r h.
-11/3, -2, -1
Let u(o) = o**2. Let p(n) = -21*n**2 - 69*n - 36. Let y(a) = -p(a) + 12*u(a). Determine s, given that y(s) = 0.
-12/11, -1
Let q(c) be the first derivative of 4*c**6/21 + 4*c**5/35 - 3*c**4/7 - 4*c**3/21 + 2*c**2/7 + 164. Find u, given that q(u) = 0.
-1, 0, 1/2, 1
Let x be (2/2)/(1/4). Solve 7*o + 11*o**2 - 5 - 7*o**x - 19*o + 12*o**3 + 1 = 0 for o.
-1, -2/7, 1, 2
Suppose 6/5*k - 7/5*k**3 - 3/5*k**5 + 0 - 17/5*k**2 + 13/5*k**4 = 0. What is k?
-1, 0, 1/3, 2, 3
Suppose u + 15 = 3*g, -2*u + 5 + 0 = g. Suppose -3 = i - g. Determine d, given that -d - 1/2*d**i + 3/2 = 0.
-3, 1
Let k(m) be the third derivative of m**7/6300 - m**6/450 - m**4/6 - 31*m**2. Let g(s) be the second derivative of k(s). Solve g(a) = 0 for a.
0, 4
Let j(b) = 36*b**2 + 69*b + 33. Let y(d) = -5*d**2 - 10*d - 5. Let z(a) = -2*j(a) - 15*y(a). Solve z(u) = 0 for u.
-3, -1
Let m(b) be the second derivative of -b**5/60 - b**4/36 + 5*b**3/9 - 4*b**2/3 - 22*b. Solve m(r) = 0 for r.
-4, 1, 2
Factor 20*f**2 + 37*f**3 - 36*f**4 - 64 - 244*f**2 + 31*f**5 - 5*f**3 + 192*f - 27*f**5 + 96*f**3.
4*(f - 2)**4*(f - 1)
Let p = -2058 - -6227/3. Let j = -362/21 + p. Factor 0 - 3/7*k**2 - 6/7*k**3 + j*k**4 + 6/7*k.
3*k*(k - 2)*(k - 1)*(k + 1)/7
Let r = 9 - -7. Let x = r + -14. Factor -8/3*w**3 + 4/3 + x*w + 0*w**4 - 4/3*w**2 + 2/3*w**5.
2*(w - 2)*(w - 1)*(w + 1)**3/3
Let k be ((-32)/48)/((-119)/408). Factor 0 + k*a - 4/7*a**2.
-4*a*(a - 4)/7
Let t = -1/1653 - -4961/3306. Factor 5/2*x**3 + 7/6*x**2 + t*x**4 + 0 + 1/6*x.
x*(x + 1)*(3*x + 1)**2/6
Let c(h) be the second derivative of h**4/72 - h**3/9 - h**2 + 26*h. Factor c(l).
(l - 6)*(l + 2)/6
Let k(y) = y**3 - 4*y**2 + y. Let w be k(4). Let a(u) = 2 + 4 - 3*u + w*u**2 + 8*u**2. Let m(g) = g**2. Let b(c) = -a(c) + 15*m(c). Factor b(d).
3*(d - 1)*(d + 2)
Suppose 20*v = -13*v + 165. Solve 14/5*r**v - 2*r**4 + 8/5 - 46/5*r**3 + 2/5*r**2 + 32/5*r = 0.
-1, -2/7, 1, 2
Let f(b) be the first derivative of 2*b**4 + 0*b**3 + 1 + 0*b + 0*b**2 + 4/5*b**5 - 2/3*b**6. Solve f(c) = 0 for c.
-1, 0, 2
Let u(y) = -9*y**2 + 3*y + 3. Let g be (1/3)/((-1)/12). Let c(h) = -h**4 + h**3 - 9*h**2 + 3*h + 2. Let j(m) = g*u(m) + 3*c(m). Factor j(l).
-3*(l - 2)*(l - 1)*(l + 1)**2
Let x(j) be the third derivative of j**8/336 - 2*j**7/105 + 4*j**5/15 - 2*j**4/3 - 24*j**2 + 1. Solve x(q) = 0 for q.
-2, 0, 2
Solve -11*h**3 + 8*h**3 + 44 + 87*h**2 - 148*h - 11*h**3 - h**4 + 32 = 0 for h.
-19, 1, 2
Let o(k) be the first derivative of -3*k**5/5 - 6*k**4 - 15*k**3 + 12*k**2 + 48*k + 1. Determine q, given that o(q) = 0.
-4, -1, 1
Let r(z) = -20*z**3 + 55*z**2 - 50*z + 15. Let t = 75 + -30. Let x(l) = 220*l**3 - 605*l**2 + 550*l - 165. Let j(p) = t*r(p) + 4*x(p). Factor j(d).
