w + 1/2*w**2.
(w - 3)*(w + 4)/2
Let q(z) be the second derivative of -z**4/60 - z**3/6 + 3*z**2/5 + 207*z. Solve q(j) = 0 for j.
-6, 1
Let t = -17629 - -123451/7. Factor -9/7*z**2 + 36/7 - t*z.
-3*(z + 6)*(3*z - 2)/7
Let m(s) be the second derivative of s**5/60 - 7*s**4/18 + 16*s**3/9 + 64*s**2/3 - 4*s + 11. Factor m(l).
(l - 8)**2*(l + 2)/3
Determine a so that 64*a + 4*a**2 - 21 - 12 - 49 + 14 = 0.
-17, 1
Let x be 1 + -1 + 0 + 2. Let d = 548/35 - 104/7. What is h in 8/5*h + d*h**3 + 0 - 12/5*h**x = 0?
0, 1, 2
Suppose 10 = -7*w + 38. Suppose -3*k - 10 = p + 4*p, -2*p = k + w. Solve -9/4*m**2 - 3/4*m**3 + k - 3/2*m = 0 for m.
-2, -1, 0
Suppose 2*l - 11 = 5*u, -9*l - 5*u + 1 = -7*l. Let d(h) be the second derivative of -1/110*h**5 + 0 - 2/33*h**l - 1/22*h**4 + 0*h**2 - 4*h. Factor d(v).
-2*v*(v + 1)*(v + 2)/11
Suppose -6*c - 30 = -16*c. Suppose -4*q - 20 = d, -q + c = -d + 8. Solve -2/13*g**4 - 2/13*g**5 + d*g + 0 + 2/13*g**2 + 2/13*g**3 = 0.
-1, 0, 1
Let d(g) be the third derivative of 1/120*g**6 + 1/2016*g**8 + 1/144*g**4 + 0*g**3 + 1/90*g**5 + 0 - 24*g**2 + 1/315*g**7 + 0*g. Factor d(i).
i*(i + 1)**4/6
Let a(x) be the second derivative of x**6/3 + 17*x**5/4 - 95*x**4/8 + 295*x**3/24 - 25*x**2/4 + 66*x. Solve a(v) = 0.
-10, 1/2
Determine t so that 211*t**2 + t**3 + t**3 - 10 - 18*t - 112*t**2 - 105*t**2 = 0.
-1, 5
Let p(j) = 3*j - 13. Let y be p(5). Factor -2 - 2 - x**y - x**3 + 4.
-x**2*(x + 1)
Suppose 0 = t - 5*t. Let q = -2/3455 - -6924/24185. Factor -2/7*k**2 + q + t*k.
-2*(k - 1)*(k + 1)/7
Let d(t) be the second derivative of -t**7/21 + t**6/15 + 3*t**5/10 - t**4/6 - 2*t**3/3 - 17*t + 4. Suppose d(l) = 0. What is l?
-1, 0, 1, 2
Let f(c) be the second derivative of -c**7/112 + 11*c**6/240 + c**5/16 - 17*c**4/48 - 13*c**3/16 - 9*c**2/16 + 211*c. Let f(t) = 0. What is t?
-1, -1/3, 3
Solve 4*z**2 + 52/3*z + 16/3 = 0.
-4, -1/3
Let g(h) = -10*h**3 - 3*h**2 + 2. Let s be g(-1). Suppose -s = -0*f - 4*f + z, -2*f + 21 = 5*z. Factor 0*l**4 - 1/2*l**f + 1/4*l + 0 + 1/4*l**5 + 0*l**2.
l*(l - 1)**2*(l + 1)**2/4
Let j(c) be the second derivative of 2/5*c**2 - 8*c - 1/50*c**5 + 0 - 1/3*c**3 + 2/15*c**4. Factor j(d).
-2*(d - 2)*(d - 1)**2/5
Let p be (-54)/8 + 218/3815 + (-243)/(-35). Let 0*o + 0 + 0*o**2 - 1/4*o**4 + p*o**3 = 0. Calculate o.
0, 1
Let z(v) = v**3 - 5*v**2 + 6*v - 6. Let a be z(4). Let p(t) be the first derivative of -3 + 2/9*t**a + 0*t + 2/9*t**3 + 1/18*t**4. Factor p(c).
2*c*(c + 1)*(c + 2)/9
Let w(l) = 2*l**4 + 2*l**3 - l**2 - l + 1. Let g(u) = 5*u**5 - 40*u**4 - 10*u**3 + 165*u**2 + 5*u - 5. Let p(o) = g(o) + 5*w(o). Let p(j) = 0. What is j?
-2, 0, 4
Let m = 121 + -2540/21. Let j = 5/7 - m. Find y, given that j*y**2 + 0 + 4/3*y = 0.
