*(r + 1)**3/5
Let m(i) = 2*i**3 + 2*i**2 + i - 7. Let n(r) = r + 1. Let v(l) = m(l) + 3*n(l). Let f(t) = t**3 + 2*t**2 + 4*t - 3. Let q(s) = -4*f(s) + 3*v(s). Factor q(u).
2*u*(u - 2)*(u + 1)
Let m(z) be the second derivative of -z**7/315 - z**6/20 - 3*z**5/10 - 3*z**4/4 - z**2/2 - 5*z. Let d(w) be the first derivative of m(w). Factor d(v).
-2*v*(v + 3)**3/3
Let h(b) be the first derivative of b**3/6 + b**2/2 + b/2 - 23. Factor h(a).
(a + 1)**2/2
Let q(w) be the second derivative of -1/90*w**6 + 0*w**3 + 0 + 1/18*w**4 - 3*w - 1/6*w**2 + 0*w**5. Suppose q(a) = 0. What is a?
-1, 1
Let h(f) be the second derivative of -3*f + 0 - 5/48*f**4 - 5/8*f**2 + 5/12*f**3. Suppose h(s) = 0. What is s?
1
Suppose -2/5*v**3 + 0 + 0*v - 2*v**2 = 0. What is v?
-5, 0
Let a be 36/4 + -6 + 3/(-1). Suppose 6*k - 10 = k. Solve 0 + a*p - 1/3*p**k + 1/3*p**3 = 0 for p.
0, 1
Let i be -8*(-3 - 24/(-9)). Factor 2/3*s**2 - i*s + 8/3.
2*(s - 2)**2/3
Factor 2*i**2 + 8*i - 9*i**2 + 3*i**2 - 12 + 8*i**2.
4*(i - 1)*(i + 3)
Let j(c) be the third derivative of c**6/540 + c**5/180 + c**3/2 + 3*c**2. Let t(a) be the first derivative of j(a). Factor t(q).
2*q*(q + 1)/3
Let b = -77 - -80. Let c(j) be the third derivative of 0*j**b + 1/240*j**5 + 0*j + 0 - j**2 + 1/96*j**4. Find q, given that c(q) = 0.
-1, 0
Let x(j) be the first derivative of j**3/21 - 4*j**2/7 + 16*j/7 + 8. Factor x(a).
(a - 4)**2/7
Let g(j) be the first derivative of 2/5*j**3 - 3/10*j**2 + 3/20*j**4 + 2 - 6/5*j. Suppose g(c) = 0. What is c?
-2, -1, 1
Let z(f) = -3*f**4 + 3*f**2 + 9*f - 9. Suppose 4*d - 4 = 3*d. Let l(m) = -m**4 + m**2 + 4*m - 4. Let r(j) = d*z(j) - 9*l(j). Factor r(c).
-3*c**2*(c - 1)*(c + 1)
Let v(w) be the third derivative of 0*w - 1/100*w**5 - 1/200*w**6 + 1/350*w**7 + 0 + 0*w**3 - 4*w**2 + 0*w**4 + 1/560*w**8. Suppose v(o) = 0. Calculate o.
-1, 0, 1
Let n(h) be the third derivative of h**9/10080 + h**8/10080 + h**5/20 - h**2. Let u(z) be the third derivative of n(z). Solve u(i) = 0.
-1/3, 0
Let b(l) = 3*l - l**2 + 0*l**2 + 2*l**2 - 1. Let d be b(-4). Find j such that 2/9*j**4 - 2/9*j - 2/9*j**2 + 2/9*j**d + 0 = 0.
-1, 0, 1
Find o such that -32/5*o - 2/5*o**4 - 36/5*o**2 - 2 - 16/5*o**3 = 0.
-5, -1
Let y(w) = -2*w - 12. Let i be y(-6). Suppose 2/3*x**3 + 0*x**2 + i*x - 2/3*x**4 + 0 = 0. Calculate x.
0, 1
Let p be (-126)/(-36)*4/7. Factor 2*v - 4*v**2 - 4*v - v + v**p.
-3*v*(v + 1)
Let u(z) be the first derivative of 2*z**6/3 + 8*z**5/5 - 2*z**4 - 16*z**3/3 + 2*z**2 + 8*z - 6. Solve u(v) = 0 for v.
-2, -1, 1
Suppose -z - 18 = -4*z. Factor -o**2 + o**2 + 3*o**2 - z*o**2.
-3*o**2
Suppose -10*o = -o. Factor o*s + 3/2*s**2 - 2 + 1/2*s**3.
(s - 1)*(s + 2)**2/2
Let h(c) = -4*c**4 + 2*c**3 - 2*c**2 + 10*c. Let k(f) = f**4 - f**3 - f. Let l(g) = -h(g) - 6*k(g). Determine d, given that l(d) = 0.
