2/9
Let g(q) be the third derivative of -q**8/11200 - q**7/4200 + q**4/24 - 2*q**2. Let t(u) be the second derivative of g(u). Factor t(k).
-3*k**2*(k + 1)/5
Let g(m) be the first derivative of -4*m**5/5 - m**4 + 8*m**3/3 - 43. What is f in g(f) = 0?
-2, 0, 1
Factor -5*j**5 + 10*j**4 - 25*j**3 + 10*j**4 + 27*j**2 - 17*j**2.
-5*j**2*(j - 2)*(j - 1)**2
Let w(r) be the third derivative of r**8/20160 + r**7/7560 - r**4/6 - 5*r**2. Let d(u) be the second derivative of w(u). What is t in d(t) = 0?
-1, 0
Let n = 125 + -247/2. Determine s so that 3 + 3/2*s - n*s**2 = 0.
-1, 2
Let a(j) = -j**3 - 3*j**2 - 18*j - 22. Let t(n) = -2*n**3 - 4*n**2 - 19*n - 23. Let v(b) = -3*a(b) + 2*t(b). Factor v(o).
-(o - 5)*(o + 2)**2
Factor -3*u - 2*u**2 + 2*u**2 - u**2 + 4*u**2.
3*u*(u - 1)
Let q(m) = m + 6. Let b(k) = 1. Let a(r) = -2*b(r) + q(r). Let y be a(-4). Let y*x**3 - 2*x**3 - x**4 + 0*x**3 - x**2 = 0. What is x?
-1, 0
Let a = 143/54 - 4/27. Let -3/2*o - 1 + a*o**2 = 0. Calculate o.
-2/5, 1
Let r = 473 - 3301/7. Let s be ((-8)/(-6))/(7/3). Let r*i**3 + 2/7*i**2 - 6/7*i**4 - 10/7*i + s = 0. Calculate i.
-1, 2/3, 1
Let l(r) be the first derivative of -r**7/735 + r**6/105 - r**5/35 + r**4/21 - r**3/21 + 2*r**2 - 7. Let n(j) be the second derivative of l(j). Factor n(i).
-2*(i - 1)**4/7
Let d(v) be the first derivative of -1/2*v**2 + v**3 + 1/5*v**5 - 3/4*v**4 + 2 + 0*v. Factor d(i).
i*(i - 1)**3
Let a = 128/345 + 2/69. Factor -1/5*m**2 + 0 - a*m.
-m*(m + 2)/5
Suppose 4*i - 35 = 2*j + j, -2*i + 30 = -4*j. Let k = 305/1859 + 3/169. Factor 0*v**3 + 0 + 4/11*v**4 - 4/11*v**2 - k*v + 2/11*v**i.
2*v*(v - 1)*(v + 1)**3/11
Let k(l) be the second derivative of 50*l**7/21 - 68*l**6/3 + 349*l**5/5 - 304*l**4/3 + 232*l**3/3 - 32*l**2 - 32*l. Let k(t) = 0. What is t?
2/5, 1, 4
Let m(j) be the first derivative of 2*j**6/15 - 3*j**5/100 - j**4/30 + 3*j + 1. Let c(g) be the first derivative of m(g). Solve c(d) = 0.
-1/4, 0, 2/5
Let i(q) be the first derivative of -2 + 1/3*q**3 + 0*q + 0*q**2 + 1/4*q**4. Solve i(f) = 0.
-1, 0
Let w(y) = -y**3 + 15*y**2 - 17*y + 44. Let l be w(14). Factor 2/9*a**3 + 8/9*a**l + 10/9*a + 4/9.
2*(a + 1)**2*(a + 2)/9
Suppose 8*t + 1064 = 1080. Let 19/2*f + 3 - 7/2*f**t = 0. What is f?
-2/7, 3
Let b(d) be the third derivative of 1/120*d**4 + 0*d + 1/1050*d**7 + 0*d**3 - 1/300*d**5 + 0 - 3*d**2 - 1/600*d**6. Factor b(x).
x*(x - 1)**2*(x + 1)/5
Let z(y) be the second derivative of -y**7/840 + y**6/80 - y**5/20 + y**4/6 + 7*y. Let j(h) be the third derivative of z(h). Let j(k) = 0. What is k?
1, 2
Let v be ((-9)/6)/((-2)/4). Suppose 0 = -2*x + 3*x. Factor x + 0*u**v + 1/3*u - 2/3*u**2 + 2/3*u**4 - 1/3*u**5.
-u*(u - 1)**3*(u + 1)/3
Let k(a) be the third derivative of a**5/35 + 5*a**4/56 + a**3/14 + 19*a**2. Determine j so that k(j) = 0.
-1, -1/4
Let w(c) = 3*c**3 - 4*c + c**3 + 4*c - 12*c**2 - 8. Let d(k) = -9*k**3 + 25*k**2 - k + 17. Let p(s) = -6*d(s) - 13*w(s). Find z such that p(z) = 0.