-5*(d - 1)**2*(4*d - 3)
Let y(g) be the first derivative of 4 + 1/3*g - 1/9*g**3 + 1/6*g**2 - 1/12*g**4. Factor y(i).
-(i - 1)*(i + 1)**2/3
Let g(s) be the first derivative of -s**4/10 + s**3/15 + s**2/2 + 2*s/5 - 204. Let g(q) = 0. What is q?
-1, -1/2, 2
Let a(c) be the first derivative of -5 + 4/5*c - 2/15*c**3 + 1/5*c**2. Factor a(q).
-2*(q - 2)*(q + 1)/5
Let t(d) = 16*d**3 + 20*d**2 + 25*d + 21. Let h be 2/(-10 + 2) + (-92)/16. Let y(v) = 3*v**3 + 4*v**2 + 5*v + 4. Let b(l) = h*t(l) + 33*y(l). Factor b(o).
3*(o + 1)**2*(o + 2)
Let r(w) be the first derivative of 2*w**3 - w**4 + 1/5*w**5 - 2*w**2 + w + 23. Factor r(c).
(c - 1)**4
Let o(g) be the second derivative of -g**6/30 + 2*g**5/5 + 13*g**4/6 - 28*g**3 - 441*g**2/2 + 31*g - 4. Find v, given that o(v) = 0.
-3, 7
Let w be 6/(-5)*60/(-45). Suppose -3*x = 2*x - 10. Factor w - 56/5*l + 98/5*l**x.
2*(7*l - 2)**2/5
Let i(t) be the third derivative of -t**11/166320 - t**10/37800 - t**9/30240 + 7*t**5/60 + 12*t**2. Let a(m) be the third derivative of i(m). Factor a(w).
-2*w**3*(w + 1)**2
Factor 30*o**2 + 20*o + 96 + 4*o**4 - 136 - 9*o**4 + 0*o**3 - 5*o**3.
-5*(o - 2)*(o - 1)*(o + 2)**2
Let l(j) = -j**2 + 8*j - 12. Let k be l(5). Factor -6*a + a**2 + 1 - k*a**2 - 5.
-2*(a + 1)*(a + 2)
Let c = 26453/4 + -6613. Solve -3/4*x**5 - 3/4*x + 3/2*x**3 + 1/2*x**2 - c - 1/4*x**4 = 0.
-1, -1/3, 1
Let j be (207 + -198)*(-3)/(45/(-4)). Solve -18/5 - 2/5*o**2 + j*o = 0 for o.
3
Let f be ((-5)/(-9))/((5 - 16)/(-33)). Suppose -5/6*m**2 - f + 5/2*m = 0. Calculate m.
1, 2
Let t(o) be the third derivative of -1/5*o**4 - 30*o**2 - 1/150*o**5 + 0 + 0*o - 12/5*o**3. Find y, given that t(y) = 0.
-6
Suppose -12*w + 18 + 18 = 6*w. Solve -2/3*u + 8/7 + 2/21*u**w = 0 for u.
3, 4
Let a(k) = 13*k**3 - 16*k**2 + 5*k + 16. Let n(m) = m**3 - m**2 + m + 2. Let v(w) = -a(w) + 6*n(w). Factor v(x).
-(x - 1)**2*(7*x + 4)
Factor 0 + 3/2*w**3 + 0*w + 0*w**2.
3*w**3/2
Factor 2/3*v**2 + 8 + 16/3*v.
2*(v + 2)*(v + 6)/3
Factor -2/7*f**4 + 10/7*f**3 + 0 + 6/7*f - 2*f**2.
-2*f*(f - 3)*(f - 1)**2/7
Let a = 17 + 0. Suppose 2*z = 55 - a. Factor 5*c**3 + 2*c**2 + 2*c**2 - z*c**3.
-2*c**2*(7*c - 2)
Determine v so that -v**5 + 16*v + 2*v**3 + v**4 - 5*v**2 + 19*v - 33*v + v**3 = 0.
-2, 0, 1
Let q(b) be the first derivative of b**4/4 - 2*b**3/3 - b**2 - b + 1. Let z be q(3). Factor -y**3 + z*y**2 - 3*y**3 - 2 + 3*y**3 + y.
-(y - 2)*(y - 1)*(y + 1)
Let s(v) be the first derivative of v**5/15 + v**4/3 - 16*v**3/3 + 47*v**2/2 + 35. Let l(m) be the second derivative of s(m). Factor l(g).
4*(g - 2)*(g + 4)
Factor 0*x**2 + 40/23*x**4 - 200/23*x**3 + 0 + 0*x - 2/23*x**5.
-2*x**3*(x - 10)**2/23
Let c(g) be the first derivative of -g**4/18 - 98*g**3/27 + 34*g**2/3 - 425. Factor c(o).
