)*((-50)/4 + 2/4). Let n(f) be the second derivative of 1/18*f**z + 0 + 2/9*f**3 + 1/3*f**2 - 37*f. What is l in n(l) = 0?
-1
Let w = 627 - 615. Let p(f) = f - 8. Let g be p(w). Determine i so that -10/3*i**3 - 2/3*i**g - 2*i - 14/3*i**2 + 0 = 0.
-3, -1, 0
Let f(l) be the second derivative of 3/7*l**4 + 1/70*l**5 + 0*l**2 + 2 - 3*l + 27/7*l**3. Factor f(z).
2*z*(z + 9)**2/7
Let a(p) be the first derivative of -p**2 - 24*p + 13. Let c be a(-13). Factor -8*m - 4*m**2 - m**c + 2*m + m.
-5*m*(m + 1)
What is u in 746/5*u**3 + 72/5*u + 0 - 472/5*u**2 - 8*u**4 = 0?
0, 1/4, 2/5, 18
Let j be (-6)/4 + -4 + 354/60. Let c(i) be the second derivative of j*i**6 + 0 - 2/3*i**4 + 2/21*i**7 - 2*i**3 - 2*i**2 + 2/5*i**5 + 9*i. Factor c(p).
4*(p - 1)*(p + 1)**4
Suppose 49 = 16*m + 1. Factor -74*c + 22*c - 26*c**2 - 72 - 2*c**m - 44*c.
-2*(c + 1)*(c + 6)**2
Let s(u) be the third derivative of -u**6/180 - 2*u**5/105 + 23*u**3/3 + 2*u**2 + 43. Let i(w) be the first derivative of s(w). Suppose i(b) = 0. What is b?
-8/7, 0
Factor 8 + 2356*u + 9 - 3 - 9 - 788*u**2 + 19.
-4*(u - 3)*(197*u + 2)
Let y(m) = 1. Let i(v) = -6*v**3 + 9*v**2 + 6*v - 4. Let g(z) = z - 7. Let h be g(2). Let o(w) = h*y(w) + i(w). Let o(n) = 0. What is n?
-1, 1, 3/2
Let u(z) be the second derivative of z**5/120 + 11*z**4/72 + 5*z**3/12 - 9*z**2/4 - 1446*z. Let u(q) = 0. Calculate q.
-9, -3, 1
Let z(n) be the first derivative of 11*n**3 - 13 - 2*n**6 - 15/2*n**2 + 0*n + 99/4*n**4 + 39/5*n**5. What is o in z(o) = 0?
-1, 0, 1/4, 5
Let w(a) be the second derivative of a**7/105 - 8*a**6/75 + 11*a**5/50 + 4*a**4/15 - 4*a**3/5 + 813*a + 2. Let w(y) = 0. What is y?
-1, 0, 1, 2, 6
Let a(i) = 3*i**2 + 30*i + 72. Let p(t) be the second derivative of t**4/2 + 10*t**3 + 145*t**2/2 - 22*t. Let r(l) = 5*a(l) - 3*p(l). Solve r(k) = 0.
-5
Factor 1759/4*s + 1/4*s**2 + 0.
s*(s + 1759)/4
Let v(w) be the first derivative of -4*w**5/5 - 9*w**4 - 52*w**3/3 + 90*w**2 + 200*w + 1390. Find r such that v(r) = 0.
-5, -1, 2
Let a(k) be the first derivative of 2*k**3/51 + 1270*k**2/17 - 2542*k/17 - 6527. Factor a(v).
2*(v - 1)*(v + 1271)/17
Let m be 0*(-25 - -21)/4. Let p(r) be the second derivative of m + 5/12*r**4 - 42*r + 0*r**2 + 1/12*r**5 - 10/9*r**3. Factor p(f).
5*f*(f - 1)*(f + 4)/3
Let v(i) be the second derivative of i**6/150 + 13*i**5/100 + 7*i**4/10 + 4*i**3/15 - 32*i**2/5 - 7*i + 4. Let v(y) = 0. Calculate y.
-8, -4, -2, 1
Let s = -998 + 1000. Let v(f) be the third derivative of 0 + 0*f**6 + 0*f - 1/114*f**4 + 0*f**3 + 18*f**s - 1/190*f**5 + 1/1995*f**7. Factor v(b).
2*b*(b - 2)*(b + 1)**2/19
Factor -1090*y**2 + 116*y - 1072*y**2 + 6768*y + 2160*y**2 - 5923682.
-2*(y - 1721)**2
Let n(j) be the second derivative of 0 + 65*j + 1/15*j**4 + 0*j**2 + 1/50*j**5 - 1/5*j**3. Suppose n(y) = 0. Calculate y.