-1
Let d(p) be the first derivative of 9/20*p**4 + 0*p + 1/5*p**5 + 1/5*p**2 + 7/15*p**3 + 4 + 1/30*p**6. Suppose d(t) = 0. What is t?
-2, -1, 0
Let x = 6 + -10. Let y = x + 9. Factor -2/3*a**y + 0 - 4/3*a**2 + 4/3*a**4 + 0*a**3 + 2/3*a.
-2*a*(a - 1)**3*(a + 1)/3
Let n = 10 - 9. Determine k so that 1 + 3*k**3 - 9*k + n + 4 = 0.
-2, 1
Let c(r) be the third derivative of 1/12*r**4 + 0 + 0*r + 0*r**3 + 1/60*r**6 + 1/15*r**5 - 2*r**2. Solve c(a) = 0 for a.
-1, 0
Let o be 4/5*(-7)/((-84)/6). Factor o*m - 2/5*m**2 + 4/5.
-2*(m - 2)*(m + 1)/5
Factor -14/9*l**2 - 2/3*l - 10/9*l**3 + 0 - 2/9*l**4.
-2*l*(l + 1)**2*(l + 3)/9
Let m be (-1)/(-1)*(-1)/(-2). Let l(h) be the first derivative of -1/5*h**5 + 2/3*h**3 - 1/6*h**6 + 2 - 1/2*h**2 - h + m*h**4. Solve l(b) = 0 for b.
-1, 1
Suppose 0 + 10/7*b + 2/7*b**2 = 0. What is b?
-5, 0
Let p(h) = -54*h**5 - 45*h**4 + 57*h**3 + 45*h**2 - 3*h. Let s(c) = c**5 - c. Let f(o) = -p(o) - 3*s(o). Solve f(r) = 0 for r.
-1, 0, 2/17, 1
Let y(a) be the third derivative of a**8/1344 + a**7/840 - 5*a**2. Factor y(x).
x**4*(x + 1)/4
Let y(w) = -12*w - 24. Let a be y(-2). Find d, given that 0 + a*d + 0*d**2 - 1/4*d**4 - 1/4*d**3 = 0.
-1, 0
Factor 20/3*l**3 - 15*l - 10/3 - 5*l**2.
5*(l - 2)*(l + 1)*(4*l + 1)/3
Factor -10*u + 0*u**2 + 5*u**2 + 19 - 14.
5*(u - 1)**2
Suppose 4*x - 2*x + 12 = 0. Let d be 0/2 + x/(-9). Factor -4/3*a + 2/3 + d*a**2.
2*(a - 1)**2/3
Let h(l) be the third derivative of -8*l**2 + 0*l + 0 + 1/10*l**5 + 4/315*l**7 - 11/180*l**6 - 1/9*l**3 - 1/36*l**4. Factor h(m).
2*(m - 1)**3*(4*m + 1)/3
Let x = -9/5 + 197/15. Find f, given that x*f + 80/3*f**2 + 4/3 + 32/3*f**3 = 0.
-2, -1/4
Let b = 214 + -212. Factor 3/7 + 9/7*l - 12/7*l**b.
-3*(l - 1)*(4*l + 1)/7
Let b(c) = -12*c**4 + 49*c**3 - 27*c**2 - 16*c - 5. Let r(l) = -18*l**4 + 74*l**3 - 40*l**2 - 24*l - 8. Let g(y) = 8*b(y) - 5*r(y). Let g(j) = 0. Calculate j.
-1/3, 0, 2
Factor 16/7*o - 2/7*o**2 - 32/7.
-2*(o - 4)**2/7
Let y(u) = -u**3 - 6*u**2 - 5*u + 4. Suppose 0 = -4*i - i - 25. Let b be y(i). Solve -9*w**2 + 5*w**3 - 5*w**5 + 9*w**b - 3*w + 5*w - 2*w**5 = 0 for w.
-1, 0, 2/7, 1
Suppose -1 - 9*w**2 + 48*w**3 - 19*w**2 + 9 - 28*w = 0. Calculate w.
-2/3, 1/4, 1
Let w(x) be the second derivative of 3*x**7/8 + 8*x**6/5 + 17*x**5/10 - 2*x**3/3 - 3*x. Let w(h) = 0. What is h?
-2, -2/3, 0, 2/7
Let p(q) be the second derivative of -q**7/168 + q**6/40 - 3*q**5/80 + q**4/48 + 34*q. Let p(g) = 0. What is g?
0, 1
Let j be -4 + (2/8 - (-583)/132). Suppose 0*h + 0 - 2/3*h**3 + 2/3*h**2 - 2/3*h**4 + j*h**5 = 0. Calculate h.
