*m**3.
-2*m*(m - 1)**2/3
Let d(v) be the third derivative of 0*v**3 + 0*v - 1/96*v**4 - 1/240*v**5 - 2*v**2 + 0. Find y such that d(y) = 0.
-1, 0
Let v(z) be the second derivative of -z**7/5880 - z**6/560 + z**4/6 + 6*z. Let w(k) be the third derivative of v(k). Let w(x) = 0. Calculate x.
-3, 0
Let p(y) be the first derivative of -y**7/42 - y**6/90 + 3*y - 3. Let b(f) be the first derivative of p(f). Suppose b(z) = 0. What is z?
-1/3, 0
Determine k so that -4/3*k**3 - 1/3*k**4 - 4/3*k - 2*k**2 - 1/3 = 0.
-1
Factor 0*q + 0 + 2/7*q**2 + 2/7*q**3.
2*q**2*(q + 1)/7
Let j = 10/11 + 14/33. Factor -4/3*u**3 + 0*u**2 - 2/3*u**4 + j*u + 2/3.
-2*(u - 1)*(u + 1)**3/3
Let j(x) be the third derivative of 4*x**5/15 - 7*x**4/6 + 10*x**3/3 + 8*x**2. Let y(c) = 33*c**2 - 55*c + 41. Let q(a) = -9*j(a) + 4*y(a). Factor q(b).
-4*(b - 2)*(3*b - 2)
Suppose r - 39 = -2*r. Suppose -3*u - 15 = -2*w, 4*w + 2*u = -r + 3. Solve -h**2 + 1 - 2*h + w*h**2 + 2*h**2 = 0.
1
Let g(p) be the third derivative of 9*p**8/784 + 3*p**7/98 + p**6/40 + p**5/140 - 9*p**2. Solve g(w) = 0.
-1, -1/3, 0
Factor -4/3*w**3 - 76/3*w + 12 + 44/3*w**2.
-4*(w - 9)*(w - 1)**2/3
Let -14 - 3*c**5 - 18 + 32 + 9*c**4 = 0. Calculate c.
0, 3
Let y(j) = j**2 + 18*j + 21. Let s be y(-17). Suppose -6*l**3 + s*l + 8*l**4 + 0*l**3 - 6*l**3 = 0. Calculate l.
-1/2, 0, 1
Suppose 2*k - 58 - 24 = -g, -4*k - 196 = -3*g. Solve -318*r**3 + 3 - 81/2*r + 480*r**5 - g*r**4 + 381/2*r**2 = 0.
-1, 1/4, 2/5
Let j(p) = 3*p**4 + 4*p**3 + 2*p**2 - 4*p - 5. Let a(u) = -u**4 - 2*u**3 - u**2 + 2*u + 2. Let v(q) = 15*a(q) + 6*j(q). What is y in v(y) = 0?
-1, 0, 1, 2
Suppose 3*y - 4*n - 4 = 0, 6*y - 14 = 3*y - n. Let j(r) be the first derivative of r - 1/2*r**2 - 4/5*r**5 - 11/4*r**y - 3 - 3*r**3. Factor j(u).
-(u + 1)**3*(4*u - 1)
Let t = 32/13 - 563/234. Let h(q) be the first derivative of 0*q + 1/27*q**6 - 1 + 0*q**2 - t*q**4 + 0*q**5 + 0*q**3. Suppose h(z) = 0. Calculate z.
-1, 0, 1
Let a be 85/75 + -5 + 4. Determine b so that 2/15*b**4 - 2/15*b**2 - a*b**5 + 0 + 2/15*b**3 + 0*b = 0.
-1, 0, 1
Find u such that -3*u**3 + 0*u**2 - 2*u + 2 + 6*u**2 + 8*u + 5*u**3 = 0.
-1
Let y(i) be the second derivative of -5*i**4/12 + 10*i**3/3 - 15*i**2/2 - 8*i. Factor y(w).
-5*(w - 3)*(w - 1)
Let m be (3 + -2 + -2)*-9. Let p = -7 + m. Factor -2*o**4 - o**3 - 2*o**3 + 6*o**4 - 5*o**4 - 2*o**p.
-o**2*(o + 1)*(o + 2)
Let d = -160 + 1925/12. Let p(l) be the first derivative of 5/6*l**2 + 1 + 1/5*l**5 - 1/9*l**3 - 2/3*l - d*l**4. Solve p(v) = 0 for v.
-1, 2/3, 1
Let w(y) = -98*y**3 + 2*y**2 - 1. Let i be w(-1). Let q be 2/7 + i/21. Determine a, given that 5*a - a - 5 + q*a**2 - 3*a**3 + 1 = 0.
-1, 2/3, 2
Let t(u) = -u**3 + 8*u**2 - 5*u - 9. Let v be t(7). Let j be 12/5 + (-2)/v. Find w, given that -1/3 - 2/3*w - 1/3*w**j = 0.