-1, 0, 1, 2
Let b be (-3 + 2 + 2)*2. Let 2*m**3 - b*m**3 - 3*m**3 + m**2 - 4*m**2 = 0. Calculate m.
-1, 0
Let d(s) = -s**3 + 3*s**2 - s + 6. Let n be d(3). Let q(t) be the first derivative of 0*t + 1/4*t**2 - 1/12*t**n + 3. Let q(i) = 0. What is i?
0, 2
Let m(b) = -b**2 + b. Let h(z) = 5*z**2 + z - 6. Let w(v) = -h(v) - 2*m(v). Suppose w(s) = 0. Calculate s.
-2, 1
Let i = 90 - 90. Let p = -26 - -53/2. Find c, given that i + p*c - 1/4*c**2 = 0.
0, 2
Let d(l) = l**2 + l - 2. Let o be d(-3). Suppose 12 = -0*j + o*j. Factor -5*x**2 + 4*x**2 + 4*x**j - x**2 + 0*x**4 - 2*x**4.
-2*x**2*(x - 1)**2
Let h(p) be the first derivative of -2/9*p**4 + 2 + 2/9*p + 4/9*p**3 + 2/45*p**5 - 4/9*p**2. Find j such that h(j) = 0.
1
Let d(w) be the first derivative of -w**3/18 + w**2/4 - w/3 - 24. Factor d(a).
-(a - 2)*(a - 1)/6
Suppose s = 5*d + 5, -4*d - 8*s + 4*s - 28 = 0. Let z be (-2)/8 + d/(-8). Find o such that 2/7*o + z - 6/7*o**2 = 0.
0, 1/3
Let z(c) be the second derivative of -c**4/36 - c**3/9 - c**2/6 + 12*c. Factor z(u).
-(u + 1)**2/3
Factor -4/5*i**2 + 1/5*i + 6/5 + 1/5*i**3.
(i - 3)*(i - 2)*(i + 1)/5
Let w = 14/15 - 3/5. Let k(p) be the second derivative of 2*p + 0 + w*p**3 - 1/2*p**2 - 1/12*p**4. Let k(x) = 0. Calculate x.
1
Let z(x) be the third derivative of 0*x**4 + 1/50*x**6 + 0*x**3 + 3/175*x**7 + 1/150*x**5 - 5*x**2 + 1/210*x**8 + 0*x + 0. Factor z(g).
2*g**2*(g + 1)**2*(4*g + 1)/5
Suppose 2*p + 6 = n - 0, 3*n + 5*p = -4. Factor -d**4 + n*d**3 + 3*d**2 + d**2 - d**4.
-2*d**2*(d - 2)*(d + 1)
Suppose -7*t + 35 = -2*t. Let j be t/5 - (2 + -1). Factor -j + 2/5*z**2 + 2/5*z - 2/5*z**3.
-2*(z - 1)**2*(z + 1)/5
Let n(y) be the first derivative of -y**6/30 + y**5/20 + y**4/12 - y**3/6 - y - 1. Let f(t) be the first derivative of n(t). Factor f(k).
-k*(k - 1)**2*(k + 1)
Let b(q) be the third derivative of 1/12*q**4 + 0 + 11*q**2 + 0*q**3 + 0*q**5 + 0*q - 1/80*q**6 - 1/420*q**7. Let b(g) = 0. What is g?
-2, 0, 1
Let u(z) be the third derivative of 27*z**5/100 - 3*z**4/10 + 2*z**3/15 + 14*z**2. Let u(w) = 0. Calculate w.
2/9
Let y(x) = x + 17. Let z be y(-14). Solve -6*h**2 + 0 - z - 3*h**2 - 9*h - 3*h**3 + 0 = 0.
-1
Factor 4/5*r**3 + 2/5 - 4/5*r**2 - 2/5*r**5 - 2/5*r + 2/5*r**4.
-2*(r - 1)**3*(r + 1)**2/5
Let x(p) = 5*p - 19. Let f(v) = 11*v - 38. Let l(g) = -4*f(g) + 9*x(g). Let b be l(19). Factor -1/5*y**5 + 0*y**4 + b*y**2 + 2/5*y**3 - 1/5*y + 0.
-y*(y - 1)**2*(y + 1)**2/5
Let r(l) be the second derivative of -l**8/6720 - l**7/840 - l**6/360 + l**4/3 + 2*l. Let p(a) be the third derivative of r(a). Factor p(f).
-f*(f + 1)*(f + 2)
Let j(w) = 11*w**3 - 10*w**2 - 29*w - 20. Let h(f) = -45*f**3 + 40*f**2 + 115*f + 80. Let r(l) = 6*h(l) + 25*j(l). Factor r(t).
