v + 13)/2
Factor n**5 - n**5 + 108*n**4 - 71*n**4 + 3*n**5 - 3*n**3 - 61*n**4 + 24*n**2.
3*n**2*(n - 8)*(n - 1)*(n + 1)
Let r be (-367198)/(-31655) + 6/15*(-1)/2. Let n = -7182/5 + 1446. Solve -15*x**2 - 21/5*x**4 + n*x - 12/5 + 3/5*x**5 + r*x**3 = 0.
1, 2
Let z(x) = -72*x**3 + 291*x**2 - 678*x + 459. Let g(v) = 7*v**3 - 29*v**2 + 68*v - 46. Let r(d) = 21*g(d) + 2*z(d). Determine q, given that r(q) = 0.
1, 4
Let i(b) = -226*b + 414. Let w be i(5). Let c = w - -718. Factor -1/6*m - 1/6*m**c + 0.
-m*(m + 1)/6
Let y = 20092 + -20092. Let w(s) be the third derivative of 0*s**3 - 1/24*s**6 + 0 + 5/24*s**4 - 1/126*s**7 + 1/36*s**5 + y*s + 23*s**2. Factor w(r).
-5*r*(r - 1)*(r + 1)*(r + 3)/3
Let k = -124 + 129. Determine y so that -6*y**k + 11*y**5 - 19*y**3 + 14*y**3 = 0.
-1, 0, 1
Let -483*a**3 - 303*a + 194*a**2 - 37*a**2 + 93*a**4 - 162 + 1086*a + 212*a**2 = 0. What is a?
-1, 6/31, 3
Suppose 12*z - 36 = -6*z. Suppose -78*t**z - 5*t**5 + 19*t**5 - 36*t - 58*t**3 - 16*t**5 - 18*t**4 = 0. What is t?
-3, -2, -1, 0
Let d(y) be the first derivative of -y**5/30 - y**4/3 - 5*y**3/9 - 90*y - 195. Let u(f) be the first derivative of d(f). Factor u(o).
-2*o*(o + 1)*(o + 5)/3
Let s(o) be the first derivative of 5*o**4/4 + o**3/3 - 5*o**2 - 6*o + 127. Let z(v) = -26*v**3 - 6*v**2 + 48*v + 28. Let k(r) = -14*s(r) - 3*z(r). Factor k(u).
4*u*(u + 1)*(2*u - 1)
Factor 1/4*s**2 + 1139/2*s + 2277/4.
(s + 1)*(s + 2277)/4
Let m(s) = s**2 - 24*s + 137. Let w be m(9). Factor 8*z**3 - 22 + 35*z - 3*z**2 - 11*z**w + 2*z**3 + 9*z**3 - 18*z**3.
(z - 11)*(z - 2)*(z - 1)
Let w = -3215/68 + 808/17. Let -w*d**2 + 21/2 + 11/4*d = 0. Calculate d.
-3, 14
Let o(y) be the second derivative of -3*y**5/100 + 141*y**4/10 - 20433*y**3/10 + 115926*y**2/5 + 165*y - 2. Solve o(t) = 0 for t.
4, 139
Let f(o) be the second derivative of 5/48*o**4 - 3/2*o**2 + 0 - 79*o - 7/6*o**3. Factor f(z).
(z - 6)*(5*z + 2)/4
Let u(l) = -l**3 + 99*l**2 - 1110*l - 685. Let m be u(86). Factor -34/3*a**4 - 128/3*a**2 + 0*a - 160/3*a**m + 0 - 2/3*a**5.
-2*a**2*(a + 1)*(a + 8)**2/3
Let q(d) = 85*d**2 + 13*d - 27. Let w be q(-5). Let a = -22347/11 + w. Determine t, given that -6/11*t**2 - a*t - 8/11 = 0.
-2, -2/3
Let d(h) be the third derivative of 1 - 17*h**2 + 1/28*h**8 - 1/10*h**6 + 0*h**4 + 0*h**3 + 0*h - 1/30*h**5 + 1/105*h**7. Suppose d(a) = 0. Calculate a.
-1, -1/6, 0, 1
Suppose 0 = -3*j - u - 2, 6*j + u + 9 = 10*j. Let s(o) = -3*o**2 - 26*o + 2. Let t(r) = -r**2 - 2*r + 1. Let k(l) = j*s(l) - 2*t(l). Factor k(g).
-g*(g + 22)
Factor 2*z**3 - 6400 + 15552*z**2 - 7856*z**2 + 3520*z - 7860*z**2.
2*(z - 40)**2*(z - 2)
Let u(z) = 19*z**3 + 2878*z**2 + 3731*z - 3828. Let v(q) = -78*q**3 - 11511*q**2 - 14907*q + 15312. Let p(s) = -21*u(s) - 5*v(s). Find n such that p(n) = 0.
