1, 2/3, 1
Let s(h) be the first derivative of 8 + 1/8*h - 1/32*h**4 + 1/16*h**2 - 1/24*h**3. Let s(d) = 0. Calculate d.
-1, 1
Factor -1/2*v**3 - 3/2*v**2 + 2 + 0*v.
-(v - 1)*(v + 2)**2/2
Let j(o) be the first derivative of -2*o**3/33 - o**2/11 + 4*o/11 + 39. Factor j(y).
-2*(y - 1)*(y + 2)/11
Let v = -84/319 + -56043/1595. Let a = -35 - v. Factor -a*y - 4/5*y**2 - 2/5*y**5 + 2/5*y**4 + 2/5 + 4/5*y**3.
-2*(y - 1)**3*(y + 1)**2/5
Suppose 1 = -12*g + 13. Let i(s) be the first derivative of 2*s - 2*s**2 + 2/3*s**3 - g. What is p in i(p) = 0?
1
Let g(j) = -35*j - 4*j**3 - j**4 + 34*j + 6*j**3 + 2*j**2. Let n(i) = -i**2 - i. Let c(m) = -g(m) + n(m). Suppose c(o) = 0. What is o?
-1, 0, 3
Factor -2/7*m**2 + 8/7 + 6/7*m.
-2*(m - 4)*(m + 1)/7
Let l(a) = -8*a - 3. Let u be l(-5). Factor -37*h**2 + u*h**2 - 2*h**4 + 2*h**5.
2*h**4*(h - 1)
Let -1/4*h**2 + 3/4*h + 0 = 0. What is h?
0, 3
Let b(n) be the second derivative of 81*n**7/28 + 99*n**6/10 + 57*n**5/10 + n**4 - 33*n. Determine v, given that b(v) = 0.
-2, -2/9, 0
Suppose 0 = b + 5*b. Let s(r) be the first derivative of r**3 + b*r - 3/4*r**4 - 1 - 1/2*r**2 + 1/5*r**5. What is d in s(d) = 0?
0, 1
Let x = 2/121 + 470/847. Suppose 2/7*f**2 - x*f + 2/7 = 0. Calculate f.
1
Let s(m) = -8*m**4 + 64*m**3 - 36*m**2. Let d(l) = -l**4 + 9*l**3 - 5*l**2. Let v(c) = 20*d(c) - 3*s(c). Suppose v(h) = 0. What is h?
0, 1, 2
Let x(n) be the second derivative of -n**6/30 + 3*n**5/20 - n**4/6 + n. Factor x(a).
-a**2*(a - 2)*(a - 1)
Let g(w) be the first derivative of 2*w**3/9 + w**2/3 - 4*w/3 + 12. Factor g(m).
2*(m - 1)*(m + 2)/3
Suppose 3*i - 2*t + 1 = 6, 5 = -3*i + 4*t. Suppose -i*v + 14 = -0*v + 3*m, m + 6 = v. Factor 0*p**3 - 1/2*p**v + 0 + 0*p + 1/2*p**2.
-p**2*(p - 1)*(p + 1)/2
Let k(n) be the first derivative of -n**5/10 - 11*n**4/40 - n**3/15 + 16. Factor k(b).
-b**2*(b + 2)*(5*b + 1)/10
Let r = -15 - -19. Let c be r/14 + (-702)/(-91). Find a, given that 16/3*a + 2/3*a**4 + c*a**2 + 4*a**3 + 0 = 0.
-2, 0
Suppose -2*k - 3*k - 30 = 0. Let n be k/(-3)*4/4. Factor 3/4*z - 1/4*z**n + 1/4 - 3/4*z**3.
-(z - 1)*(z + 1)*(3*z + 1)/4
Let w(f) be the first derivative of 4 - 6*f + 11*f**3 + 3/2*f**2 - 15/2*f**4. Factor w(l).
-3*(l - 1)*(2*l - 1)*(5*l + 2)
Let k(x) be the first derivative of x**4/2 + 2*x**3 + 2*x**2 + 2. Factor k(b).
2*b*(b + 1)*(b + 2)
Let i(v) be the third derivative of v**9/12096 - v**7/3360 - v**3/2 + 3*v**2. Let a(m) be the first derivative of i(m). Factor a(o).
o**3*(o - 1)*(o + 1)/4
Let d(h) = h**2. Let u be d(1). Let q(x) be the first derivative of 0*x**5 + 1/12*x**6 + 0*x + 0*x**3 - 1/8*x**4 + 0*x**2 - u. Solve q(c) = 0.
-1, 0, 1
Let g(d) be the first derivative of 2*d**6/3 + 24*d**5/5 + 12*d**4 + 40*d**3/3 + 6*d**2 - 28. Let g(h) = 0. Calculate h.
