 8/5 + 6/5*r**j + 8/5*r = 0 for r.
-2, 1
Let w(s) be the second derivative of -1/45*s**6 + 7/30*s**5 - 5/6*s**4 + s**3 + 0*s**2 - 15*s + 0. Factor w(n).
-2*n*(n - 3)**2*(n - 1)/3
Suppose -12*p = -17*p + 3*d + 48, 47 = 5*p - 2*d. Factor 2*h**5 + 18*h - 9*h**3 - 7*h**5 - p*h**4 + 8*h**5 + 21*h**2.
3*h*(h - 3)*(h - 2)*(h + 1)**2
Let p(s) be the second derivative of s**4/6 - 5*s**3/6 + 2*s**2 + 3*s. Let a be p(2). Determine n, given that 5 + 3*n**3 + 3*n**a - 6*n - 2 - 3 = 0.
-2, 0, 1
Suppose -454*p + 4 = -452*p. Let v(t) be the second derivative of 0*t**p + t + 1/3*t**4 - 1/3*t**3 + 0. Let v(s) = 0. Calculate s.
0, 1/2
Let r(w) = -w**3 + 9*w**2 + 10*w + 2. Let m be r(10). Factor 0*y - 5*y**2 + 9*y**m + 0*y - 4.
4*(y - 1)*(y + 1)
Let a = 47 + -44. Suppose -2*s**4 + 6 + 0*s**3 + 5*s**2 + 16*s + 0*s**a + 7*s**2 = 0. What is s?
-1, 3
Let h(y) be the third derivative of -y**5/270 - 31*y**4/54 - 961*y**3/27 + 3*y**2 + 7*y. Find z, given that h(z) = 0.
-31
Let z(m) be the second derivative of 2*m**4/3 + 29*m**3/6 - 5*m**2/2 - 33*m. Let w(g) = -12*g**2 - 44*g + 8. Let c(a) = -5*w(a) - 8*z(a). Solve c(k) = 0.
-3, 0
Let p(x) be the third derivative of 1/12*x**3 + 1/96*x**4 + x**2 - 1/480*x**6 + 0*x - 1/120*x**5 + 0. Let p(q) = 0. What is q?
-2, -1, 1
Let o(g) be the third derivative of g**8/84 - 4*g**7/105 - g**6/30 + 2*g**5/15 + 31*g**2 + 1. Suppose o(p) = 0. What is p?
-1, 0, 1, 2
Let o(s) be the third derivative of s**5/420 - 31*s**4/42 + 1922*s**3/21 + 87*s**2. Solve o(w) = 0.
62
Let w(r) be the first derivative of 2*r**3/33 - 2*r**2/11 - 48*r/11 + 493. Let w(q) = 0. What is q?
-4, 6
Let z(f) be the second derivative of -1/14*f**7 + 5/2*f**4 + 1/2*f**6 - 5/2*f**3 - 5*f + 3/2*f**2 + 0 - 3/2*f**5. Factor z(r).
-3*(r - 1)**5
Let i(y) be the first derivative of -2*y**6/15 + 12*y**5/25 + 81*y**4/5 + 396*y**3/5 + 648*y**2/5 - 198. Factor i(r).
-4*r*(r - 12)*(r + 3)**3/5
Suppose -h - 2*h = 0. Suppose -2*i = -h*i - 18. Solve -6*n**4 - 21*n - 21*n**5 + 12*n**2 + 23*n**3 + 19*n**3 + 3 - i = 0 for n.
-1, -2/7, 1
Let j(y) be the second derivative of -1/60*y**5 - 8/3*y**3 - 7*y + 0 - 1/2*y**2 + 1/3*y**4. Let c(s) be the first derivative of j(s). Factor c(u).
-(u - 4)**2
Let k be -7 + (-357)/(-49) - (-12)/7. Find j, given that -14 + 2*j**2 + 4*j + k*j**2 + j**3 + 14 = 0.
-2, 0
Let i(f) = 31*f**5 - 45*f**4 + 14*f**3. Let s(l) = 185*l**5 - 270*l**4 + 85*l**3. Let a(r) = 25*i(r) - 4*s(r). Factor a(d).
5*d**3*(d - 1)*(7*d - 2)
Let a(p) be the second derivative of p**7/5040 + p**6/360 + p**5/80 + 2*p**4/3 - 23*p. Let b(g) be the third derivative of a(g). Solve b(l) = 0.
-3, -1
Factor -6/11*m - 8/11 + 2/11*m**2.
2*(m - 4)*(m + 1)/11
Let u = 2 + 1. Let i = 15697/1710 - -7/342. Let i*h**2 - 4/5 - 36/5*h**u - 6/5*h = 0. Calculate h.