-319, -2, 2/3
Let p(v) be the first derivative of -v**6/18 - v**5 - 5*v**4/12 + 115*v**3/9 - 25*v**2 + 56*v/3 - 854. Find b such that p(b) = 0.
-14, -4, 1
Let o(z) = -8*z**2 - 345*z - 3716. Let a be o(-22). Factor 20/3 + 10/3*q**a - 15*q.
5*(q - 4)*(2*q - 1)/3
Let w(p) = 3*p**5 - 5*p**4 + 26*p**3 - 32*p**2 - 2*p + 2. Let m(x) = 5*x**5 - 6*x**4 + 27*x**3 - 34*x**2 - 3*x + 3. Let s(o) = -2*m(o) + 3*w(o). Factor s(r).
-r**2*(r - 2)**2*(r + 7)
Let s(m) be the third derivative of m**6/5 - 49*m**5/20 + 37*m**4/4 - 33*m**3/2 + 2396*m**2. Factor s(k).
3*(k - 1)**2*(8*k - 33)
Let p = -27/16 + 113/48. Suppose 57*g - 36*g - 84 = 0. Factor 10/3*m - g - p*m**2.
-2*(m - 3)*(m - 2)/3
Factor -64/9 - 28/3*s**2 + 64/3*s + 10/9*s**3.
2*(s - 4)**2*(5*s - 2)/9
Suppose 0 = 2*n - 3*m, 2*n + 4*m = -1494 + 1494. Factor 2*g + g**4 + 1/2*g**5 - 2*g**2 + n - 3/2*g**3.
g*(g - 1)**2*(g + 2)**2/2
Let i(l) be the third derivative of 0 + 0*l - 1/72*l**5 - 5/6*l**3 + 37*l**2 - 25/144*l**4. Let i(u) = 0. Calculate u.
-3, -2
Suppose -9*z + 169 = -11. Let q be (18/255)/(12/z). Find s such that q*s**3 + 0 + 6/17*s**2 + 4/17*s = 0.
-2, -1, 0
Let i(s) = 7*s**3 - 69*s**2 + 20*s + 78. Let x(h) = 6*h**3 - 60*h**2 + 18*h + 79. Let l(o) = -5*i(o) + 6*x(o). Factor l(r).
(r - 14)*(r - 3)*(r + 2)
Let u(i) be the third derivative of -i**6/50 + 9*i**5/25 + 61*i**4/40 + 21*i**3/10 - 282*i**2 - 5. Find t such that u(t) = 0.
-1, -1/2, 21/2
Let b(z) = 32*z + 136. Let n be b(-4). Let w be 16/n - (1 + -5)/(-8). Factor 3/2 - 3*f + w*f**2.
3*(f - 1)**2/2
Let h(k) = -7*k**2 - 233*k - 900. Let g(i) = 8*i**2 + 227*i + 900. Let z(u) = 2*g(u) + 3*h(u). Factor z(b).
-5*(b + 4)*(b + 45)
Let q(k) be the third derivative of k**5/20 + 3*k**4/8 + k**3 + 3083*k**2 + 2*k. What is g in q(g) = 0?
-2, -1
Let x(p) = -p**2 + 4*p. Let c be x(2). Factor -644*a**3 + 330*a**3 - 10*a**2 + 319*a**3 + 5*a**c.
5*a**2*(a - 1)*(a + 2)
Let h = 551/1143 + -33/127. Factor 0 + 2/9*j + h*j**2.
2*j*(j + 1)/9
Let h(c) be the second derivative of 2/9*c**3 + 1/120*c**5 + 1/3*c**2 - 70 + c + 5/72*c**4. Let h(l) = 0. Calculate l.
-2, -1
Determine a so that 3/2 + 85/2*a + 14*a**2 = 0.
-3, -1/28
Let x(j) be the third derivative of j**6/300 - 193*j**5/300 + 473*j**4/120 - 47*j**3/5 - 1731*j**2 - 2*j. Factor x(b).
(b - 94)*(b - 1)*(2*b - 3)/5
Let q(v) = -v**3 + 26*v**2 + 108*v - 48. Let j be q(-4). Factor 0 + 0*a + j*a**2 - 3/2*a**3 + 1/4*a**4.
a**3*(a - 6)/4
Suppose 11832 + 5148 = 20*a. Find w, given that -425*w**2 + a*w**2 - w - 423*w**2 = 0.
0, 1
Let s(c) be the second derivative of c**4/6 - c**2/2 - 3*c + 1. Let x(o) = o**2 - 140*o - 3. Let m(z) = -3*s(z) + x(z). Solve m(b) = 0.
