*(7*d + 2)/3
Let g(q) = -7*q - 56. Let r be g(-6). Let h be 4/r + 2 + (-12)/7. Solve h*a**2 + 6/7*a**3 - 2/7*a - 4/7*a**4 + 0 = 0 for a.
-1/2, 0, 1
Let y(w) = w**3 + w**2 + w + 1. Let i be (1/(-4))/(6/(-24)). Let j(s) = -s**3 - s**2. Let f(k) = i*y(k) + 2*j(k). What is t in f(t) = 0?
-1, 1
Let n(b) be the third derivative of -b**6/120 - 19*b**5/60 - 17*b**4/12 + 1045*b**2. Find r such that n(r) = 0.
-17, -2, 0
Let n = -29212 + 29212. Factor -10*f**3 + 19/3*f**2 + n - 2/3*f.
-f*(2*f - 1)*(15*f - 2)/3
Suppose 24*m = 17090 - 17042. Let 3/2*x**3 + 0 - x**m - 1/2*x**4 + 0*x = 0. Calculate x.
0, 1, 2
Let c = -24 - -27. Suppose -w - c = -2*w. Factor -3/2*u + 1/2*u**w + 1 + 0*u**2.
(u - 1)**2*(u + 2)/2
Let a = -38 + 36. Let l be (11 + -38)/(10/a). Determine g, given that -15*g**2 - l - 18*g = 0.
-3/5
Let x = -3958/9 - -440. Let y(i) be the first derivative of -i**2 + 0*i - 2 - x*i**3. Suppose y(s) = 0. What is s?
-3, 0
Suppose -d**3 + 172 + 2*d**3 - 2*d**2 - 167*d - 155*d + 238*d + 188 = 0. What is d?
-10, 6
Let q = 21770 + -21770. Factor 0*b - 2/5*b**2 + 1/5*b**3 + q.
b**2*(b - 2)/5
Let z(d) be the second derivative of -d**4/84 - d**3/42 + 3*d**2 - 39*d. Solve z(l) = 0 for l.
-7, 6
Let w(f) be the first derivative of 6 - 2*f**2 - 1/40*f**4 + 0*f + 1/200*f**6 + 0*f**5 + 0*f**3. Let c(l) be the second derivative of w(l). Solve c(q) = 0.
-1, 0, 1
Let b(d) be the third derivative of 1/105*d**7 + 0*d**4 - 2/15*d**5 + 0 - 6*d**2 + 0*d + 1/15*d**6 - 1/168*d**8 + 0*d**3. Let b(p) = 0. What is p?
-2, 0, 1, 2
Let k = 17 - 13. Suppose 0 = -5*c + 3*c + 6. Suppose -4*f**2 - 2*f + 6*f - k*f**c + 0*f + 5 - 1 = 0. Calculate f.
-1, 1
Let u be (-3)/15*(3 - 66/12). Let s(b) be the first derivative of u*b**4 - b - 1 + 1/6*b**6 - 2/3*b**3 - 3/2*b**2 + 3/5*b**5. Determine t, given that s(t) = 0.
-1, 1
Factor -14*q**3 + 19*q**3 - 48*q**2 + 231*q - 2*q**3 - 294.
3*(q - 7)**2*(q - 2)
Suppose 5*o + 13 = -5*n + 3, -4*n = 20. Find z, given that 7*z + 0*z**o - 3*z**3 - 12 + 6*z**3 + 17*z - 15*z**2 = 0.
1, 2
Let j(n) = -3*n**4 - 2*n**3 + 7*n**2 + 6*n - 2. Let p(f) = -f**4 + f**2 - 1. Let s(d) = 3*j(d) - 6*p(d). Determine l so that s(l) = 0.
-3, -1, 0, 2
Let 2/3*u**2 - 16*u + 88/3 = 0. Calculate u.
2, 22
Suppose 14*b = 13*b. Let m(w) be the first derivative of 0*w**4 + b*w**2 - 3 - 1/2*w**6 + 3/20*w**5 + 0*w + 0*w**3. Factor m(k).
-3*k**4*(4*k - 1)/4
Let v be 4/26 + (-2188)/14898. Let f = v - -13724/4011. Solve f*s**2 + 0 - 18/7*s**3 - 8/7*s = 0.
0, 2/3
Let l be 2/2 - (-3)/(-6). Let g = -285 - -571/2. Factor 0 + g*h**3 - l*h - 1/4*h**4 + 1/4*h**2.
-h*(h - 2)*(h - 1)*(h + 1)/4
Let b(s) be the first derivative of -5*s - 20*s**2 - 35/3*s**3 - 14. Factor b(i).