-1
Let j(y) be the second derivative of 1/60*y**4 + 1/100*y**5 + 0 + 3*y + 0*y**3 + 0*y**2. Factor j(t).
t**2*(t + 1)/5
Let k(o) = o**2 + 2*o - 4. Let r be k(2). Let u be 16 + -14 + (-7)/r. Let -1/2*y - 1/4*y**2 - u = 0. Calculate y.
-1
Let 15*f**4 - 612/5*f - 102*f**3 + 108/5 + 1047/5*f**2 = 0. Calculate f.
2/5, 3
Let f(n) be the third derivative of n**8/3360 - n**6/360 - n**4/24 - 3*n**2. Let u(w) be the second derivative of f(w). Factor u(d).
2*d*(d - 1)*(d + 1)
Solve -2/3*h**4 - 4/3*h + 4/3*h**2 - 1/3*h**5 + 0 + h**3 = 0.
-2, 0, 1
Let u be (0 + 8)/(21/(-42)). Let p be u/(-24)*(-30)/(-4). Factor 0*x**3 + 1/3*x**p + 0 + 0*x + 1/3*x**4 + 0*x**2.
x**4*(x + 1)/3
Let f(u) = u + 7. Let s be f(-5). Suppose 0*c + 9 = 3*c. Factor s*p**4 - 3*p**5 - 10*p**4 - c*p**5 - 2*p**3.
-2*p**3*(p + 1)*(3*p + 1)
Suppose 5 = 2*u - 5. Let x(t) be the third derivative of -1/105*t**7 - 2*t**2 - 1/6*t**4 + 0 + 0*t**u + 0*t + 1/30*t**6 + 1/3*t**3. Factor x(i).
-2*(i - 1)**3*(i + 1)
Factor -4/3*h**2 + 2/3*h**3 - 2/3*h + 4/3.
2*(h - 2)*(h - 1)*(h + 1)/3
Let b(m) = -2*m**2 + m - 2. Let p(v) = -v**2. Let i(s) = 2*b(s) - 6*p(s). Factor i(t).
2*(t - 1)*(t + 2)
Factor -2*l**3 - 3*l**2 - 7 - 2*l**3 + 6*l**3 + l**4 - 8*l + 3.
(l - 2)*(l + 1)**2*(l + 2)
Let j(c) be the third derivative of 0*c**4 + 0*c + 0*c**6 - 5*c**2 + 0 + 1/30*c**5 - 1/210*c**7 - 1/6*c**3. Let j(r) = 0. Calculate r.
-1, 1
Let x(z) be the first derivative of -z**3/12 - z**2/8 - 4. Factor x(f).
-f*(f + 1)/4
Suppose -3*m = m. Let c(k) be the second derivative of m*k**2 - 1/40*k**5 + 2*k + 0*k**4 + 0 + 1/12*k**3. Factor c(n).
-n*(n - 1)*(n + 1)/2
Factor 14 - 3 - 4*h - 4*h**2 - 3.
-4*(h - 1)*(h + 2)
Let i(a) = a**3 - a**2 - 2. Let w(k) = -24*k**3 + 30*k**2 - 6*k + 44. Let b(c) = 44*i(c) + 2*w(c). Factor b(f).
-4*f*(f - 3)*(f - 1)
Factor -7*o**2 - 1 + 2 + o**3 + 6*o**2 + 0*o**2 - o.
(o - 1)**2*(o + 1)
Let y(a) be the third derivative of 1/245*a**7 + 2*a**2 - 1/784*a**8 + 0*a - 1/70*a**5 + 0 + 0*a**3 + 0*a**6 + 1/56*a**4. Factor y(u).
-3*u*(u - 1)**3*(u + 1)/7
Let i(n) = 17*n - 34. Let o be i(2). Factor -1/5*b**3 + 6/5*b**2 + o - 9/5*b.
-b*(b - 3)**2/5
Factor 0 + 0*i**4 + 0*i**2 + 2/9*i**5 + 0*i - 8/9*i**3.
2*i**3*(i - 2)*(i + 2)/9
Suppose 96*n = 91*n. Factor n - 2/5*z**3 + 0*z + 2/5*z**4 + 0*z**2.
2*z**3*(z - 1)/5
Let f(r) = -r**2 - 11*r - 10. Let y be f(-10). Let u = y - -5/3. Factor -1/3*q - u*q**3 + 2/3*q**4 + 4/3*q**2 + 0.
q*(q - 1)**2*(2*q - 1)/3
Let v(b) = b**3 + 3*b**2 - 3*b + 5. Let d be v(-4). Let p be (8/(-36))/(d/(-6)). Suppose 6*o - 28/3*o**3 - 2*o**2 - p = 0. What is o?
-1, 2/7, 1/2
Let b(j) be the second derivative of -j**5/40 - j**4/24 + j**3/6 - 3*j. Factor b(u).
