4/34 - 2480/(-2040). Let z(g) be the second derivative of 5*g - n*g**3 + 1/3*g**4 + 1/5*g**5 + 0*g**2 + 0. Solve z(i) = 0 for i.
-2, 0, 1
Find n, given that -20*n**4 - 5/4*n**2 + 0 - 10*n**3 + 0*n = 0.
-1/4, 0
Let m(y) be the first derivative of -y**4/16 - 39*y**3/4 - 4563*y**2/8 - 59319*y/4 - 19. What is a in m(a) = 0?
-39
Let r be 16/40 + (-16)/(-10). Factor -t**2 + r*t + 23*t**2 - 21*t**2.
t*(t + 2)
Find q such that 2/3*q**3 + 2/3*q**2 - 2/3*q + 0 - 2/3*q**4 = 0.
-1, 0, 1
Let k = -258/5 + 52. Let h = 373 - 1863/5. Factor -6/5 - 2*c - h*c**2 + k*c**3.
2*(c - 3)*(c + 1)**2/5
Suppose 39*u + 45 = 48*u. Let s(h) be the first derivative of 2*h**2 - 8/3*h**3 + 4*h - 8 - 2*h**4 + 2/3*h**6 + 4/5*h**u. Factor s(m).
4*(m - 1)**2*(m + 1)**3
Factor 20/3*n**2 + 2/9*n**3 + 200/3*n + 2000/9.
2*(n + 10)**3/9
Let m(j) be the second derivative of j**4/12 - 32*j**3/3 + 512*j**2 + 49*j. Find g such that m(g) = 0.
32
Factor 90/7 + 78/7*r + 2/7*r**3 + 22/7*r**2.
2*(r + 3)**2*(r + 5)/7
Let d = -121 + 172. Let w = -46 + d. Find a such that 3/4*a - 3*a**2 - 3*a**4 + 0 + 3/4*a**w + 9/2*a**3 = 0.
0, 1
Let n(s) = 35*s**3 + 255*s**2 + 750*s + 700. Let w(v) = -v**3 - 2*v**2 - v. Let b(m) = -n(m) - 30*w(m). Factor b(o).
-5*(o + 2)**2*(o + 35)
Let m = 12116/9 + -1346. Find h such that 4/9*h**2 - 4/9*h**3 + 2/9*h**5 - 2/9*h**4 - 2/9 + m*h = 0.
-1, 1
Let m be ((-4)/(-90))/((-23)/(-414)). Let f be (-6)/(-15) + 0 + 0. Determine o so that m*o**2 - f + 2/5*o = 0.
-1, 1/2
Let l(k) be the second derivative of k**5/5 + 25*k**4 + 962*k**3 + 2738*k**2 + 88*k. Factor l(z).
4*(z + 1)*(z + 37)**2
Suppose 3*z - 13 = -37. Let d be (-18)/z + (-10)/40. Suppose 8/5*i - 4/5 + 7/5*i**d - 17/5*i**3 - 3/5*i**4 + 9/5*i**5 = 0. What is i?
-1, 2/3, 1
Let i be (-3)/21*-82 - 6/(-21). Factor -28*z**2 + i*z + 2 + 24*z**2 - 10.
-4*(z - 2)*(z - 1)
Find s, given that 8/3*s + 0*s**2 + 0 - 2/3*s**3 = 0.
-2, 0, 2
Let p(k) = k**3 - 12*k**2 - 24*k - 13. Let v(r) = 33 + r**2 - r**3 - 6 + 23*r**2 + 48*r. Let t(y) = -5*p(y) - 3*v(y). Factor t(x).
-2*(x + 2)**3
Let w be ((-606)/(-1111))/(9/22). Suppose 8/9*m**4 - 2/9*m + 8/9*m**2 - 2/9*m**5 - w*m**3 + 0 = 0. Calculate m.
0, 1
Suppose -5*o - o = -12. Factor -2 + h**3 + 6 - 10*h - 3*h**3 + 8*h**o.
-2*(h - 2)*(h - 1)**2
Let f(y) be the second derivative of y**5/120 - 8*y**2 + 20*y. Let p(o) be the first derivative of f(o). Solve p(m) = 0.