-3, -1, 0
Let t = 8 - 5. Factor -4*p**t + 2*p**2 - p**3 + 3*p**3.
-2*p**2*(p - 1)
Let j(d) be the first derivative of -d**4/2 + 7*d**3/3 - 2*d**2 - 4*d - 8. Factor j(o).
-(o - 2)**2*(2*o + 1)
Let 20/3 + 4/9*q**2 - 64/9*q = 0. What is q?
1, 15
Let i = 9 - 3. Let j(m) = -m**2 + 5*m + 1. Let q be j(i). Let l(x) = x**2 - x. Let o(c) = -c**2 + 3*c. Let d(a) = q*l(a) - o(a). Suppose d(v) = 0. Calculate v.
0, 1/2
Let w = -98 - -101. Factor -2/7*g**w + 6/7*g - 4/7 + 0*g**2.
-2*(g - 1)**2*(g + 2)/7
Let v(a) be the first derivative of a**7/560 + a**6/80 + 3*a**5/80 + a**4/16 + 2*a**3/3 + 6. Let u(o) be the third derivative of v(o). Factor u(d).
3*(d + 1)**3/2
Let 1/3*w**2 + 0 - 1/3*w = 0. What is w?
0, 1
Let m(j) be the third derivative of -j**6/480 + j**4/32 - j**3/12 - 22*j**2. Find q, given that m(q) = 0.
-2, 1
Let f(o) be the second derivative of o**6/360 - o**5/120 + o**3/2 + 2*o. Let l(v) be the second derivative of f(v). Solve l(g) = 0 for g.
0, 1
Factor -4*n**3 - 6*n**4 + 20*n**3 - 12*n + 7*n**2 + 3*n**2.
-2*n*(n - 3)*(n + 1)*(3*n - 2)
Let d(l) be the second derivative of 0 - 1/3*l**3 - 1/12*l**4 - l - 1/2*l**2. Factor d(j).
-(j + 1)**2
Let c = -5 + 4. Let a be 3 + 0 + (c - -1). Let -7*m**a - m**2 - 3*m**4 - 4*m**2 - m + 0*m = 0. Calculate m.
-1, -1/3, 0
Let j(y) be the second derivative of -4*y + 1/5*y**5 - 1/3*y**3 + 0*y**2 + 0*y**4 - 1/21*y**7 + 0*y**6 + 0. Factor j(x).
-2*x*(x - 1)**2*(x + 1)**2
Let a(j) be the first derivative of 2*j**5/5 + 3*j**4 + 26*j**3/3 + 12*j**2 + 8*j + 1. Suppose a(r) = 0. Calculate r.
-2, -1
Let q(g) be the third derivative of -g**6/30 + 2*g**5/15 + g**4/6 - 4*g**3/3 + 9*g**2. Find b, given that q(b) = 0.
-1, 1, 2
Let s(l) be the third derivative of l**6/1080 + l**5/180 - 2*l**3/27 - 4*l**2 + 7. Factor s(m).
(m - 1)*(m + 2)**2/9
Let b(r) = r**2 - 1. Let h(t) = -t**3 + 8*t**2 + 10. Let k be h(8). Let m(v) = 12 - 2*v + v**2 - v**2 - k*v**2. Let z(i) = 22*b(i) + 2*m(i). Factor z(s).
2*(s - 1)**2
Suppose 0 = 2*p - 7 - 1. Factor -21*q + 9*q**3 + p*q**4 + 3*q**4 + 2*q**2 + 21*q.
q**2*(q + 1)*(7*q + 2)
Let c(a) be the third derivative of -a**7/1470 - a**6/210 - a**5/70 - a**4/42 - a**3/42 - 15*a**2. Solve c(z) = 0.
-1
Suppose 10 = 3*t + n, -3*n - 3 = -2*t - 0*t. Factor -4*d**2 + 0*d - 3*d + d - 2*d**t.
-2*d*(d + 1)**2
Let t(g) = 7*g**2 + 6*g - 6. Let y(w) be the second derivative of 5*w**4/3 + 17*w**3/6 - 17*w**2/2 + 4*w. Let m(k) = 17*t(k) - 6*y(k). Factor m(x).
-x**2
Let k(v) = -2*v**2 - 4*v + 3. Let x = -29 - -19. Let f(h) be the second derivative of h**4/12 + h**3/3 - h**2/2 - 11*h. Let g(q) = x*f(q) - 4*k(q). Factor g(j).
-2*(j + 1)**2
Let b(k) = 53*k**3 + 72*k**2 + 27*k + 3. Let f(x) = -52*x**3 - 72*x**2 - 27*x - 3. Let m = 4 - 0. Let y(a) = m*b(a) + 5*f(a). Factor y(u).