-u*(u - 1)*(u + 2)/2
Let c = 11 - 7. Factor -8*f**2 + 2*f**2 - 2 + 2*f**c - 5*f + 2*f**3 - 2 - 5*f.
2*(f - 2)*(f + 1)**3
Let o be (-2 - (-5)/3) + (-21)/(-63). Determine q so that 4/3*q**2 + o - 2/3*q - 2/3*q**3 = 0.
0, 1
Let n = 3 + -1. Factor 2/5 + 0*z - 2/5*z**n.
-2*(z - 1)*(z + 1)/5
Let a(s) be the third derivative of s**8/504 - s**7/126 - s**6/90 + 11*s**5/180 + s**4/18 - 2*s**3/9 - 8*s**2. What is r in a(r) = 0?
-1, 1/2, 2
Let f = -124/3 - -42. Suppose -1/3 + 0*l**2 - f*l + 1/3*l**4 + 2/3*l**3 = 0. What is l?
-1, 1
Let y(x) be the second derivative of -x**7/14 - x**6/10 + 3*x**5/20 + x**4/4 + 4*x. What is g in y(g) = 0?
-1, 0, 1
Let s(o) = o**2 - o + 4. Let y(n) = n. Let m(c) = s(c) - 3*y(c). Factor m(h).
(h - 2)**2
Factor 0 - 8/3*i**2 - 7/3*i**4 + 19/3*i**3 - 4/3*i.
-i*(i - 2)*(i - 1)*(7*i + 2)/3
Let n(q) be the third derivative of 0*q + q**3 + 18/35*q**7 - 27/20*q**5 + 3/8*q**4 - 4*q**2 + 0 + 1/5*q**6. What is o in n(o) = 0?
-1, -2/9, 1/2
Let f(i) be the second derivative of 1/36*i**4 - 1/3*i**2 + 0 + i + 1/18*i**3. Determine z, given that f(z) = 0.
-2, 1
Factor 2/3*j**4 - 2/3*j**2 + 0 + 0*j**3 + 0*j.
2*j**2*(j - 1)*(j + 1)/3
Factor -11*m**3 - 5*m**4 + 102*m**5 - 3*m**3 + 4*m**3 - 97*m**5.
5*m**3*(m - 2)*(m + 1)
Let -1/3 - 8*r**2 - 3*r - 16/3*r**3 = 0. Calculate r.
-1, -1/4
Let v(h) be the first derivative of 7/9*h**3 - 3 + 1/3*h**2 + 0*h. Factor v(m).
m*(7*m + 2)/3
Let t(c) be the third derivative of 0*c + 0*c**4 - 1/9*c**3 + 0 - 4*c**2 + 1/90*c**5. Find f such that t(f) = 0.
-1, 1
Let v(b) be the first derivative of 1/60*b**5 + 0*b**2 + 2/9*b**3 + b + 1/9*b**4 + 2. Let f(n) be the first derivative of v(n). Solve f(a) = 0 for a.
-2, 0
Let y(m) be the third derivative of -m**5/15 + 4*m**4/3 - 32*m**3/3 - 14*m**2. Find p, given that y(p) = 0.
4
Let y(m) = -m**3 - 14*m**2 - 17*m - 50. Let o be y(-13). Factor -3/5*w**o + 0 + 3/5*w**3 - 6/5*w.
3*w*(w - 2)*(w + 1)/5
Let m be (4/7)/(6/21). Suppose -3*o = -4*o - 2, -q + 4*o = -9. Suppose 3 + p**m + p**2 - 4*p**2 - 2*p + q = 0. What is p?
-2, 1
Let m = 56/9 - 109/18. Let d(i) be the second derivative of -m*i**3 + 0 + 1/12*i**4 + 1/20*i**5 - 1/2*i**2 + 3*i. What is f in d(f) = 0?
-1, 1
Let n(a) be the third derivative of -a**5/30 - a**4/12 + 2*a**3/3 + a**2. Find d such that n(d) = 0.
-2, 1
Let w(h) be the first derivative of h**4/4 + 4. Let v(m) = -m**3 + m**2 - 5*m + 3. Let n(r) = 3*v(r) + 6*w(r). Factor n(c).
3*(c - 1)**2*(c + 3)
Suppose -5*y + 8 = 33, 33 = i - y. Let v be -6*(3 + i/(-8)). Suppose -3/2*f**5 + 3/2*f + 0 - v*f**2 + 3*f**4 + 0*f**3 = 0. Calculate f.
-1, 0, 1
Suppose 3*j + j + 2*j**3 - 6*j - 5 + 1 + 4*j**2 = 0. What is j?
-2, -1, 1
Let r = -2 - -5. Suppose 5*m - 2*t - 3 = 7, m - t = 2. Let -4*z**4 - 2*z**4 - 2*z**3 - 2*z**3 - 2*z**5 + m*z**r + 4*z + 6*z**