-5*(i + 1)*(7*i + 1)
Let j(m) = -m**3 - 10*m**2 - 14*m + 18. Let l be j(-8). Let c be 8/(-6)*9/(-6). Factor -2*n**c - 7*n**2 + 4*n**l.
-5*n**2
Let l(z) be the third derivative of z**7/1050 + z**6/75 + 11*z**5/150 + z**4/5 + 3*z**3/10 - z**2 + 48*z. Factor l(u).
(u + 1)**2*(u + 3)**2/5
Let b be (-3*4/(-42))/((-72)/(-126)). Suppose b*x**3 + 0*x**2 + 0 - 1/2*x = 0. Calculate x.
-1, 0, 1
Let a(g) be the third derivative of g**7/840 - g**6/240 - g**5/48 + g**4/16 + 65*g**2. Factor a(b).
b*(b - 3)*(b - 1)*(b + 2)/4
Let p(d) be the first derivative of 2*d**7/63 - 2*d**6/45 - 18*d - 3. Let w(k) be the first derivative of p(k). Find v, given that w(v) = 0.
0, 1
Suppose 20 = -4*c, 3*y + 2*c + 25 = -0*y. Let x be (-474)/(-15) - 2/y. Find z, given that 4*z**3 + 36*z**2 - x*z**3 + 35 - 8*z - 35 = 0.
0, 2/7, 1
Let x(m) = -3*m**4 + m**3 - 7*m**2 - 21*m + 10. Let i(c) = -4*c**4 - 8*c**2 - 23*c + 10. Let d(q) = -4*i(q) + 5*x(q). Determine t so that d(t) = 0.
-5, -2, 1
Suppose 12 - 3*x**3 - 5*x - 13 - 14 - 12 + 27*x**2 + 8*x = 0. What is x?
-1, 1, 9
Let d(z) = 5*z**2 - 131*z - 128. Let v(x) = -69*x**2 + 1704*x + 1665. Let w(i) = -27*d(i) - 2*v(i). Factor w(u).
3*(u + 1)*(u + 42)
Let r(m) be the first derivative of m**6/21 + 4*m**5/35 + m**4/14 + 197. Suppose r(g) = 0. What is g?
-1, 0
Let x(s) = 1. Let q(l) = l**2 - 2*l - 2. Let a(g) = g**2 - 7*g - 16. Let h be a(9). Let k(w) = h*q(w) + 6*x(w). Determine z so that k(z) = 0.
1
What is p in -54 + 12*p**2 + p**3 - 715*p + 706*p + 2*p**3 = 0?
-3, 2
Let x(t) be the first derivative of -2*t**6/3 - 8*t**5/5 + 19*t**4/4 + 23*t**3/3 + 3*t**2 - 202. Find y, given that x(y) = 0.
-3, -1/2, 0, 2
Let w = 57 + -48. Factor 12*i + 11*i**3 - w*i**3 + 72 - 6*i**3 - 16*i**2.
-4*(i - 2)*(i + 3)**2
Let k(u) = 7*u**2 - 5*u. Let a = 53 + -58. Let o(s) = 6*s**2 - 6*s. Let t(c) = a*o(c) + 4*k(c). Solve t(l) = 0 for l.
0, 5
Let q be 1 + (-1 - -2) + 0. Solve h + 4*h**3 + h**3 + 0*h**2 - 5*h**q + 5 - 6*h = 0.
-1, 1
Let j(v) be the third derivative of v**5/40 + 191*v**4/16 + 95*v**3/2 + 5*v**2 - 88*v. Determine u, given that j(u) = 0.
-190, -1
Let m(z) be the third derivative of z**8/20160 - z**7/168 + 5*z**6/16 + 13*z**5/60 - 28*z**2. Let f(l) be the third derivative of m(l). Factor f(i).
(i - 15)**2
Let t(r) be the first derivative of r**8/336 - r**6/72 + 11*r**3/3 + 3. Let a(z) be the third derivative of t(z). Factor a(m).
5*m**2*(m - 1)*(m + 1)
Let f(v) be the first derivative of -v**6/12 + v**5/2 - v**4/4 - 10*v**3/3 + 6*v**2 - 287. What is n in f(n) = 0?
-2, 0, 2, 3
Suppose 9 + 3 = -y. Let v be (y/16)/((-42)/16). Factor v*f**2 + 4/7*f + 2/7.
2*(f + 1)**2/7
Suppose 63*g - 3 = 66*g. Let s be ((-18)/(-3) - -2) + g - 2. Find z such that 3/4*z - 3/2*z**3 + 1/2*z**4 - z**2 + 3/4*z**s + 1/2 = 0.