-3*(u + 1)*(4*u + 1)**2
Let c(m) be the third derivative of -1/1008*m**8 - 2*m**2 + 0*m + 1/180*m**6 + 0 - 1/18*m**3 - 1/630*m**7 + 1/90*m**5 - 1/72*m**4. Determine x so that c(x) = 0.
-1, 1
Let b = 351 + -347. Suppose 0*w**2 + 2/15*w**3 + 0 - 2/15*w**5 + 0*w**b + 0*w = 0. Calculate w.
-1, 0, 1
Let k be 1 + ((-7203)/2241 - -2). Let h = 2/249 - k. Suppose 2/9 - h*x**2 - 2/9*x + 2/9*x**3 = 0. What is x?
-1, 1
Let k be 10/(-5) + (32 - 0). Let c(p) be the first derivative of 25/2*p**4 + 24*p**2 - 1 - k*p**3 - 8*p. Factor c(z).
2*(z - 1)*(5*z - 2)**2
Let j(m) = m**5 + m**2 + 1. Let i(o) be the third derivative of o**8/56 - o**7/35 + o**6/40 + o**5/20 + o**3/2 - 4*o**2. Let f(a) = i(a) - 3*j(a). Factor f(r).
3*r**3*(r - 1)**2
Let y(b) = b**2 - b - 1. Let j(g) = g**2 - 2*g - 1. Let d(q) = q**2 - 5*q + 4. Let s be d(4). Let x = 2 - s. Let i(v) = x*y(v) - j(v). Solve i(c) = 0.
-1, 1
Let u(g) be the third derivative of -g**8/1120 - g**7/280 + g**5/40 + g**4/16 + g**3/6 + 2*g**2. Let x(k) be the first derivative of u(k). Factor x(i).
-3*(i - 1)*(i + 1)**3/2
Let -30 - 29*p - 13*p + 17*p + 5*p**2 = 0. Calculate p.
-1, 6
Factor 3*g + 0*g**2 - 4 + 2*g**2 - g - 4*g.
2*(g - 2)*(g + 1)
Let k(h) = -10*h**4 + 40*h**3 - 60*h**2 + 52*h + 2. Let u(v) = 4*v**4 - 16*v**3 + 24*v**2 - 21*v - 1. Let g(p) = 5*k(p) + 12*u(p). Factor g(y).
-2*(y - 1)**4
Let u = -2/105 + 37/105. Let i(t) be the first derivative of 0*t - 2 + 1/2*t**2 - u*t**3. Factor i(r).
-r*(r - 1)
Let a(w) be the first derivative of w**7/1960 - w**6/840 + 2*w**3 + 3. Let y(t) be the third derivative of a(t). Factor y(i).
3*i**2*(i - 1)/7
Let p(n) = -4*n**3 - 24*n**2 - 4*n + 4. Let s(o) = -o**2 - o + 1. Let i(b) = p(b) - 4*s(b). Factor i(t).
-4*t**2*(t + 5)
Factor 3*w + 0 + 0 - 3*w**2 - 2 + 2*w**2.
-(w - 2)*(w - 1)
Let p(s) be the first derivative of -s**7/840 + s**6/240 - s**4/48 + s**3/24 - s**2 - 1. Let d(w) be the second derivative of p(w). Factor d(u).
-(u - 1)**3*(u + 1)/4
Suppose -2 - 8 = -5*j. Factor -6*g + 1 - g**2 - 5 + j*g + 0.
-(g + 2)**2
Let a(h) = -3*h + 31. Let u be a(9). Suppose l + 21 = 3*i + u*l, 0 = i - 4*l + 18. Solve -6*w**i + 2*w**3 + 0 - 14*w**5 - 4/3*w + 58/3*w**4 = 0.
-1/3, -2/7, 0, 1
Let n(f) = 10*f**5 - 10*f**4 + 20*f**3 - 5*f**2 + 5*f - 5. Let p(m) = -m**5 - m**4 - m**3 - m + 1. Let v(s) = n(s) + 5*p(s). Factor v(t).
5*t**2*(t - 1)**3
Let m(k) be the first derivative of -k**5/30 - k**4/36 + 2*k**3/9 - k**2/2 + 4. Let c(h) be the second derivative of m(h). Solve c(s) = 0.
-1, 2/3
Suppose 2*u = 3*g - g, -5*u - 3*g + 32 = 0. Suppose 5*a = 4*d - 19, -3*d + a = -u*d - 2. Let 5 - 6*o + d - 2 + 2*o**3 = 0. Calculate o.
-2, 1
Suppose 1 + 5 = 3*v. Factor -v*r**4 - 2*r**2 + 0*r**2 + 4*r**3 + 0*r**4 + 0*r