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Let r(i) be the second derivative of i**4/3 + 6*i**3 + 40*i**2 + 72*i. Solve r(s) = 0.
-5, -4
Let -3/4*u**2 + 3/4*u**3 - 11/4*u + 1/4*u**4 - 3/2 = 0. Calculate u.
-3, -1, 2
Factor 10*l + 9*l - 4*l + 0*l - 5*l**2 + 0*l**2.
-5*l*(l - 3)
Let y(l) be the third derivative of -l**6/75 + 7*l**5/50 - l**4/2 + 13*l**3/15 + 170*l**2. Factor y(k).
-2*(k - 1)**2*(4*k - 13)/5
Let g(w) = -w**3 + 7*w**2 + 18*w + 7. Let k be g(9). Determine f so that -2*f**5 + 2*f**3 - 10*f**2 + 0*f**4 - 7*f**3 + k*f**5 + 10*f**4 = 0.
-2, -1, 0, 1
Solve -4*n**3 + 13605*n - n**3 - 13545*n + 20*n**2 = 0 for n.
-2, 0, 6
Suppose 1/3*h**5 + 14/3*h**4 + 4*h**2 + 0 + 0*h + 25/3*h**3 = 0. What is h?
-12, -1, 0
Let n(t) = 6*t**4 + 19*t**3 - 241*t**2 - 219*t + 2393. Let o(a) = 2*a**4 + 6*a**3 - 80*a**2 - 74*a + 798. Let u(b) = 4*n(b) - 14*o(b). What is i in u(i) = 0?
-5, 4
Solve -3/4*j + j**2 - 1/4*j**3 + 0 = 0.
0, 1, 3
Let b(i) be the third derivative of -1/160*i**6 + 0 + 0*i + 1/840*i**7 - 13*i**2 + 1/32*i**4 - 1/12*i**3 + 1/240*i**5. Factor b(z).
(z - 2)*(z - 1)**2*(z + 1)/4
Let -429*s**2 + 849*s**2 + 39*s - 108 - 423*s**2 = 0. Calculate s.
4, 9
Let a(p) = -p**3 + 4*p**2 + p - 7. Let m(z) be the second derivative of -z**4/3 + 3*z**2 + 33*z. Let b(r) = -2*a(r) - 3*m(r). What is d in b(d) = 0?
-2, -1, 1
Let t(v) be the third derivative of 10*v**2 + 1/84*v**5 + 1/84*v**4 + 0*v**3 + 1/1470*v**7 + 0*v + 0 + 1/210*v**6. Factor t(h).
h*(h + 1)**2*(h + 2)/7
Let m(w) be the second derivative of 1/10*w**3 - 1/20*w**4 + 0 - 3/100*w**5 + 0*w**2 + 1/50*w**6 + 15*w. Find f, given that m(f) = 0.
-1, 0, 1
Let c(z) be the second derivative of z**7/210 - z**6/24 + z**5/15 + 23*z**2/2 - 4*z. Let o(g) be the first derivative of c(g). Solve o(p) = 0.
0, 1, 4
Let b(v) be the second derivative of v**5/10 - 67*v**4/6 + 1088*v**3/3 + 1156*v**2 + 183*v. Determine x so that b(x) = 0.
-1, 34
Let -3195*r**2 + 1599*r**2 - 20*r + 1600*r**2 - 56 = 0. Calculate r.
-2, 7
Let w = 73/458 + 5/687. Factor 4/3*x + w*x**2 + 8/3.
(x + 4)**2/6
Let g = -6 + 11. Find x such that 16*x + 2*x**2 - 10*x**4 - 7*x**3 + 8 + 3*x**g - 5*x**5 - 7*x**3 = 0.
-2, -1, 1
Let p be (8 + -9 + 7)/(-4 + (-2 - -11)). Factor 0 + 2/5*c**2 + p*c.
2*c*(c + 3)/5
Let v = -30727/2 - -15364. Let i + 0 - 4*i**3 - v*i**2 - 5/2*i**4 = 0. What is i?
-1, 0, 2/5
Let j(y) be the second derivative of 11/16*y**3 + 5*y + 3/4*y**2 + 0 - 3/32*y**4. Factor j(h).
-3*(h - 4)*(3*h + 1)/8
Let o(i) be the third derivative of i**5/450 + i**4/3 - 415*i**2. Factor o(b).
2*b*(b + 60)/15
Let a(p) be the second derivative of 0 + 1/12*p**3 + 1/8*p**2 + 1/48*p**4 + 23*p. Factor a(l).
(l + 1)**2/4
Let u(f) = -3*f**3 + 48*f**2 - 49*f - 2. Let d(q) = -3*q**3 + q - 1. Let p(w) = -2*d(w) + u(w). Factor p(y).