-2/9, 1/2, 1
Let s = -69 - -72. Factor -67 + 4*k**3 + 24*k - k**s + 19 - 2*k**2 + 23*k**2.
3*(k - 1)*(k + 4)**2
Let s(d) be the second derivative of -d**4/12 + 7*d**3/6 - 10*d + 2. Let n be s(7). Factor n - 2/11*u**2 + 2/11*u.
-2*u*(u - 1)/11
Let l = 7694/3 + -2564. Factor 0 + l*d - 1/3*d**2 - 1/3*d**3.
-d*(d - 1)*(d + 2)/3
Factor 3*j**2 + 20 - 4*j**2 + 2*j**2 + 11*j - 32 + j**2 - j**3.
-(j - 4)*(j - 1)*(j + 3)
Suppose 2*l - 8*u - 6 = 6, -3*u = 5*l - 7. Suppose -1/2*z + 1 - z**l + 1/2*z**3 = 0. What is z?
-1, 1, 2
Let v = -349 + 5585/16. Let h(b) be the first derivative of 0*b - 8 - 1/20*b**5 + 1/12*b**3 - v*b**4 + 1/8*b**2. Solve h(c) = 0.
-1, 0, 1
Determine c so that -32/3*c + 2/3*c**4 + 0 + 1/3*c**5 - 40/3*c**2 - 4*c**3 = 0.
-2, 0, 4
Let k = -253333/11 + 23031. Determine p, given that k*p**2 - 2/11*p**3 - 8/11 + 2/11*p = 0.
-1, 1, 4
Let b(q) = 1 + 12*q + 2*q**3 - 11*q - q**3. Let p(w) = -w**3 - 7*w - 4. Let v(k) = -4*b(k) - p(k). Factor v(c).
-3*c*(c - 1)*(c + 1)
Let b(n) be the first derivative of -14 - 4860*n**3 + 32805*n**4 - 40/3*n + 360*n**2 - 177147/2*n**5. What is a in b(a) = 0?
2/27
Let u be 9/(-6 - ((-10)/8 - 1185/60)). Factor 36/5*w - 33/5 - u*w**2.
-3*(w - 11)*(w - 1)/5
Let x(f) be the third derivative of f**6/80 + f**5/10 - f**4/4 - 4*f**3 + 46*f**2. Factor x(d).
3*(d - 2)*(d + 2)*(d + 4)/2
Let u(d) be the second derivative of d**4/3 - 140*d**3/3 + 2450*d**2 + 2*d + 8. Factor u(a).
4*(a - 35)**2
Suppose 147 = -4*y + 111. Let s be (2 + y)/35*-3. Factor s*u**2 - 6/5*u + 3/5.
3*(u - 1)**2/5
Let q be (0 + (-10)/(-44))/(14 - 935/68). Solve 0 - 26/11*j**3 + 8/11*j - 8/11*j**2 - q*j**4 = 0.
-2, -1, 0, 2/5
Let y(k) be the third derivative of -k**5/105 + 9*k**4/7 - 486*k**3/7 + 4*k**2. Determine w so that y(w) = 0.
27
Let q be (-15)/(-3) + -8 + 3. Let o be 8/(2/(-1)) + 6. Factor q + 1/4*x**o + 1/2*x.
x*(x + 2)/4
Let x(i) be the second derivative of 2*i**6/15 - 14*i**5/5 - 49*i**4 + 2744*i**3/3 + 19208*i**2 - 7*i - 17. Factor x(c).
4*(c - 14)**2*(c + 7)**2
Let f be ((-170)/(-50) + -3)/(6/10). Let t(x) be the first derivative of 4*x**2 - 2 + f*x**3 + 8*x. Factor t(b).
2*(b + 2)**2
Factor 8/9*n - 2/9*n**3 + 32/9 - 8/9*n**2.
-2*(n - 2)*(n + 2)*(n + 4)/9
Let t = 361 - 359. Let v(a) be the first derivative of -1/5*a**5 + 1 - 2*a**3 - a - a**4 - t*a**2. What is s in v(s) = 0?
-1
Let j(f) be the second derivative of f**7/2016 - f**6/288 - f**5/32 - 8*f**4/3 - 14*f. Let d(z) be the third derivative of j(z). Suppose d(v) = 0. Calculate v.
-1, 3
Let i(u) be the second derivative of u**7/42 + 7*u**6/15 + 7*u**5/4 + 11*u**4/6 - u - 203. Factor i(n).
n**2*(n + 1)*(n + 2)*(n + 11)
Let d = 2 - 10. Let t = d + 14. Suppose 2*c + 3*c**2 - 6 - 2*c**2 + t = 0. What is c?
