 - 10922. Find h such that -t*h - 5/2*h**3 - 25/2*h**2 - 15/2 = 0.
-3, -1
Let x = 21 - -33. Factor 6*r**2 + 18*r - 2*r**3 + r**2 + 11*r**2 + x - 72*r.
-2*(r - 3)**3
Suppose 2*v + 2 = -3*r + 20, -v + r + 9 = 0. Let d = v + -7. Factor -7*a**5 + d*a**5 + 3*a**5 + 34*a**3 - 2*a - 30*a**3.
-2*a*(a - 1)**2*(a + 1)**2
Let b(v) be the second derivative of v**6/180 - v**4/12 + 2*v**3 - 16*v. Let q(h) be the second derivative of b(h). Factor q(m).
2*(m - 1)*(m + 1)
Let u(f) be the second derivative of -f**5/200 - f**4/60 - f - 4. Determine q, given that u(q) = 0.
-2, 0
Let q = -2087/3696 + 51/88. Let c(o) be the third derivative of 0*o**3 - 1/42*o**7 + 1/12*o**5 + 0*o + 0 + 7*o**2 - q*o**8 + 0*o**4 + 1/24*o**6. Factor c(d).
-5*d**2*(d - 1)*(d + 1)**2
Suppose 2*k - 5 = -1. Factor -30 + 23*z + 2*z**k - 7*z**2 + z + 11*z.
-5*(z - 6)*(z - 1)
Let n(l) = 9*l**2 + 2*l + 1. Suppose 7*x + 3 = 4*x. Let v be n(x). Solve -i**2 - 2*i + 3*i**2 + v - 6*i = 0.
2
Let t(g) be the third derivative of -g**5/60 - 11*g**4/4 - 363*g**3/2 - 47*g**2 + 2*g. Factor t(q).
-(q + 33)**2
Let o be (-8)/(-2) + (-2)/2. Suppose -5*p = -o*p - 74. Suppose 1 + p*d - 1 - 38*d - d**2 = 0. Calculate d.
-1, 0
Let j(p) be the first derivative of p**4/6 + 10*p**3/9 - 13*p**2/3 + 14*p/3 + 146. Factor j(v).
2*(v - 1)**2*(v + 7)/3
Let j(p) be the third derivative of -p**5/390 - 49*p**4/78 - 2401*p**3/39 - 12*p**2 - 2. Factor j(m).
-2*(m + 49)**2/13
Suppose 6 - 2/3*w**2 + w**3 - 9*w = 0. Calculate w.
-3, 2/3, 3
Suppose b = 4*h - b - 8, -4*b + 28 = 3*h. Find s such that -s + 4*s**3 + 12 + 0*s**3 - 11*s - h = 0.
-2, 1
Find x such that -3/5*x**3 + 0 + 3/5*x**2 + 6/5*x = 0.
-1, 0, 2
Let q(x) be the second derivative of x**4/20 - 2*x**3 + 30*x**2 - x + 23. Let q(h) = 0. Calculate h.
10
Let b(s) be the first derivative of -s**3/3 - 11*s**2 - 121*s + 125. What is u in b(u) = 0?
-11
Let z(k) = 84*k + 420. Let p be z(-5). Let 2/9*a**2 + p + 4/9*a - 2/9*a**3 = 0. Calculate a.
-1, 0, 2
Let z be (2/(-3))/((-12)/198). Factor -2 - 25*b**3 + z*b**2 - 8 - 3*b**2 + 32*b**2 - 5*b.
-5*(b - 1)**2*(5*b + 2)
Let x(v) be the third derivative of v**8/336 - 3*v**7/35 - v**6/120 + 3*v**5/10 + v**2 + 358*v. Factor x(s).
s**2*(s - 18)*(s - 1)*(s + 1)
Let r(d) = -2*d**3 + 5*d**2 - 4*d + 6. Let f be r(2). Let h(z) be the first derivative of 0*z**4 + 4/5*z**3 + 6/5*z - 8/5*z**2 - 2/25*z**5 - f. Factor h(m).
-2*(m - 1)**3*(m + 3)/5
Let h = 21 - 19. Let -2*p**4 + p - 4*p**2 + 0*p**3 + p**2 - p**3 + 5*p**h = 0. Calculate p.
-1, -1/2, 0, 1
Let i(w) = 17*w**4 - 38*w**3 + 17*w**2 + 10*w - 2. Let n(f) = -18*f**4 + 37*f**3 - 18*f**2 - 10*f + 3. Let a(j) = 3*i(j) + 2*n(j). Factor a(o).