3*y*(y - 1)*(y + 17)
Suppose 4*b - 4 = 2*b. Solve 5*i**2 - 11*i**b - 18*i + 33*i**3 - 31*i**3 - 10 = 0 for i.
-1, 5
Factor -3*w**3 + 0*w + 23*w + 6*w**2 - 14*w - 29*w**3 - 32*w**4.
-w*(2*w - 1)*(4*w + 3)**2
Suppose 0 = -55*f + 51*f + 200. Determine c so that 6*c**2 + f*c - 3 - 50*c - 3*c**4 = 0.
-1, 1
Let a(q) = -q**3 + 4*q**2 - 2*q - 2. Let m be a(2). Factor 108 - 66*w**2 + 33*w**2 + 5*w**3 + 29*w - m*w**3 + 43*w.
3*(w - 6)**2*(w + 1)
Let r be ((-6)/9 + 0)/(23/(-621)). Factor 39/2*w - r*w**2 + 27/8*w**3 - 6.
3*(w - 4)*(3*w - 2)**2/8
Let k(c) be the third derivative of -c**8/4200 + c**7/2100 + c**6/450 - 3*c**3 - 19*c**2. Let d(b) be the first derivative of k(b). Factor d(a).
-2*a**2*(a - 2)*(a + 1)/5
Suppose 0*s**3 - 32/5*s + 2/5*s**5 + 8*s**2 - 2*s**4 + 0 = 0. What is s?
-2, 0, 1, 2, 4
Suppose -3*t + 3 + 3 = 0. Factor 120*a**5 - 2 - 1 - 2*a**2 + 20*a**t + 30*a**3 - 9*a - 63*a**4 - 93*a**5.
3*(a - 1)**3*(3*a + 1)**2
Factor -32*b - 2/7*b**4 - 14 - 156/7*b**2 - 32/7*b**3.
-2*(b + 1)**2*(b + 7)**2/7
Let n(j) = 4*j**5 - 84*j**4 - 1182*j**3 - 5488*j**2 - 12*j - 12. Let g(y) = -y**5 + y**3 + 2*y + 2. Let h(c) = -6*g(c) - n(c). Factor h(x).
2*x**2*(x + 14)**3
Suppose 1817*h - 1827*h = 0. Solve 6/11*z**2 + 4/11*z**3 + 0 + h*z - 2/11*z**4 = 0.
-1, 0, 3
Suppose 103*m = 105*m - 6. Factor -4*v**2 - 2/3 - 2/3*v**4 - 8/3*v**m - 8/3*v.
-2*(v + 1)**4/3
Suppose 5/3*g**2 - 7/9*g + 1/9*g**4 - g**3 + 0 = 0. What is g?
0, 1, 7
Let h(w) be the first derivative of 0*w + 1/12*w**4 + 1/30*w**5 - 4/3*w**3 - 1/60*w**6 + 0*w**2 + 5. Let v(f) be the third derivative of h(f). Factor v(a).
-2*(a - 1)*(3*a + 1)
Suppose 2*u + 36 - 42 = 0. Suppose -5 = -4*p + 11. Find x, given that 4*x**u + 12*x**4 - 8*x**5 - 16*x**2 + 5*x**3 - x**3 + p = 0.
-1, -1/2, 1
Let s(f) be the third derivative of f**7/1260 + f**6/72 - 11*f**4/24 - f**3/2 + 3*f**2 + 4. Let z(q) be the second derivative of s(q). Factor z(d).
2*d*(d + 5)
Let w(x) be the second derivative of -1/18*x**4 - 16/3*x**2 + 8/9*x**3 + 6*x + 0. Let w(h) = 0. What is h?
4
Let w(p) be the third derivative of p**6/30 + 13*p**5/5 + 60*p**4 - 800*p**3/3 - 122*p**2 + 2*p. Factor w(c).
4*(c - 1)*(c + 20)**2
Let f(t) be the second derivative of -3*t**5/80 - 17*t**4/16 - 63*t**3/8 + 243*t**2/8 - 2*t - 565. Factor f(l).
-3*(l - 1)*(l + 9)**2/4
Factor 8/23*d + 2/23*d**2 + 8/23.
2*(d + 2)**2/23
Suppose -106*b + 227*b = 242. Suppose -6/5 - b*w**2 - 2/5*w**3 - 14/5*w = 0. Calculate w.
-3, -1
Let -1924*j**3 - j**2 + j**5 - j**4 + 2*j + 1921*j**3 + 2*j**4 = 0. What is j?
-2, -1, 0, 1
Let l(a) be the first derivative of -1/2520*a**6 + 7/3*a**3 + 0*a + 1/420*a**5 + 0*a**2 - 1/168*a**4 + 4. Let y(d) be the third derivative of l(d). Factor y(r).
-(r - 1)**2/7
Let h(c) be the second derivative of c**7/105 - c**5/25 + c**3/15 - 24*c - 8. Factor h(j).