-2, 0
Let w(k) = -k - 19 + k**3 - 3 + 21 + 0*k. Let t(i) = -3*i**4 + 3*i**3 + 7*i**2 + i - 1. Let f = 4 + -3. Let m(p) = f*w(p) - t(p). Solve m(v) = 0.
-1, -1/3, 0, 2
Let z(u) be the second derivative of -u**6/360 + u**5/12 - 25*u**4/24 - 7*u**3/3 - 9*u. Let d(f) be the second derivative of z(f). Determine m so that d(m) = 0.
5
Let c(b) = -2*b**3 + 14*b**2 + 64*b + 96. Let u(g) = g**3. Let z(d) = -4*c(d) - 12*u(d). Factor z(l).
-4*(l + 4)**2*(l + 6)
Let x(h) be the second derivative of 1/10*h**6 + 4*h + 6*h**3 + 9/10*h**5 - 4 + 6*h**2 + 13/4*h**4. Factor x(i).
3*(i + 1)**2*(i + 2)**2
Let r(n) = n**2 - 340*n + 33 + 340*n. Let a be r(0). Solve 75*d**4 + 6*d**3 - 2*d**2 - a*d**4 - 34*d**4 = 0.
-1, 0, 1/4
Factor -44*r**2 + 5*r**3 - 39*r**2 - 20*r + 16*r**2 + 240 + 7*r**2.
5*(r - 12)*(r - 2)*(r + 2)
Let r be (30/(-20))/((-234)/24 + 6). Determine x so that -2/5*x + 0 + r*x**2 = 0.
0, 1
Suppose 38 = 4*l + 2. Let q be 12/14*42/l. Let 3 + 2*w - 18*w + 9*w**2 + q*w = 0. What is w?
1/3, 1
Let p be 6/4 + 4/8. Suppose 8*r**p - 7*r**5 + 30*r**4 - 7*r**4 + 0*r - 27*r**3 - 2*r + 5*r**2 = 0. Calculate r.
0, 2/7, 1
Let q be (-291)/(-1008) + (-18)/63. Let g(l) be the third derivative of 0*l**6 + 4*l**2 + 0*l**4 - q*l**8 + 0*l**5 + 0 + 0*l**7 + 0*l + 0*l**3. Factor g(m).
-m**5
Factor -4/5*g**2 + 8/5*g + 96/5.
-4*(g - 6)*(g + 4)/5
Let s = 649/2470 + 108/247. Factor 0*b + 0 - 1/5*b**2 + s*b**4 - 1/2*b**3.
b**2*(b - 1)*(7*b + 2)/10
Let r(g) be the first derivative of g**5/20 - 2*g**3 - 3*g**2/2 + 52. Let a(x) be the second derivative of r(x). Factor a(o).
3*(o - 2)*(o + 2)
Let i(p) be the second derivative of 3*p**5/20 + 2*p**4 - 5*p**3/2 - 126*p**2 + p + 675. Let i(v) = 0. Calculate v.
-7, -4, 3
Let g(v) be the second derivative of v**5/90 + 7*v**4/18 + 11*v**3/3 - 121*v**2/9 - 2*v + 3. Factor g(z).
2*(z - 1)*(z + 11)**2/9
Let v(i) be the second derivative of i**7/2520 + i**6/144 + i**5/30 - i**4/12 + i. Let u(a) be the third derivative of v(a). Factor u(x).
(x + 1)*(x + 4)
Let -12696/13*i - 276/13*i**2 - 2/13*i**3 - 194672/13 = 0. Calculate i.
-46
Let j(s) be the third derivative of -s**8/84 + 172*s**7/735 - 5*s**6/7 - 944*s**5/105 + 187*s**4/6 - 28*s**3 + 27*s**2. Solve j(m) = 0.
-3, 2/7, 1, 7
Suppose 4*k = 2*p - 1 - 3, 5*k + 12 = -p. Let v be ((-2)/3 + 0)*8/p. Solve -4/3 - 4/3*j**5 + 4*j**4 - v*j**3 - 8/3*j**2 + 4*j = 0 for j.
-1, 1
Factor -3*s - 20*s**4 + 38*s**4 - 39*s**3 + 13*s**2 + 11*s**2.
3*s*(s - 1)**2*(6*s - 1)
Suppose -3*o + 2 = j - 8*o, -2*j - 32 = 2*o. Let u be (j/((-91)/14))/(8/9). Find a, given that 3/4*a + u*a**5 + 9*a**3 - 15/2*a**4 - 9/2*a**2 + 0 = 0.
0, 1/3, 1
Let k(v) be the first derivative of -v**7/168 + v**6/60 - v**4/24 + v**3/24 + 13*v - 3. Let j(z) be the first derivative of k(z). Fac