/4
Let u(k) be the second derivative of -k**4/18 - 10*k**3/27 - k**2/3 - 229*k. Factor u(h).
-2*(h + 3)*(3*h + 1)/9
Let z = 24 + -19. Let a be 4/((-100)/(-15))*z. Let -5 - a*u**2 - 10*u**2 - 20*u - 2*u**2 + 0*u**2 = 0. What is u?
-1, -1/3
Let -42*w + 171/4 - 3/4*w**2 = 0. What is w?
-57, 1
Let l(o) = -4*o**4 - 70*o**3 + 184*o**2 - 192*o + 62. Let t(s) = s**4 + 23*s**3 - 61*s**2 + 64*s - 21. Let b(w) = -6*l(w) - 20*t(w). Factor b(d).
4*(d - 6)*(d - 2)*(d - 1)**2
Find b, given that 57/5*b**2 + 84/5*b + 36/5 + 6/5*b**3 - 3/5*b**4 = 0.
-2, -1, 6
Let d(m) be the first derivative of -1/6*m**3 - 4*m - 11 + 0*m**2 - 1/12*m**4. Let h(r) be the first derivative of d(r). Suppose h(t) = 0. Calculate t.
-1, 0
Factor 2/21*w**3 + 4/21*w**2 + 0 - 2/7*w.
2*w*(w - 1)*(w + 3)/21
Suppose 0*i - 243 = -4*c - 3*i, 4*i - 4 = 0. Factor c*u**4 - 36*u**2 + 44*u**3 + 129*u**2 - 46*u**2 - 39*u**2.
4*u**2*(3*u + 1)*(5*u + 2)
Let y(k) be the first derivative of k**6/15 - 4*k**5/5 + 13*k**4/6 - 2*k**3 + 33*k + 42. Let g(q) be the first derivative of y(q). Factor g(x).
2*x*(x - 6)*(x - 1)**2
Suppose -13*c + c - 53*c = -3*c. Factor c + 0*o**2 - o**4 + 1/2*o**3 + 1/2*o**5 + 0*o.
o**3*(o - 1)**2/2
Let f(c) be the third derivative of -c**8/1848 - 2*c**7/385 - c**6/660 + 4*c**5/55 - 4*c**4/33 - 424*c**2. Suppose f(u) = 0. Calculate u.
-4, 0, 1
Determine h, given that 1/5*h - 1/10*h**2 + 3/10 = 0.
-1, 3
Let y be 14/21 + (-12)/54. Factor -56/9*u**2 + y - 2/9*u.
-2*(4*u - 1)*(7*u + 2)/9
Let d(c) = -11*c**2 + 16*c - 17. Let y(l) = -4*l**2 + 5*l - 6. Let a(v) = -3*d(v) + 8*y(v). Let f be a(8). Factor 23*h - 64*h**2 + 62*h**2 - f*h - 50.
-2*(h - 5)**2
Let r(d) be the third derivative of -d**5/270 - 4*d**4/27 - 64*d**3/27 - 136*d**2. What is c in r(c) = 0?
-8
Factor 8/3*m**3 + 0 + 4/9*m**4 + 32/9*m**2 + 0*m.
4*m**2*(m + 2)*(m + 4)/9
Let m = -1132/3 + 380. Solve 2/3*d**3 - d**2 + 1/3*d**4 - m*d - 4/3 = 0.
-2, -1, 2
Let p = 8 - -7. Factor p*s**2 - 7*s**2 - 15*s - 10 + 17*s**2 + 0*s**2.
5*(s - 1)*(5*s + 2)
Let k(o) be the second derivative of -o**6/255 - o**5/170 + 7*o**4/102 + 13*o**3/51 + 6*o**2/17 + 70*o. Determine d, given that k(d) = 0.
-2, -1, 3
Let g(t) be the second derivative of -t**5/120 - 5*t**4/12 + 7*t**3/4 - 8*t**2/3 + t. Find c such that g(c) = 0.
-32, 1
Suppose -2*u - 38 = -4*v, 3*v - 3*u = -v + 41. Let o(j) = 2*j - 14. Let k be o(v). Factor 10*r**k + 8*r - 5*r**2 + 4 - r**2.
4*(r + 1)**2
Let a(w) be the first derivative of -4*w**3/3 - w**2 + 6*w + 7. Let f(z) = 13*z**2 + 5*z - 18. Let h(g) = -14*a(g) - 4*f(g). Factor h(i).
4*(i - 1)*(i + 3)
Let s(v) be the second derivative of 5*v**7/252 + 13*v**6/180 + 11*v**5/120 + v**4/24 + 4*v. Factor s(g).
g**2*(g + 1)**2*(5*g + 3)/6
Factor -165*x + 99*x**2 + 223*x**3 - 600*x - 226*x**3 - 867.