-2, 0
Let h(q) be the second derivative of 1/30*q**4 + 8/5*q**3 + q + 144/5*q**2 + 7. Determine x, given that h(x) = 0.
-12
Suppose 48 = 3*l + 3*w - 6, 4*l - 60 = 2*w. Suppose -l*k = -17*k + 2. Determine c, given that 8/3 - 2/3*c**3 - 16/3*c + 10/3*c**k = 0.
1, 2
Factor 5*a**3 - 80*a**2 - 9*a**3 - 308*a - 207 + 1175.
-4*(a - 2)*(a + 11)**2
Let s = 42 - 37. Factor -153*y + 8*y**3 + 0*y**3 + 153*y + 4*y**s + 12*y**4.
4*y**3*(y + 1)*(y + 2)
Let q be (60 + -89)*4/(-58). Let 8/3*k - 32/3*k**q + 2/3*k**4 + 0 - 134/3*k**3 + 52*k**5 = 0. Calculate k.
-2/3, -1/2, 0, 2/13, 1
Suppose x = -1 - 10. Let f(j) = -j**3 - 12*j**2 - 11*j + 2. Let b be f(x). Determine g so that -57 + g**2 - 3*g**b + 57 + 2*g**3 = 0.
0, 1
Let g(n) = -40*n**4 + 4*n**3 + 36*n**2 + 68*n + 4. Let w(f) = 8*f**4 - f**3 - 7*f**2 - 14*f - 1. Let s(y) = -5*g(y) - 24*w(y). Factor s(r).
4*(r - 1)*(r + 1)**2*(2*r - 1)
Let 7521 - x**2 - 9*x - 14*x - 7651 = 0. What is x?
-13, -10
Let p be (-328)/(-40) - 1/5. Suppose 5*t = 3*t + p. Factor 11*q**3 + 3*q**t + 12 + 39*q**2 + 7*q**3 + 12*q + 24*q.
3*(q + 1)**2*(q + 2)**2
Let q = -37 - -42. Let -7*n**3 + n**3 - 6*n**4 + 123*n**2 - 125*n**2 - 2*n**q = 0. Calculate n.
-1, 0
Let j(w) be the second derivative of -w**9/1512 + w**8/105 - 4*w**7/105 + 13*w**3/6 - 21*w. Let v(d) be the second derivative of j(d). Solve v(f) = 0 for f.
0, 4
Let p(x) be the third derivative of -x**8/112 + x**7/70 + 7*x**6/40 - 13*x**5/20 + 3*x**4/4 + 123*x**2. Determine h, given that p(h) = 0.
-3, 0, 1, 2
Let n(m) be the first derivative of 5*m**6/6 + 12*m**5 + 275*m**4/4 + 200*m**3 + 310*m**2 + 240*m + 68. Let n(x) = 0. Calculate x.
-4, -3, -2, -1
Determine m so that -2/13*m**2 - 36/13*m - 162/13 = 0.
-9
Suppose -11*c - 123*c = 0. Find n such that -2/7*n**2 - 2/7*n + c = 0.
-1, 0
Let q = -744649/9 - -82646. Let d = 93 + q. Factor 2/9*c**3 + d*c + 4/9*c**2 + 0.
2*c*(c + 1)**2/9
Let j(v) be the second derivative of -v**5/110 + v**4/2 - 92*v**3/33 + 60*v**2/11 + v + 46. Suppose j(n) = 0. Calculate n.
1, 2, 30
Let v(g) be the second derivative of g**7/105 - 2*g**6/25 + 6*g**5/25 - g**4/3 + g**3/5 + 9*g. Factor v(a).
2*a*(a - 3)*(a - 1)**3/5
Let z(v) = -6*v**3 - 93*v**2 + 272*v + 40. Let r be z(-18). Determine g so that 12/7*g**3 - 24/7*g**2 - 2/7*g**r + 0 + 16/7*g = 0.
0, 2
Suppose s - 10 = -s. Suppose -l - 3*v = -4*l + 6, -l - s*v + 20 = 0. Let -1 + l*w**2 - 7*w + 3 + 0*w = 0. What is w?
2/5, 1
Let l(r) = -6*r**2 - r + 1. Let c(q) = 128*q**2 - 55*q - 7. Let b(z) = 2*c(z) + 22*l(z). Factor b(u).
4*(u - 1)*(31*u - 2)
Let j be 4/18*(17 - 240/16). Find y, given that -2/9*y**2 - j - 2/3*y = 0.
-2, -1
Suppose 71 - 75 = d. Let f be 10/d + 238/84. Factor 1/3*g**3 + 1/3*g**2 + 0 - f*g**5 + 0*g - 1/3*g**4.