5*(t - 4)*(t + 1)**2
Suppose -5*f - 28 = -r, 0 = -5*f + 7*r - 2*r - 20. Let d be -2 - -1 - (f - -3). Factor 0 - 1/2*o**4 + 1/2*o**d + 0*o + 0*o**3.
-o**2*(o - 1)*(o + 1)/2
Let q = 3 - -3. Suppose 4*r - q = 2. Let 2*f**2 - f**2 - r*f - 4*f**4 + f**3 + f + 3*f**4 = 0. Calculate f.
-1, 0, 1
Let k be (-6756)/(-63) + -2 + -3. Let f = 311/3 - k. Find b, given that -f*b**2 + 6/7*b**3 - 8/7*b + 8/7 = 0.
-1, 2/3, 2
Factor 3 + 1 - 19 + 10*h + h**2 + 4*h**2.
5*(h - 1)*(h + 3)
Let a = 11 + -11. Let d be (2/(-21) - a)*-3. Factor 0 + d*l + 4/7*l**2.
2*l*(2*l + 1)/7
Let f(z) be the third derivative of z**9/30240 - z**8/10080 - z**7/1260 + z**5/60 - z**2. Let n(a) be the third derivative of f(a). Factor n(i).
2*i*(i - 2)*(i + 1)
Let c(x) be the first derivative of x**6/18 + 2*x**5/15 - 2*x**3/9 - x**2/6 + 4. Factor c(l).
l*(l - 1)*(l + 1)**3/3
Let t(b) be the second derivative of -b**5/90 - b**4/18 + 8*b**3/9 - 28*b**2/9 + 3*b + 10. Factor t(s).
-2*(s - 2)**2*(s + 7)/9
Factor 0*m**2 + 3/2 - 9/4*m + 3/4*m**3.
3*(m - 1)**2*(m + 2)/4
Let l(i) = -i - 1. Let f be l(-1). Suppose 3*y - 12 = f, -2*d + 28 = 2*d + 2*y. Suppose d + c**2 - 4 + c + c = 0. What is c?
-1
Let w = -47 - -50. Suppose 8/7 + 0*q - 6/7*q**2 + 2/7*q**w = 0. Calculate q.
-1, 2
Let a(f) be the second derivative of 4*f**2 + 1/24*f**4 + 2/3*f**3 + 6*f + 0. Factor a(g).
(g + 4)**2/2
Suppose 0*v = -v + 4. Suppose -4*o = -v*w - 4, 0 = -w - 4*w + 2*o + 7. Factor k - 4 + w*k**2 + 0 + 2.
(k + 1)*(3*k - 2)
Let w(x) be the first derivative of -4*x**6/21 + 16*x**5/35 - 5*x**4/14 + 2*x**3/21 + 9. Let w(h) = 0. What is h?
0, 1/2, 1
Let v(w) be the second derivative of w**5/5 - 2*w**3/3 + 3*w. What is f in v(f) = 0?
-1, 0, 1
Let f be (-18)/(-15)*30/18. Let g(m) be the third derivative of -1/210*m**7 + 0*m**3 - 1/60*m**6 - 1/60*m**5 + 0*m + 0*m**4 + 0 + 2*m**f. Factor g(k).
-k**2*(k + 1)**2
Let a(j) = 8*j**4 - 8*j**2 - 8*j. Let x(v) = 7*v**4 + v**3 - 7*v**2 - 7*v. Let f(o) = 3*a(o) - 4*x(o). Factor f(m).
-4*m*(m - 1)*(m + 1)**2
Let n = -1 + 3. Factor h**2 - 5*h**2 - 3*h**3 + n*h + 4*h**3 + h**3.
2*h*(h - 1)**2
Let s = -56 + 61. Factor 0*r**3 + 0 + 0*r - 1/2*r**4 - 1/2*r**s + 0*r**2.
-r**4*(r + 1)/2
Let t(g) = 3*g**4 - 4*g**3 - 3*g**2 + 9*g + 5. Let h(j) = j**4 - j**2 + j + 1. Suppose -z = 5*i, -2*i + 3*i + 4 = -z. Let x(m) = i*t(m) - 5*h(m). Factor x(l).
-2*l*(l - 1)*(l + 1)*(l + 2)
Factor -12*t**3 - 12*t**2 - t**4 + 42*t**2 + 4*t**4 - 18*t**2.
3*t**2*(t - 2)**2
Let l(c) be the second derivative of -c**6/45 - c**5/15 + 2*c**4/3 - 14*c**3/9 + 5*c**2/3 + 10*c. Find j such that l(j) = 0.
-5, 1
Let s be 4873 + (4 - 7/1). Let j = -24242/5 + s. Factor 486/5*q**2 + 729/5*q**3 + j*q + 8/5.
(9*q + 2)**3/5
Let w be 10/(-9)*210/(-350). Let z be (-2