-1, 0, 1
Let w(b) = b + 7. Let u(c) = -2*c - 10. Let d(m) = 5*u(m) + 7*w(m). Let t be d(-2). Suppose -6*g**2 - 1 + 4*g + 6*g + t = 0. What is g?
-1/3, 2
Suppose -15 = -5*m - 4*f, -10 = -m + 5*f + 22. Suppose -m*u + 12 = -4*u. Let 11/4*w**3 + 4*w**2 + 0 - 15/4*w**5 - 4*w**u + w = 0. Calculate w.
-1, -2/3, -2/5, 0, 1
Find k, given that -4/9*k**4 + 4/3*k**3 - 16/9*k + 0*k**2 + 0 = 0.
-1, 0, 2
Let s(q) be the first derivative of -q**5 - 5*q**4/2 - 5*q**3/3 - 21. Factor s(x).
-5*x**2*(x + 1)**2
Let w = 12 + -8. Suppose 2*t = 3*t - w. Factor 2*i**3 - i**4 - i**t + 2*i**5 + i**2 - 4*i**3 + i**2.
2*i**2*(i - 1)**2*(i + 1)
Let b(q) = q + 5. Let s be b(-7). Let z be s/(-1) - 3 - -3. Suppose -6*r**z + 9*r**3 + 2*r - 3*r**3 - r**4 - r**4 = 0. Calculate r.
0, 1
Let b(p) = -4*p**5 + 4*p**4 + 9*p**3 - 7*p**2 + 3. Let h(o) = 3*o**5 - 4*o**4 - 8*o**3 + 6*o**2 + o - 2. Let x(d) = 4*b(d) + 5*h(d). Factor x(u).
-(u - 1)*(u + 1)**3*(u + 2)
Let f(s) = 8 + 3*s**2 + 8*s - 1 - 5 + 9. Let a(q) = -q**2 - 3*q - 4. Let t(o) = -11*a(o) - 4*f(o). Determine d, given that t(d) = 0.
0, 1
Let g(f) be the first derivative of -1/2*f**4 - 4/3*f**3 + 4*f + f**2 - 6. Factor g(u).
-2*(u - 1)*(u + 1)*(u + 2)
Factor -2/13*j**2 + 0*j + 2/13.
-2*(j - 1)*(j + 1)/13
Let s(c) be the second derivative of 2/21*c**7 + 7*c + 0 + 0*c**3 - 2/15*c**6 + 1/3*c**4 - 1/5*c**5 + 0*c**2. Solve s(w) = 0.
-1, 0, 1
Let n = -20798/21 + 990. Let z = n - -22/21. What is x in -10/3*x**2 + z + 1/3*x = 0?
-2/5, 1/2
Let t = -127 - -131. Let f(h) be the first derivative of 3/20*h**t - 3/25*h**5 + 1/5*h**3 + 0*h - 3/10*h**2 - 3. Factor f(c).
-3*c*(c - 1)**2*(c + 1)/5
Let s(o) be the second derivative of o**5/100 + o**4/4 + 5*o**3/2 + 25*o**2/2 + 17*o. Factor s(r).
(r + 5)**3/5
Suppose 0 = -y - 3*y. Let b(x) be the third derivative of 1/420*x**7 + 0*x + 0*x**3 + 1/120*x**5 + 0 + 2*x**2 + y*x**4 + 1/120*x**6. Factor b(a).
a**2*(a + 1)**2/2
Let y(h) = -4*h - 6. Let p be y(-3). Let u(v) be the first derivative of -1/4*v**2 + 0*v - 1/3*v**3 + 1/5*v**5 + 0*v**4 + 1/12*v**p - 2. Factor u(m).
m*(m - 1)*(m + 1)**3/2
Solve 18/5*y**4 - 2/5*y**5 - 12*y**3 + 92/5*y**2 - 66/5*y + 18/5 = 0 for y.
1, 3
Let x(o) be the third derivative of 0*o**3 + 0*o**5 + 1/84*o**8 + o**2 + 0 - 1/105*o**7 + 0*o**4 - 1/60*o**6 + 0*o. Factor x(p).
2*p**3*(p - 1)*(2*p + 1)
Let d(n) = n**2 + 4*n + 2. Let f be d(-4). Factor 4*s**2 - s - s**2 - 6*s**f + 4*s**2.
s*(s - 1)
Let v = -1132/9 - -126. Let p = -49 + 51. Factor 0 - 4/9*n**3 - v*n - 2/3*n**p.
-2*n*(n + 1)*(2*n + 1)/9
Let r(a) = a**2 + a + 1. Let v = -1 + 2. Let p(w) = -3*w**4 - 6*w**3 - 4*w**2 - w - 1. Let f(l) = v*r(l) + p(l). Factor f(q).
-3*q**2*(q + 1)**2
Let b(n) be the first derivative of n**6/30 - n**4/12 + 4*n + 5. Let 