-3, 0, 1
Let l(n) be the first derivative of 40/3*n**2 - 4/3*n**4 + 4/3*n**3 + 43 + 50/3*n + 2/15*n**5. Solve l(v) = 0 for v.
-1, 5
Factor 369*q - 2407 + 1248 - 4*q**2 + 1067.
-(q - 92)*(4*q - 1)
Let t be ((-10)/3)/((-2)/(-15)*5). Let j = t + 10. Factor 14*o**5 + 15*o**5 - 24*o**j - 10*o**3 + 5*o.
5*o*(o - 1)**2*(o + 1)**2
Suppose -4*m - 2*m + 12 = 0. Suppose 28 = z - 5*l - 7, -14 = -z - m*l. Factor -z*c**2 + 5*c**2 - 10*c + 19*c.
-3*c*(5*c - 3)
Let u(v) be the second derivative of 4*v**6 - 175*v**5/2 - 875*v**4/12 + 625*v**3/2 - 663*v - 4. What is q in u(q) = 0?
-5/4, 0, 5/6, 15
Suppose -p = 4*z + 3, z + p - 5*p + 5 = 0. Let c be (27/(-21) - z)/((-120)/70). Factor 0 + c*u**3 - 1/6*u**5 + 1/6*u**2 - 1/6*u**4 + 0*u.
-u**2*(u - 1)*(u + 1)**2/6
Let g = 303 - 283. Factor -g*d**2 - 20*d**2 - 335*d**3 + 45*d + 330*d**3.
-5*d*(d - 1)*(d + 9)
Let d(z) = -24*z**2 - 2853*z. Let n(q) = -q**2 + q. Let k(m) = -d(m) + 21*n(m). What is l in k(l) = 0?
-958, 0
Suppose 370*f - 1634 = -277*f + 15835. Determine h, given that -77/6*h**5 + 2/3*h - f*h**4 - 89/6*h**3 + 0 + 0*h**2 = 0.
-1, -2/7, 0, 2/11
Let b(k) be the third derivative of -k**6/12 - 2216*k**5/15 + 2663*k**4/12 + 1774*k**3/3 - 35*k**2 - 2*k + 11. Factor b(t).
-2*(t - 1)*(t + 887)*(5*t + 2)
Let q(x) be the third derivative of -x**5/15 - 1595*x**4/6 - 2124*x**3 - 4925*x**2. Let q(i) = 0. What is i?
-1593, -2
Let y(v) be the first derivative of v**5/40 - 3*v**4/16 + v**3/2 + 20*v**2 + 2. Let h(f) be the second derivative of y(f). Factor h(m).
3*(m - 2)*(m - 1)/2
Suppose -6*m + 16 = -2. Determine p, given that -1152 - 4*p**2 - 138*p - 2*p**4 - 342*p + 50*p**2 - 3*p**m + 21*p**3 + 2*p**3 = 0.
-3, 8
Let m(i) = 6*i - 9 - 31*i**3 + 21*i**3 + 2*i**2 + 9*i**3. Let p be m(2). Determine z, given that 2/5*z**4 + 7/5 + 39/5*z**2 + 29/5*z + 19/5*z**p = 0.
-7, -1, -1/2
Let f(n) be the third derivative of 0*n**3 + 0*n**5 + 0*n**4 + 0 + 2*n - 30*n**2 + 1/480*n**6. Factor f(s).
s**3/4
Let i(t) = -3*t**2 - 118*t - 36. Let u be i(-39). Let a(q) be the second derivative of -1/30*q**4 - 10*q + 4/15*q**u + q**2 + 0. Factor a(l).
-2*(l - 5)*(l + 1)/5
Determine z so that -2/7 - 202026945806*z**4 - 1441524*z**2 + 1048*z + 881251672*z**3 = 0.
1/917
Let h(r) be the first derivative of r**6/36 - 37*r**5/60 + 7*r**4/6 - 76*r**3/3 - r**2 - 94. Let b(q) be the third derivative of h(q). Factor b(v).
2*(v - 7)*(5*v - 2)
Let m(a) be the first derivative of -66 - a**2 - 12*a + 2/3*a**3. Factor m(i).
2*(i - 3)*(i + 2)
Let g = 4294 + -4292. Let f(t) be the first derivative of 0*t - 19 - 3/5*t**g - 2/15*t**3. Determine i, given that f(i) = 0.
-3, 0
Let m be -8 + (1716/60)/13*(-1 - -6). Let g(p) be the third derivative of -1/210*p**5 + 0 + 1/84*p**4 + 0*p + 26*p**2 + 2/7*p**m. Factor g(n).