-1, -2/3, 1
Let l(d) be the third derivative of -d**5/30 - 7*d**4/12 + 4*d**3/3 + 35*d**2. Let p(n) = -n**2 - 5*n + 3. Let w(z) = 3*l(z) - 8*p(z). Let w(v) = 0. What is v?
0, 1
Let t = -577 + 581. Let z(p) be the first derivative of 1/4*p**t + 5/3*p**3 + 4*p + 4 + 4*p**2. Determine a so that z(a) = 0.
-2, -1
Let i = -22 - 15. Let l = 41 + i. Let 0 - 3/5*r**l + 0*r + 9/5*r**3 - 6/5*r**2 = 0. Calculate r.
0, 1, 2
Let j = -447 + 451. Let d(u) be the second derivative of 1/42*u**7 + 1/2*u**2 - 1/2*u**3 + 8*u - 1/10*u**6 + 1/10*u**5 + 0 + 1/6*u**j. Factor d(c).
(c - 1)**4*(c + 1)
Let a(r) be the third derivative of 0*r**6 + 0*r**3 - 1/735*r**7 + 18*r**2 + 0*r + 0 + 1/42*r**4 + 1/70*r**5. What is g in a(g) = 0?
-1, 0, 2
Factor 75/2*m**4 + 135*m**3 + 0*m + 0 + 243/2*m**2.
3*m**2*(5*m + 9)**2/2
Factor -14 - 44/3*h - 2/3*h**2.
-2*(h + 1)*(h + 21)/3
Let u(r) = -20*r + 542. Let v be u(27). Let 0 - 1/2*i + 1/4*i**v = 0. What is i?
0, 2
Let h(x) be the second derivative of -3/11*x**4 + 3*x + 1/22*x**5 + 0 + 8/11*x**2 + 4/11*x**3. Factor h(s).
2*(s - 2)**2*(5*s + 2)/11
Let o(u) = 191*u + 5. Let b be o(1). Let p = 1768/9 - b. Find m, given that 0*m**2 + 2/9*m - p*m**4 - 2/3*m**3 + 0 = 0.
-1, 0, 1/2
Solve 50/19*m**2 + 20/19*m**5 - 8/19 - 20/19*m**3 - 42/19*m**4 + 0*m = 0 for m.
-1, -2/5, 1/2, 1, 2
Let x(j) be the third derivative of -3*j**7/280 - 13*j**6/480 + 7*j**5/120 + j**4/12 - 2*j**2 + 103*j. Factor x(b).
-b*(b - 1)*(b + 2)*(9*b + 4)/4
Let d(j) be the second derivative of j**6/160 + j**5/80 + 16*j**2 - 20*j. Let m(v) be the first derivative of d(v). Factor m(p).
3*p**2*(p + 1)/4
Let q be 1720/80 - (-294)/(-14). Find a such that 0*a**2 + 0 + 1/2*a**4 + 0*a + q*a**5 - a**3 = 0.
-2, 0, 1
Let i(l) be the second derivative of -l**5/4 - 10*l**4/3 + 15*l**3/2 - 37*l. Factor i(g).
-5*g*(g - 1)*(g + 9)
Suppose -7 = -i - o, 4 = o - 1. Factor -2/3*s**3 - 4/9*s**i + 0 - 2/9*s**4 + 0*s.
-2*s**2*(s + 1)*(s + 2)/9
Let f = 48/79 + -3935/10507. Let y = f - -1/19. Factor -4/7*g + 2/7*g**2 + y.
2*(g - 1)**2/7
Let v(u) be the second derivative of u**6/1620 - u**5/90 + u**4/12 - 5*u**3/6 + u. Let m(w) be the second derivative of v(w). Factor m(a).
2*(a - 3)**2/9
Let t = -1348/39 + 458/13. Factor 2*g**4 + t*g + 14/3*g**3 + 0 + 10/3*g**2.
2*g*(g + 1)**2*(3*g + 1)/3
Let d(q) be the first derivative of 0*q + 5/2*q**2 + 5/3*q**3 - 5/4*q**4 + 3 - q**5. Factor d(c).
-5*c*(c - 1)*(c + 1)**2
Let p(f) be the second derivative of -1/20*f**4 + 1/100*f**5 + 0 + 0*f**3 - 13*f + 2/5*f**2. Suppose p(y) = 0. What is y?
-1, 2
Determine u so that 1/5*u**3 + 1/5*u**2 - 1/5*u**4 + 0*u + 0 - 1/5*u**5 = 0.
-1, 0, 1
Let w(k) be the first derivative of -2*k**3/3 - 4*k**2 - 8*k - 22. Factor w(t).
-2*(t + 2)**2
Let i = 67365/7 + -9623. What is a in -24/7*a + 22/7*a**2 - 2/7*a**4 + i*a**3