 0, 2*c - i = -2*c + 10. Let j(n) be the first derivative of -6 + 6*n + 4*n - n**c - 7*n. Suppose j(l) = 0. Calculate l.
-1, 1
Factor 10*n**4 + 25*n**3 - 19*n**3 - 35*n - 10 - 30*n**2 - n**3.
5*(n - 2)*(n + 1)**2*(2*n + 1)
Factor 8/5*m**2 - 2/5*m**3 - 12/5 - 2/5*m.
-2*(m - 3)*(m - 2)*(m + 1)/5
Let z(i) = -2*i**2 - 8*i - 5. Let h be z(-9). Let n be 24/(-42) + h/(-105). Factor 0 - 2/3*u**3 - 1/3*u**2 + n*u.
-u*(u + 1)*(2*u - 1)/3
Let n = 49 + -44. Suppose 4*r - 2 = n*u - 5, -3*u = -3*r. Solve 8/5*s**r - 2/5*s**5 + 0*s**4 - 6/5*s - 4/5 + 4/5*s**2 = 0.
-1, 1, 2
Let m be 10/(-34) + (32/14)/8. Let u = m - -5/17. Suppose u*r - 2/7*r**2 + 0 = 0. What is r?
0, 1
Let y = 4093/2 - 2043. Determine k so that y*k**3 - 2 - 8*k - 5/2*k**2 = 0.
-1, -2/7, 2
Find a, given that -76/5*a - 72/5 + 39/5*a**3 + 10*a**2 - 1/5*a**5 - 16/5*a**4 = 0.
-18, -1, 2
Let z(l) be the third derivative of l**8/168 + l**7/21 + l**6/12 - l**5/6 - l**4/2 - 53*l**2 - 1. Solve z(o) = 0 for o.
-3, -2, -1, 0, 1
Let c = 286/3 + -94. Factor 2*n + 2/3*n**2 + c.
2*(n + 1)*(n + 2)/3
Let f be (-4)/(-18) + (-74)/9 + 0. Let y(v) = -v**2 - 12*v - 30. Let k be y(f). Find z such that z**4 - 1/5*z**5 + k*z**2 + 1/5 - z - 2*z**3 = 0.
1
Determine r so that 8*r + 92 - r**2 - 191 + 87 = 0.
2, 6
Let p(v) be the third derivative of -4*v**2 - 7/40*v**6 + v**4 + 0*v + 1/14*v**7 - 2*v**3 - 1/20*v**5 - 1/112*v**8 + 0. Suppose p(m) = 0. What is m?
-1, 1, 2
Let o = -507 - -511. Let a(j) be the first derivative of 3/10*j**o + 26/15*j**3 + 8/5*j - 1 + 16/5*j**2. Determine s so that a(s) = 0.
-2, -1/3
Suppose 0 = l - 5*l - 0*l. Let r(y) be the third derivative of -1/12*y**4 + 1/10*y**5 - 1/30*y**6 + 0*y**3 + 0*y + l - 8*y**2. Factor r(k).
-2*k*(k - 1)*(2*k - 1)
Let x(m) = -m**2 + 2*m + 2. Let y(i) = 5*i**3 - 20*i**2 + 10*i - 10. Let d(t) = 5*x(t) + y(t). Factor d(k).
5*k*(k - 4)*(k - 1)
Factor -12*f**4 + 3*f**3 + 22*f**4 + 2*f**2 + 3*f**2 + f**2 - 13*f**4.
-3*f**2*(f - 2)*(f + 1)
Let q(j) be the second derivative of -j**6/180 - 47*j**5/40 - 2209*j**4/24 - 103823*j**3/36 + 193*j. Factor q(a).
-a*(a + 47)**3/6
Let k(b) be the third derivative of b**8/24 - 31*b**7/420 + b**6/120 + b**5/120 + 30*b**2 - 2. Suppose k(x) = 0. Calculate x.
-1/7, 0, 1/4, 1
Let u(w) be the second derivative of w**6/6 + w**5/2 - 5*w**4/4 - 10*w**3/3 + 10*w**2 + 186*w. Factor u(l).
5*(l - 1)**2*(l + 2)**2
Factor 92/3*t**2 - 192 - 160*t - 4/3*t**3.
-4*(t - 12)**2*(t + 1)/3
Let r(p) = -7*p**4 - 4*p**3 + p**2 - 8*p. Let o be (-45)/10*(-4)/3. Let z(s) = s**4 - s**2 + s. Let t = 4 + -3. Let j(d) = o*z(d) + t*r(d). Factor j(a).
-a*(a + 1)**2*(a + 2)
Determine j, given that -29*j**2 + 6*j**3 + 68*j - 2*j**3 + 17*j**2 + 92*j**2 - 152 = 0.