-g**2*(g - 1)*(g + 1)**2/3
Let m(j) be the third derivative of 0*j + 4/195*j**5 + 0 - 19*j**2 - 1/780*j**6 + 16/39*j**3 - 5/39*j**4. Factor m(b).
-2*(b - 4)*(b - 2)**2/13
Suppose -5*m = -6*m + 6. Let i = m - 4. Factor i*w**2 + w**2 + w**2 - 2*w**2.
2*w**2
Let d(f) be the first derivative of -2*f**3/27 + 4*f**2/9 - 8*f/9 + 124. Determine h so that d(h) = 0.
2
Factor 138*p - 3*p**3 + 80*p**2 - 108*p**2 + 91*p**2.
-3*p*(p - 23)*(p + 2)
Let a(c) = 12*c**3 + 45*c**2 - 3*c - 36. Let f(h) = -7*h**3 - 23*h**2 + 2*h + 18. Let p(v) = -5*a(v) - 9*f(v). Let p(d) = 0. Calculate d.
-1, 1, 6
Let l(t) be the first derivative of -t**6/1980 - t**5/165 - t**4/33 + 16*t**3/3 - 16. Let o(g) be the third derivative of l(g). Factor o(y).
-2*(y + 2)**2/11
Factor 1/3*z**3 + 8/3*z**2 - 33*z - 270.
(z - 10)*(z + 9)**2/3
Suppose 3*l + 4*c + 6 = 0, 79 = -l - 5*c + 66. Solve 4/3*k + 4 + 1/9*k**l = 0.
-6
Let l(g) be the third derivative of -g**8/84 + 16*g**7/105 + g**6/15 - 16*g**5/15 - g**4/6 + 16*g**3/3 + 174*g**2. Let l(m) = 0. Calculate m.
-1, 1, 8
Let l(c) be the third derivative of c**7/420 - 7*c**6/240 - 3*c**5/40 + 7*c**4/48 + 2*c**3/3 + 18*c**2 + 2*c. Solve l(y) = 0.
-1, 1, 8
Let t(l) be the third derivative of l**6/24 + 77*l**5/4 + 29645*l**4/8 + 2282665*l**3/6 + 7*l**2 - 21. Find o such that t(o) = 0.
-77
Let p be (1183/(-104) - -12)*4/30. Let f(n) be the first derivative of -12 + 3/4*n + p*n**3 - 1/2*n**2. Solve f(g) = 0.
1, 3
Let d(f) be the third derivative of 1/144*f**4 + 0*f + 1/2016*f**8 - 1/36*f**3 + 0 - 7*f**2 - 1/360*f**6 + 1/180*f**5 - 1/1260*f**7. Factor d(u).
(u - 1)**3*(u + 1)**2/6
Let h = 29 - 26. Suppose -s = -0*s + 3*l - 2, -6 = -h*s - 4*l. Factor -38*q**2 - 3 + 2*q**3 + 3 + 34*q**s.
2*q**2*(q - 2)
What is p in 4/3*p**2 + 0 + 1/3*p**3 + 0*p = 0?
-4, 0
Let m(b) = -5*b**3 + b + 1. Let a(t) = 88*t**3 - 14*t**2 - 46*t - 34. Let g(c) = -2*a(c) - 36*m(c). Factor g(i).
4*(i + 1)*(i + 2)*(i + 4)
Determine p so that -62*p - p**2 + 157*p - 56*p - 52*p = 0.
-13, 0
Let c(i) be the first derivative of i**7/210 - i**5/10 + i**4/3 + 16*i**3/3 - 8. Let k(w) be the third derivative of c(w). Factor k(p).
4*(p - 1)**2*(p + 2)
Let i(u) = u**2 + 13*u + 7. Let h be i(-13). Suppose 0 = -3*v - y + 5, -v + h = -5*y. Factor -16*l - 18 - 23 - v*l**2 + 9.
-2*(l + 4)**2
Suppose -9*l - 250 = -268. Solve 15/8*p**4 - 21/8*p**3 - 3/4*p**l + 0 + 0*p + 3/2*p**5 = 0.
-2, -1/4, 0, 1
Let u(t) be the third derivative of 0*t**5 + 0 + 0*t + 0*t**4 - 3*t**2 + 1/840*t**7 + 1/480*t**6 + 0*t**3. Suppose u(a) = 0. Calculate a.
-1, 0
Let k be (-3)/6 + 30/4. Let q = 9 - k. Solve -16*h**3 + 0*h**5 - h**2 + 0*h**q - 10*h**4 - 2*h**5 - 7*h**2 = 0.
-2, -1, 0
Suppose 30/7*y - 3/7*y**4 - 9/7 + 18/7*y**3 - 36/7*y**2 = 0. What is y?
1, 3
Let p(m) = 2*m**2 + 9*m + 8. Let d be p(-4). What is g in d + 28*g**