-2*o*(o - 2)*(o + 51)/9
Suppose -10*i + 430 = -560. Suppose 0 = -i*s + 107*s. Find x such that -6/11*x**2 + s + 0*x**3 + 4/11*x + 2/11*x**4 = 0.
-2, 0, 1
Let g(i) be the first derivative of -1/2*i**3 + 1/6*i**4 + 12 - 1/60*i**5 + 4*i**2 + 0*i. Let r(o) be the second derivative of g(o). Factor r(q).
-(q - 3)*(q - 1)
Let j(i) = i - 1. Suppose -5*b = -b + 4. Let n(s) = -5*s**2 + 8*s - 3. Let p(m) = b*n(m) + 3*j(m). Suppose p(k) = 0. Calculate k.
0, 1
Let w = -1 - -4. Let h(a) = a**2 - 2*a - 5. Let z be h(4). Factor -2*b**4 + 3*b**2 + 12*b**w - z*b**4 + b**4 - 11*b**2.
-4*b**2*(b - 2)*(b - 1)
Let t(y) be the third derivative of -1/4*y**4 - 1/70*y**7 - 23*y**2 + 0*y**3 - 3/40*y**6 + 0*y + 1/4*y**5 + 1/112*y**8 + 0. Factor t(u).
3*u*(u - 1)**3*(u + 2)
Let m = -8 + 14. Suppose -m*c = -10 - 8. Let p(f) = f**3 - f**2 + f - 1. Let n(r) = -4*r**4 - r**3 + 9*r**2 + 23*r + 5. Let v(a) = c*p(a) - n(a). Factor v(j).
4*(j - 2)*(j + 1)**3
Let x(q) be the third derivative of 0*q + 0*q**4 - 1/630*q**7 - 12*q**2 + 0 - 1/360*q**6 + 1/1008*q**8 + 1/180*q**5 + 0*q**3. What is z in x(z) = 0?
-1, 0, 1
Let w = 163691/9 + -18185. Factor 14/9 - 4/9*u**2 + w*u.
-2*(u - 7)*(2*u + 1)/9
Let p be ((-1)/2)/(2/(-28)). Let r = -7 + p. Factor r + 0*q**3 - 2/3*q**2 + 2/3*q**4 + 0*q.
2*q**2*(q - 1)*(q + 1)/3
Let d = -1447 + 21707/15. Let w(b) be the second derivative of 3/10*b**5 - d*b**6 - 7*b + 0*b**4 - 1/3*b**3 + 0 + 0*b**2. Let w(l) = 0. Calculate l.
-1/2, 0, 1
Let g = -793/6 - -911/6. Let b = g + -19. Factor 0 - 2/3*h**2 - b*h.
-2*h*(h + 1)/3
Determine n so that -7/3*n**4 - 121/3*n**3 - 314/3*n**2 + 2020/3*n + 200 = 0.
-10, -2/7, 3
Let t(q) be the third derivative of 0*q**3 - 3*q**2 - 1/3*q**4 - 7/15*q**5 - 4/15*q**6 + 0*q + 0 - 2/35*q**7. Solve t(d) = 0 for d.
-1, -2/3, 0
Let n(k) be the second derivative of -5*k**4/12 - 170*k**3/3 - 335*k**2/2 + 2*k + 39. Let n(o) = 0. What is o?
-67, -1
Let q(v) be the first derivative of -v**7/280 + v**6/120 + v**5/20 - 4*v**3/3 - 8. Let k(r) be the third derivative of q(r). Factor k(z).
-3*z*(z - 2)*(z + 1)
Let l(d) = 4*d**3 + 6*d**2 + 6*d - 4. Let r(a) = -5*a**3 - 6*a**2 - 6*a + 4. Let v(b) = -4*l(b) - 3*r(b). Let c be v(-5). Factor c*x + 4 - 13 + 6 - 6*x**2.
-3*(x - 1)*(2*x - 1)
Suppose -r - 3*v + 0 = -4, -4*r = -4*v + 16. Let m be -1*r/14*1. Determine c, given that -m*c + 1/7*c**3 - 2/7 + 3/7*c**2 - 1/7*c**4 = 0.
-1, 1, 2
Let m(f) be the third derivative of -f**5/15 + 52*f**4/3 - 5408*f**3/3 - 217*f**2. Solve m(w) = 0.
52
Let o be (-2)/17 - (-2 + (-24)/204). Factor 1/3*s**o + 16/3 + 8/3*s.
(s + 4)**2/3
Solve -242/5*n - 336*n**3 - 360*n**4 + 3718/5*n**2 + 4/5 = 0 for n.
-2, 1/30, 1
Let p(h) be the second derivative of -49*h**6/90 + 91*h**5/30 - 17*h**4/3 + 4*h**3 - 109*h + 3. Solve p(o) = 0 for o.
0, 6/7, 2
Let -1/4*