-2*(n - 3)*(n + 2)/7
Let t(v) be the third derivative of 0 - 120*v**2 + 1/2205*v**7 + 1/42*v**5 - 1/28*v**4 - 1/180*v**6 + 0*v**3 + 0*v. Factor t(z).
2*z*(z - 3)**2*(z - 1)/21
Suppose -18*x = -24*x. Suppose x = -0*i + 2*i - 20. Suppose -25/4*k**5 - i + 55/2*k**4 + 35*k - 35/2*k**2 - 115/4*k**3 = 0. Calculate k.
-1, 2/5, 1, 2
Let h = 278/965 - -186082/10615. Factor -1/11*o**3 - 224/11*o - h - 29/11*o**2.
-(o + 1)*(o + 14)**2/11
Suppose 0 = x - 4, -4*y - x = -2*y - 14. Suppose 2*p - 7*p = 4*b - 6, 3*p = -y*b + 1. Factor 83*t**2 - 39*t**p + 96*t + 2*t**3 - 144 + 2*t**3.
4*(t - 1)*(t + 6)**2
Let u(r) = -2*r**2 + r. Let a = -259 + 258. Let n(s) = s**2 + 12*s + 5. Let t(y) = a*n(y) + 2*u(y). Factor t(c).
-5*(c + 1)**2
Let s(q) be the second derivative of -q**6/135 - 23*q**5/10 - 205*q**4/18 - 613*q**3/27 - 68*q**2/3 - 11*q + 167. Find u, given that s(u) = 0.
-204, -1
Let d be ((-6)/(-45))/(2/60). Let t(i) be the second derivative of 12*i**2 - 38/3*i**3 + 0 + 14*i - 7/3*i**d. Solve t(r) = 0.
-3, 2/7
Let c(o) = 14*o**2 - 580*o - 84090. Let i(v) = 3*v**2 + 2. Let p(n) = -c(n) + 5*i(n). Factor p(d).
(d + 290)**2
Let q(i) = 7*i**2 - i. Let x(m) = -23*m**2 + 93*m - 172. Let d(z) = -3*q(z) - x(z). Let d(p) = 0. What is p?
2, 43
Let s(d) be the third derivative of -d**5/15 + 721*d**4/8 + 541*d**3/6 - 1678*d**2. Factor s(t).
-(t - 541)*(4*t + 1)
Let a(c) = -9*c**3 - 3*c**2 - 4*c - 2. Let h be a(-2). Let b(t) = 3*t**2 + 39*t + 253. Let i be b(-7). Factor i*f - h*f + 2*f**3 - 65*f - 2*f**2.
2*f*(f - 2)*(f + 1)
Factor -13*f**5 - 279*f**4 + 13*f**5 - 15*f**2 - 55*f**3 + 214*f**4 - 25*f**5.
-5*f**2*(f + 1)**2*(5*f + 3)
Let g(v) be the third derivative of -v**5/150 - 273*v**4/10 - 1637*v**3/15 + 8430*v**2 - 2*v. Factor g(j).
-2*(j + 1)*(j + 1637)/5
Factor 90*j**2 + 3/4*j**3 + 177/2 + 711/4*j.
3*(j + 1)**2*(j + 118)/4
Determine q, given that 1805/2*q + 191/10*q**3 + 1/10*q**4 + 0 + 1843/2*q**2 = 0.
-95, -1, 0
Factor 174/7*y**3 + 38/7*y**4 + 233/7*y + 304/7*y**2 + 1/7*y**5 + 66/7.
(y + 1)**3*(y + 2)*(y + 33)/7
Suppose 590 + 445*k - 1701*k + 878 + 249 - 465 + 4*k**2 = 0. What is k?
1, 313
Let g = 217 - 214. Find c, given that c - 24*c**3 - 4*c**4 - g*c + 2*c = 0.
-6, 0
Factor 117/4 - 3/4*v**2 + 15/2*v.
-3*(v - 13)*(v + 3)/4
Let m be 220/(-44) - 26/12*((-112)/14 - -5). Let -45/2 + 12*k - m*k**2 = 0. What is k?
3, 5
Factor 0 + 170/3*i**3 - 335/3*i + 325/6*i**2 + 5/6*i**4.
5*i*(i - 1)*(i + 2)*(i + 67)/6
Let a(t) be the third derivative of -t**6/72 + t**5/3 - 37*t**3/6 - 50*t**2 - 2*t. Let f(c) be the first derivative of a(c). Let f(x) = 0. What is x?
0, 8
Let k be 2/((-6)/27*-3). Suppose -3*u - 15 = -5*v, -k*u - 3*v = v - 12. Factor 2/3*i**3 + 0*i + 0*i*