-19, -2, 1
What is z in 23*z**5 + 38*z**5 - 350*z**4 - 66*z**5 - 340*z**3 + 350*z**2 + 345*z = 0?
-69, -1, 0, 1
Suppose -8 = -2*b, 2*d - 4*b + 18 = 3*d. Let u be 3 - 2*(-1)/d. Factor -4*h**u - 27*h - 6*h**3 + 29*h + 0*h**3.
-2*h*(h + 1)**2*(2*h - 1)
Suppose -26*i**2 + 0 - 76/3*i**3 + 0*i + 2/3*i**4 = 0. Calculate i.
-1, 0, 39
Let t(w) = 166*w**2 + w - 1. Let b be t(1). Suppose -3*i + b = -77. Factor 210*x**2 + 121*x**3 + i*x**3 - 55*x**3 - 156*x + 24.
3*(x + 2)*(7*x - 2)**2
Determine z, given that -64 - 331*z**4 - 33*z**2 - 112*z + 16*z**3 + 330*z**4 - 2*z**3 = 0.
-1, 8
Let p(y) = y**2 + 25*y + 7. Let z(w) = w**2 + 6*w + 7. Let c be z(-6). Let n(u) = u**2 + 13*u + 4. Let s(m) = c*n(m) - 4*p(m). Factor s(k).
3*k*(k - 3)
Let a be 24*49/(-14)*(-3)/51. Determine s, given that 18/17 - a*s + 98/17*s**2 = 0.
3/7
Factor 208*g**3 + 235*g**3 + 85*g**2 + 900 + 480*g - 438*g**3.
5*(g + 5)*(g + 6)**2
Let 100 - 45*c**2 + 6051*c - 6*c**3 + c**3 - 5991*c = 0. Calculate c.
-10, -1, 2
Find z, given that 1/2*z**3 - 196 - 36*z**4 - 7/2*z**5 + 493*z**2 - 546*z = 0.
-7, -2/7, 2
Let u(j) be the first derivative of 3*j**4/4 - 38*j**3 + 111*j**2/2 + 51. Suppose u(s) = 0. Calculate s.
0, 1, 37
Let p(i) be the third derivative of -9*i**6/200 + 51*i**5/50 + 71*i**4/40 + 6*i**3/5 - 11*i**2. Factor p(j).
-3*(j - 12)*(3*j + 1)**2/5
Let j(c) be the third derivative of c**8/10080 + c**7/420 - 2*c**5/5 + 14*c**2. Let a(p) be the third derivative of j(p). Suppose a(x) = 0. What is x?
-6, 0
Suppose 4*j + 912 = -8*j. Let u be -1*9/3 + j/(-24). Suppose -1/6*a**5 + 1/6*a**3 + 0 + 1/6*a**4 + 0*a - u*a**2 = 0. What is a?
-1, 0, 1
Let r(u) be the second derivative of -u**4/30 + 122*u**3/15 - 3721*u**2/5 - 95*u + 1. Factor r(l).
-2*(l - 61)**2/5
Let o be 6/(-18) + 112/21. Let c(a) be the second derivative of a + 0*a**2 + 0 + 1/21*a**3 + 1/21*a**4 + 1/70*a**o. Factor c(q).
2*q*(q + 1)**2/7
Let g(v) be the third derivative of 0 + 4/105*v**7 + 0*v - 1/7*v**5 - 8*v**2 + 1/420*v**6 - 1/84*v**4 + 2/21*v**3. Determine r so that g(r) = 0.
-1, -2/7, 1/4, 1
Let p = -70 - -70. Let t(j) be the third derivative of p - 1/12*j**4 + 0*j + 2/15*j**3 - 11/150*j**5 + 7/150*j**6 + 4*j**2. Solve t(o) = 0.
-1/2, 2/7, 1
Let u(f) be the third derivative of 0 - 1/80*f**5 + 1/32*f**4 + 0*f + 22*f**2 - 1/160*f**6 + 1/8*f**3. Find t such that u(t) = 0.
-1, 1
Factor -225 + 105/4*q + 13/2*q**2 + 1/4*q**3.
(q - 4)*(q + 15)**2/4
Let b be 2/6 + (-116)/(-12). Let y = b - 8. Factor 2*x**3 - 4*x**y + 6*x**2 - 2*x + 0*x**3 - 2*x.
2*x*(x - 1)*(x + 2)
Let v(k) be the first derivative of -k**4/10 + 4*k**3/5 - k**2 + 176. Find t such that v(t) = 0.
0, 1, 5
Suppose -2*l = -0*l - 20. Solve g**3 + l*g + 29*g**2 + 36*g**2 + 45*g**3 + 9*g**3 = 0 for g.
-1, -2/11, 0
Let s(y) be the second derivative of -3*y**6/10 + 3*y**5/10 + 83*y**4/48 + 25*y**3/24 + y**2/4 - 173*y. Find n, given that s(n) = 0.