2*j*(j - 1)**2*(j + 1)**2/5
Let o(v) be the first derivative of -3/5*v**5 + 3/4*v**4 + 0*v + 20 + v**3 - 1/2*v**6 + 0*v**2. Factor o(a).
-3*a**2*(a - 1)*(a + 1)**2
Let t = -32966/13 - -2536. Solve 16/13*f - 10/13*f**3 + 8/13 + t*f**5 + 2/13*f**2 - 2/13*f**4 = 0 for f.
-1, 2
Let j = 2011/4464 - 3/496. Determine t, given that -j*t - 2/3*t**2 + 6*t**3 + 0 = 0.
-2/9, 0, 1/3
Let o(a) be the first derivative of 16*a**5 - 10*a**4 + 5*a**3/3 + 22. Factor o(w).
5*w**2*(4*w - 1)**2
Find m, given that -112*m**3 + 42*m**2 + 64*m - 261*m**4 + 73*m**4 - 20*m**5 - 40*m**5 + 38*m**2 = 0.
-2, -1, -4/5, 0, 2/3
Let p(v) be the third derivative of -v**5/10 - 7*v**4/8 + 15*v**3/2 + 22*v**2. Factor p(j).
-3*(j + 5)*(2*j - 3)
Let h(t) = 3*t**4 + 21*t**3 - 26*t**2 + 12*t + 5. Let p(a) = -4*a**4 - 22*a**3 + 26*a**2 - 12*a - 6. Let r(u) = -6*h(u) - 5*p(u). Factor r(s).
2*s*(s - 6)*(s - 1)**2
Let f(o) be the first derivative of o**4/34 - 22*o**3/17 - 36*o**2/17 + 8*o - 498. Factor f(m).
2*(m - 34)*(m - 1)*(m + 2)/17
Let t be 2354/642 + (-3)/(-9). Factor -3/7*n**t + 0*n**2 - 2/7*n**3 - 1/7*n**5 + 0 + 0*n.
-n**3*(n + 1)*(n + 2)/7
Suppose 0 = -2*i - 12*j + 8*j + 4, 0 = 4*i + 2*j - 20. Let v(s) be the first derivative of i - 7/9*s**3 - 2/3*s - 3/2*s**2. Factor v(t).
-(t + 1)*(7*t + 2)/3
Let p(k) be the first derivative of 5/8*k**2 - 1/2*k**5 + 0*k**3 + 4 + 1/2*k - 1/8*k**6 - 5/8*k**4. Find l, given that p(l) = 0.
-1, 2/3
Let l(x) be the third derivative of -7*x**5/240 - 5*x**4/96 + x**3/12 - 164*x**2. Determine a so that l(a) = 0.
-1, 2/7
Let u(r) be the first derivative of 0*r + 0*r**4 + 5 + 4/5*r**5 - r**2 - 4/3*r**3 + 1/3*r**6. Factor u(t).
2*t*(t - 1)*(t + 1)**3
Let k = -23 + 28. Factor 3*g**2 - 3*g**2 + 4*g**3 + 3*g**k + 14*g**4 + 5*g**5 - 2*g**2.
2*g**2*(g + 1)**2*(4*g - 1)
Let o be 3/(-18)*(140 - 1). Let v = 92/3 + o. Factor -v*f**2 + 6 + 12*f.
-3*(f - 2)*(5*f + 2)/2
Let n(a) be the third derivative of -a**8/840 + 2*a**7/175 - 11*a**6/300 + a**5/75 + a**4/5 - 8*a**3/15 + 29*a**2 + 2. Solve n(z) = 0.
-1, 1, 2
Let s(c) = -c**3 - 4*c**2 - 3*c. Let z be s(-2). Let f be 1/(4/z)*0. Find n such that -8 + 2*n**3 - 22*n**3 + 8*n**2 + 7*n + f + 13*n = 0.
-1, 2/5, 1
Let j(u) be the first derivative of -31*u**3/18 - u**2/6 - 435. Factor j(z).
-z*(31*z + 2)/6
Let c(q) be the third derivative of q**6/45 - q**5/12 + 17*q**4/144 - q**3/12 - 41*q**2. Suppose c(h) = 0. Calculate h.
3/8, 1/2, 1
Let y be (12/15)/((-6)/3 - (-50)/15). Factor -6/5*p + y*p**3 - 3/5*p**2 + 0.
3*p*(p - 2)*(p + 1)/5
Let m be 8/20*(3 - -2). Let p be (3 - 18)*(-2)/6. Solve d**p + 2*d - 2*d**2 + m*d**4 - d - 2*d + 0*d = 0.
-1, 0, 1
Let g(q) be the second derivative of q**6/6 + 3*q**5 + 15*q**4 + 80*q**3/3