-28, 0
Factor 5*u**5 - 3290*u**2 + 993*u - 1715 + 2595*u - 115*u**4 + 950*u**3 + 577*u.
5*(u - 7)**3*(u - 1)**2
Let s = 84 - 24. Let l be (5 - 2)/(s/16). Factor 24/5*h - l*h**2 + 2/5*h**4 + 18/5 - 8/5*h**3.
2*(h - 3)**2*(h + 1)**2/5
Let y(t) be the second derivative of t**4/9 - 2600*t**3/9 + 95*t. Factor y(w).
4*w*(w - 1300)/3
Let w(q) = 2*q**2 - 45*q - 11. Let u be w(23). Suppose -45*j + u*j**2 + 15*j + 14*j**2 + 5*j**2 + 4 - 5*j**2 = 0. Calculate j.
2/13, 1
Solve 26611 + 5*y**2 - 1500*y + 35299 + 36075 + 46881 - 32366 = 0.
150
Find z, given that z**3 - 3/2*z + 1/2*z**5 + 0 + 2*z**2 - 2*z**4 = 0.
-1, 0, 1, 3
Let g(q) be the first derivative of -2*q**5/35 + 4*q**4/7 + 352*q**3/21 - 768*q**2/7 - 18432*q/7 + 4331. Factor g(j).
-2*(j - 12)**2*(j + 8)**2/7
Solve 0 + 0*d**2 - 332/15*d**4 - 2/5*d**5 + 0*d - 22/3*d**3 = 0 for d.
-55, -1/3, 0
Suppose -97*l = -1149*l + 2104. Determine z so that z - 5/2*z**2 + l - 1/4*z**5 + z**4 - 1/4*z**3 = 0.
-1, 2
Let q(i) be the first derivative of 2*i**3/33 + 40*i**2/11 - 1850. Factor q(g).
2*g*(g + 40)/11
Let y(n) be the first derivative of -n**7/105 + n**6/20 + n**5/30 - n**4/4 - 38*n**2 - 67. Let p(t) be the second derivative of y(t). Solve p(b) = 0 for b.
-1, 0, 1, 3
Let z be 28/4 + -3 + -6. Let r be ((-1)/z)/(13/(-26)). Let k(b) = b**2. Let j(u) = -6*u**2 + 5*u + 10. Let f(a) = r*j(a) - k(a). Factor f(o).
5*(o - 2)*(o + 1)
Let k(j) = -15*j**3 - 2751*j**2 - 5242*j - 8. Let n(a) = -20*a**3 - 3672*a**2 - 6989*a - 11. Let c(f) = -11*k(f) + 8*n(f). Factor c(h).
5*h*(h + 2)*(h + 175)
Let l(t) = 2*t**3 + 320*t**2 + 312*t + 36. Let d(q) = 16*q**3 + 2561*q**2 + 2496*q + 294. Let o(f) = 12*d(f) - 98*l(f). Factor o(b).
-4*b*(b + 1)*(b + 156)
Let x(v) be the first derivative of 0*v**2 - 8/15*v**3 + 0*v - 1/5*v**4 + 1. Suppose x(y) = 0. Calculate y.
-2, 0
Suppose -9*z + o = -10*z, 3*z - z = -o. Let r(u) be the second derivative of 2/5*u**2 + 1/12*u**4 + 12*u + z + 4/15*u**3 + 1/100*u**5. What is t in r(t) = 0?
-2, -1
Find h such that -25*h - 666246*h**2 + 666326*h**2 - 20*h**4 + 70*h**3 + 15*h**3 = 0.
-1, 0, 1/4, 5
Let l(a) be the second derivative of 5/12*a**4 - 1/4*a**5 + 117*a + 0 + 5/6*a**3 - 5/2*a**2. Factor l(v).
-5*(v - 1)**2*(v + 1)
Let o be (4617/(-72) - 2)/(20/(-160)). Factor -23*g**2 - 1/3*g**3 - o*g - 12167/3.
-(g + 23)**3/3
Let v be (-50)/60*(-1)/(-5)*36/(-2). Factor 2/13*r**4 - 8/13*r - 10/13*r**v + 16/13*r**2 + 0.
2*r*(r - 2)**2*(r - 1)/13
Suppose 2*y + 2*j + 14 - 12 = 0, 3*j = -20*y + 31. Find n, given that 1058/3 + 2/3*n**y + 92/3*n = 0.
-23
Let c(t) be the second derivative of t**6/60 - 7*t**5/4 + 51*t**4 + 35*t**3/6 - 1225*t**2/4 + 2*t - 2. Let c(q) = 0. What is q?
-1, 1, 35
Let d(c) be the first derivative of c**5/180 - 7*c**4/72 + c**3/3 - 51*c**2 + 50. Let x(g) be the second derivative of d(g). Factor x(w).
(w - 6)