0
Let y = 8272/9 - 919. Let n(v) be the third derivative of 1/45*v**5 + y*v**3 + 0*v + 0 + 8*v**2 - 1/12*v**4. Factor n(x).
2*(x - 1)*(2*x - 1)/3
Let q(r) be the first derivative of -12*r**2 + 96*r + 12 + 1/2*r**3. Suppose q(l) = 0. What is l?
8
Solve -1 + 1434*h**2 + 1 - 1436*h**2 + 2*h**3 - 12*h = 0 for h.
-2, 0, 3
Let l(p) = -p**2 + 26*p - 20. Let t be l(25). Factor 5*g**5 + 26*g**5 + 184*g**3 - 5*g**t + 16*g - g**5 - 120*g**4 - 96*g**2.
g*(g - 2)**2*(5*g - 2)**2
Suppose -5*x + 4*s = 117, -2*x + 5*x + 78 = 5*s. Let m be (-96)/x - 12/(-28). Factor 9*o**2 - 5*o**2 + m*o**3 + 0*o**3 - 3*o**3.
2*o**2*(o + 2)
Let w = 430314/7 + -61218. Let y = w - 255. Factor y*q**2 - 3/7*q**4 + 0 + 0*q + 3/7*q**5 - 3/7*q**3.
3*q**2*(q - 1)**2*(q + 1)/7
Solve 416 + 2/13*k**2 - 16*k = 0.
52
Let n = 41203/32074 - -5/4582. Solve -n*z + 12/7 - 3/7*z**2 = 0.
-4, 1
Let n = -21164/6631797 + 2/9913. Let j = 1360/7359 + n. Solve j*p - 2/11*p**3 + 0 + 0*p**2 = 0 for p.
-1, 0, 1
Let t be (2 + -1)*(-10 - -10). Let g be 2/(-4) + (t - (-9)/2). Find b such that 0 + 3/5*b**2 + 0*b**3 - 1/5*b**g + 2/5*b = 0.
-1, 0, 2
Let r(a) = 2*a**3 - 4*a**2 - 34*a + 52. Let j(w) = -w**3 + 4*w**2 + 35*w - 54. Let u(n) = 2*j(n) + 3*r(n). Factor u(p).
4*(p - 2)**2*(p + 3)
Let f(j) be the second derivative of j**5/45 + 7*j**4/9 - 10*j**3/3 + 46*j**2/9 + 2*j + 92. Factor f(b).
4*(b - 1)**2*(b + 23)/9
Let z(r) be the third derivative of r**6/30 - 19*r**5/60 + 19*r**4/24 + r**3 + 3*r**2 + 85. Find q, given that z(q) = 0.
-1/4, 2, 3
Let z(b) be the first derivative of -1/540*b**6 + 0*b**5 + 0*b - 13/2*b**2 + 1/36*b**4 + 14 + 2/27*b**3. Let i(m) be the second derivative of z(m). Factor i(t).
-2*(t - 2)*(t + 1)**2/9
Let p be ((-14)/(-98))/((0 - (-4)/16)*2). Factor p*x + 1/7*x**2 + 0.
x*(x + 2)/7
Suppose v = 2 - 1. Suppose -5*w - 9 = -5*j + v, -2*j + 10 = w. Factor 0 + 4/7*c + 2/7*c**w.
2*c*(c + 2)/7
Solve 16 - 92*t**2 + 5 + 20*t**3 + 3 + 8 + 40*t = 0.
-2/5, 1, 4
Find u, given that 8*u**2 + 140/3*u - 50 - 2/3*u**4 - 4*u**3 = 0.
-5, 1, 3
Let k(j) be the third derivative of -1/105*j**7 + 0*j**3 + 1/336*j**8 + 1/30*j**5 - 1/120*j**6 + 0*j + 0*j**4 + 5*j**2 + 0. Solve k(b) = 0.
-1, 0, 1, 2
Let o(k) = 7*k**3 - k**2 - 2*k - 1. Let d be o(-1). Let s = -5 - d. Determine x, given that -