-3*(x - 17)**2*(x + 1)
Suppose p - 14*p + 26 = 0. Let q(s) be the first derivative of 1 + 2/3*s**3 - s**p + 0*s. Determine g so that q(g) = 0.
0, 1
Let t = -13 - -11. Let m be (-42)/35*5/t. Determine w so that -8*w**3 - 6*w**2 + 3*w**4 - 7*w**m + 18*w**3 = 0.
-2, 0, 1
Let g(t) = -t**2 + t + 1. Let h(v) = -21*v**3 - 33*v**2 - 12*v + 3. Let b = 34 - 31. Let z(a) = b*g(a) + h(a). Let z(y) = 0. What is y?
-1, 2/7
Let h(g) be the second derivative of -7*g**4/66 + 16*g**3/33 - 4*g**2/11 - 10*g. Solve h(n) = 0.
2/7, 2
Let r(h) be the first derivative of -50*h**3/39 - 20*h**2/13 - 8*h/13 + 169. Find i, given that r(i) = 0.
-2/5
Suppose -4*m = -8, -4*m + 3*m = -3*x + 4. Suppose 3*v = x*h + 6, 4*v + 3*h - 1 + 10 = 0. Solve -1 + 6*a - 2*a**2 + 2 - 5 + v*a**2 = 0.
1, 2
Let m(b) be the second derivative of -b**7/420 - b**6/240 + b**5/120 + b**4/48 + 7*b**2/2 + 5*b. Let g(k) be the first derivative of m(k). Solve g(v) = 0 for v.
-1, 0, 1
Let l = 290 - 182. Let z = l - 105. What is y in 36/5*y**z - 36/5*y - 4*y**2 - 8/5 + 28/5*y**4 = 0?
-1, -2/7, 1
Let x = -40129/2 - -20067. Let -x - 7/4*w - 1/4*w**2 = 0. Calculate w.
-5, -2
Let c = 2 - -7. Factor -2*r + c*r**2 + 0*r + 6*r + 2*r + 3*r**3.
3*r*(r + 1)*(r + 2)
Let u(d) = 4*d**3 - 13*d**2 + 17*d - 17. Let p(c) = 11*c**3 - 39*c**2 + 53*c - 49. Let o(i) = -3*p(i) + 8*u(i). What is l in o(l) = 0?
1, 11
Let g(f) = f**3 - 3*f**2 - 9*f - 2. Let t be g(5). Let p(v) be the first derivative of -1/12*v**4 - 7 - 1/6*v**t + 0*v + 1/6*v**2 + 1/10*v**5. Factor p(d).
d*(d - 1)*(d + 1)*(3*d - 2)/6
Let k = 11 + 7. Factor 4 + 11*q**3 - 4*q**3 - k*q + 6*q - 9*q**2.
(q - 2)*(q + 1)*(7*q - 2)
Let 1479117/8 + 56169/8*f + 711/8*f**2 + 3/8*f**3 = 0. What is f?
-79
Let 5*b**5 + 4*b**4 + 4*b**4 + 7*b**4 - 10*b**4 = 0. Calculate b.
-1, 0
Let q(p) be the first derivative of 20*p + 2 + 5/4*p**4 + 25/3*p**3 + 20*p**2. Factor q(r).
5*(r + 1)*(r + 2)**2
Let r(b) = -2*b + 17*b**2 - 4 - 21*b**2 - 4*b**3 + 5*b**3. Let n be r(5). Solve 19*k + 3 - 12*k + 2*k**2 - n*k - 1 = 0 for k.
1
Suppose 0 = -2*u + 5 + 19. Suppose -15*s = 6*s + u*s. Factor -12*z - 105*z**3 + 78*z**2 - 147/2*z**4 + s.
-3*z*(z + 2)*(7*z - 2)**2/2
Let i = 55 - 43. Let 7*w - 8*w**2 + 15*w - i + 18*w - 4*w**2 = 0. What is w?
1/3, 3
Find o such that -1/6*o**4 - 1/2*o**2 - 3/2*o + 0 + 5/6*o**3 = 0.
-1, 0, 3
Let u = -7577/35 - -1528/7. Determine l, given that -1/5 + 5*l**3 - 3*l**2 - u*l = 0.
-1/5, 1
Suppose c + 2*j = -0*c + 4, 3*c - 6 = -3*j. Let a be c - 0 - (21 - 23). Solve -5*l**3 - 10*l + l**3 + 12*l**a + l + l = 0 for l.
0, 1, 2
Let m(n) = -n**2 - n + 1. Let s(r) = -9*r**2 + 39*r + 54. Let x(j) = -6*m(j) + s(j). Suppose x(a) = 0. What is a?