-1, -1/6, 2
Let r = 1455/26 - 721/13. Suppose 0 + 3/2*w**2 + r*w**3 - 2*w = 0. What is w?
-4, 0, 1
Let h be (10/(-20))/((-2)/8). Suppose -h*y - 6 = -4*y. Factor 7*i**5 - 8*i**5 - i + 0*i + 2*i**y.
-i*(i - 1)**2*(i + 1)**2
Let l(r) be the first derivative of -9 + 4*r**2 - 4*r - 4/3*r**3. Determine s so that l(s) = 0.
1
Let s be 12/(-26) + 6954/2223. Solve -s + 0*v + 2*v**2 + 2/3*v**3 = 0.
-2, 1
Let y = 1/381 - -125/762. Let l(d) be the first derivative of 1 + 2/3*d - 1/18*d**6 + 2/15*d**5 - y*d**2 + 1/6*d**4 - 4/9*d**3. Solve l(s) = 0.
-1, 1, 2
Let s = -5809/2 - -2905. Let 0 - s*b**3 + 0*b + 1/2*b**2 = 0. Calculate b.
0, 1
Factor 34/11*o + 0 - 2/11*o**2.
-2*o*(o - 17)/11
Let m(b) be the second derivative of -1/42*b**4 - 81/7*b**2 + 0 + 6/7*b**3 + 3*b. Factor m(i).
-2*(i - 9)**2/7
Let u(o) be the first derivative of -3/5*o**3 - 4/5*o + 2*o**2 - 13. Factor u(t).
-(t - 2)*(9*t - 2)/5
Let t(p) = -p**3 - 6*p**2 + 13*p - 20. Let u be t(-8). Suppose -7/6*y**2 + 1/2*y**u - 2/3*y**3 + 2/3 + 2/3*y = 0. Calculate y.
-1, -2/3, 1, 2
Let k(m) = m**3 - 7*m**2 + 4*m - 22. Let w be k(7). Suppose 3*b = w*b - 9. Factor 0 + 1/5*p**2 - 2/5*p + 1/5*p**b.
p*(p - 1)*(p + 2)/5
Let v(x) be the second derivative of x**6/40 + 9*x**5/80 - x**3/2 - 6*x + 2. Solve v(t) = 0 for t.
-2, 0, 1
Let p(v) = 2*v**3 - 5*v**2 + 5*v - 4. Let c be p(2). Suppose 5*s + r = -r + 10, r = c*s - 4. Let 2/3*q - 1/6*q**s - 1/2 = 0. Calculate q.
1, 3
Let k(j) = -7*j**2 - 3*j - 2. Let c(s) = 17*s**2 + 7*s + 5. Let l(o) = 2*c(o) + 5*k(o). Factor l(q).
-q*(q + 1)
Determine n, given that -400/3 + 40/3*n - 1/3*n**2 = 0.
20
Suppose -4*t - 13 = -u + t, -7 = -5*u - 4*t. Suppose -4*l = -8, -4*l + 30 = u*h + 7. Let -1/3*w**4 + 0*w**2 + 1/6*w**h + 0 + 1/6*w**3 + 0*w = 0. What is w?
0, 1
Solve 0 - 3/8*s**3 - 3/8*s**2 + 3/8*s**4 + 3/8*s = 0 for s.
-1, 0, 1
Suppose 7 = 2*a - l, -2 - 5 = -3*a + 5*l. Let v be a - (1 - -3) - 1/(-3). Determine n so that 2/3*n**2 + 0 - 1/3*n**3 - v*n = 0.
0, 1
Let j = -12 - -14. Suppose 20 = 2*v + j*v. Find i, given that -12*i - 13 + 9 - 4*i**3 + 0*i**2 + v*i**2 - 17*i**2 = 0.
-1
Let h(m) = -165*m**3 - 178*m**2 + 317*m + 77. Let r(k) = -55*k**3 - 59*k**2 + 106*k + 26. Let u(v) = 6*h(v) - 17*r(v). Factor u(g).
-5*(g - 1)*(g + 2)*(11*g + 2)
Factor 25*c**2 - 21*c - 1 - 37*c**2 - 41*c**3 - 9 + 40*c**3.
-(c + 1)**2*(c + 10)
Suppose 0 = -797*r + 812*r. Factor 1/10 - 1/10*d**2 + r*d.
-(d - 1)*(d + 1)/10
Solve 4/11 + 8/11*y**3 - 2/11*y**5 - 4/11*y**2 - 6/11*y + 0*y**4 = 0 for y.
-2, -1, 1
Let c(k) = 29*k + 2697. Let i be c(-93). Solve 24/7*u - 4/7*u**3 - 4/7*u**2 + i = 0.
-3, 0, 2
Let q be (-3 + 13)*(-1)/(-2). Suppose 0 = 442*p - 1898*p. Determine k, gi