-1, 16
Let k(a) be the third derivative of a**8/2184 + a**7/455 + a**6/260 + a**5/390 - 470*a**2. Factor k(p).
2*p**2*(p + 1)**3/13
Let f(v) = 2*v + 8. Let w be f(-3). Let s be (-85)/34*((-116)/50 + w). Find q, given that 0 + 0*q**2 + 2/5*q**3 + 2/5*q**5 - s*q**4 + 0*q = 0.
0, 1
Factor 34/3*x**2 + 0 - 10*x + 8/3*x**3.
2*x*(x + 5)*(4*x - 3)/3
Let p be 1/(-4) - 264/32*-1. Suppose p*t - 39 = -15. Factor -2/9*z**2 + 0 - 2/9*z**t + 0*z.
-2*z**2*(z + 1)/9
Find r such that 32/11 - 10/11*r**3 - 56/11*r - 56/11*r**2 = 0.
-4, -2, 2/5
Factor -14*w**2 + 2/3*w**4 - 10/3*w**3 - 16/3 - 46/3*w.
2*(w - 8)*(w + 1)**3/3
Let h(j) = 2*j - 21. Let w be h(14). Let o = w + -7. What is s in -6*s**2 + o*s**2 + 4*s**2 + 2 = 0?
-1, 1
Let d be -38 + 32 - -17*1. Let h(x) be the third derivative of -1/120*x**6 + 0*x**4 + 1/20*x**5 + 0*x - 2/3*x**3 + 0 + d*x**2. Factor h(i).
-(i - 2)**2*(i + 1)
Let v(i) be the third derivative of i**6/150 - 32*i**5/75 - 11*i**4/10 + 204*i**2 - 2. Factor v(u).
4*u*(u - 33)*(u + 1)/5
Let y(c) be the first derivative of 3*c**4/4 - 8*c**3 - 6*c**2 + 96*c - 325. Factor y(r).
3*(r - 8)*(r - 2)*(r + 2)
Suppose 2*t + 7*t - 36 = 0. Let p(f) be the second derivative of f - 4/3*f**3 - 1/6*f**t - 4*f**2 + 0. Determine h, given that p(h) = 0.
-2
Factor 3125/4 - 5/4*p**3 - 245/4*p**2 - 2875/4*p.
-5*(p - 1)*(p + 25)**2/4
Let h(a) = -a**2 - 23*a - 30. Let b be h(-20). Let p(s) = -5*s**2 + 8*s - 15. Let d(j) = -j**2 - 1. Let c(g) = b*d(g) - 5*p(g). Factor c(n).
-5*(n - 1)*(n + 9)
Let l(r) be the first derivative of 14*r**3/3 + 18*r**2 + 46*r + 45. Let m(v) = 9*v**2 + 24*v + 31. Let d(y) = 5*l(y) - 8*m(y). Find j such that d(j) = 0.
-3
Let t(h) = -52*h**3 + 120*h**2 - 156*h - 296. Let y(d) = -33*d**3 + 80*d**2 - 104*d - 197. Let o(x) = -5*t(x) + 8*y(x). Find w such that o(w) = 0.
-1, 3, 8
Let o be (54/15 + -3)*(13 - 3). Let d(j) be the first derivative of -18*j**2 - 4 + 24*j + o*j**3 - 3/4*j**4. Determine n, given that d(n) = 0.
2
Let d(g) be the first derivative of 3*g**5/5 + 3*g**4 - 5*g**3 - 57. Determine j, given that d(j) = 0.
-5, 0, 1
Let q(a) = -2*a - 7. Let t be q(-5). Suppose -5*o + 12 = -t*o. Determine r, given that o*r + r**3 + 15*r**2 - 39*r**2 + 13*r**3 + 4 = 0.
-2/7, 1
Let j(k) be the second derivative of k**8/504 - k**6/45 + k**5/45 + k**4/12 - 2*k**3/9 - 6*k**2 + 26*k. Let r(p) be the first derivative of j(p). Factor r(o).
2*(o - 1)**3*(o + 1)*(o + 2)/3
Let u(l) be the first derivative of l**4/24 - l**3/2 + 5*l**2/3 - 2*l + 18. Factor u(y).
(y - 6)*(y - 2)*(y - 1)/6
Let k(g) be the third derivative of g**6/30 - 11*g**5/15 - 28*g**4/3 - 40*g**3 + 244*g**2. Let k(u) = 0. Calculate u.
-2, 15
Suppose -3*p - 2*g = 2*p - 2, -2*p = -5*g + 5. Factor -9/2*q + p - 1/4*q**2.
-q*(q + 18)/4
Factor 52*g**4 + 112*g**3 + 5*g**5 - g**5 + 68*g**3 - 100*g**2 