5*o*(o - 2)*(o - 1)*(3*o + 1)
Let u(v) = -5*v**4 - 27*v**3 - 9*v**2 + 135*v - 94. Let z(k) = 2*k**3 - k**2 - 1. Let c(l) = -u(l) + 4*z(l). Factor c(r).
5*(r - 1)**2*(r + 3)*(r + 6)
Let l(j) be the third derivative of j**6/180 + 13*j**5/90 - j**4/9 - 52*j**3/9 - 226*j**2 - 1. Factor l(p).
2*(p - 2)*(p + 2)*(p + 13)/3
Let m(h) = -4*h - 7. Let f be m(-3). Let f + 3 + 12*k + 3*k + 5*k**2 + 2 = 0. What is k?
-2, -1
Let f(m) be the second derivative of 8*m + 1/3*m**3 + 1/90*m**6 + 0 + 0*m**4 + 1/30*m**5 + 0*m**2. Let h(n) be the second derivative of f(n). Factor h(z).
4*z*(z + 1)
Suppose 4*z - 67 = 29. What is g in -8 + 36*g - 4 - 4 - z*g**2 + 4*g**3 = 0?
1, 4
Suppose 4*m = 8, -2*m - m - 339 = 3*s. Let g = -115 - s. Factor g - 8/11*c + 24/11*c**2 + 8/11*c**4 + 30/11*c**3.
2*c*(c + 2)**2*(4*c - 1)/11
Let t(y) be the first derivative of -y**4/4 + 7*y**3/3 + 17*y**2/2 + 11*y + 7. Let w be t(9). Factor -65*x - w*x**2 + 2 + 65*x.
-2*(x - 1)*(x + 1)
Let v(l) be the third derivative of -1/30*l**6 + 0 + 0*l + 18*l**2 + 0*l**3 - 1/20*l**5 + 0*l**4 - 1/210*l**7. Factor v(m).
-m**2*(m + 1)*(m + 3)
Let c = -48113/91692 - -1/30564. Let t = -2/81 - c. Factor r - t - 1/2*r**2.
-(r - 1)**2/2
Let s(z) = -5. Let t(j) = -j**2 + 93*j - 97. Let p(n) = -s(n) + t(n). Determine k, given that p(k) = 0.
1, 92
Let m(k) = -20*k**3 - 10*k**2 + 72*k + 66. Let i(p) = 40*p**3 + 19*p**2 - 144*p - 133. Let s(q) = -2*i(q) - 5*m(q). Find d, given that s(d) = 0.
-8/5, -1, 2
Suppose -3*y + j = 0, -7*j = -5*y - 6*j. Determine v, given that -39 - 2*v**2 - 672*v - 59 + 700*v + y*v**2 = 0.
7
Let b(x) be the second derivative of -x**5/70 - 4*x**4/21 + 11*x**3/21 + 18*x**2/7 - 39*x. Factor b(t).
-2*(t - 2)*(t + 1)*(t + 9)/7
Let z = -11 - -28. Suppose 4*n - 6*n + 2*q = -8, 4*n - 5*q - z = 0. Let -4*s**3 - 28*s + 0*s**n + s**3 + 9 + 7*s + 15*s**2 = 0. Calculate s.
1, 3
Let n be -10 + 10 + 1 + -1 + 0. Factor n + 1/4*u**2 - 1/2*u.
u*(u - 2)/4
Factor 0*y**2 - 1/4*y**4 + 3/4*y**3 + 0 + 0*y.
-y**3*(y - 3)/4
Suppose -419*a - 192*a + 730 = -492. Let 21/4*p**a - 3/2*p + 9/4*p**4 - 6*p**3 + 0 = 0. Calculate p.
0, 2/3, 1
Let g(l) = 2*l**4 - 10*l**3 + 25*l**2 + l. Let f(b) = b**4 - 5*b**3 + 12*b**2. Let o(z) = -9*f(z) + 4*g(z). Factor o(k).
-k*(k - 2)**2*(k - 1)
Let z be ((-16)/(-27))/((30/18)/5). Let j(v) be the first derivative of 20/9*v**3 - 3 + z*v + 4*v**2 + 7/18*v**4. Factor j(d).
2*(d + 2)**2*(7*d + 2)/9
Suppose 5*o + 174 = 3*b + 57, 0 = -b - 2*o + 28. Factor 19*i**4 + 18*i**4 - b*i**4 + 3*i + 7*i**2 + 9*i**3 + 2*i**2.
3*i*(i + 1)**3
Let m = -13 - -22. Let g(z) = -3*z**2 + z + 2. Let s(x) = -13*x**2 + 5*x + 9. Let h(f) = m*g(f) - 2*s(f). Let h(q) = 0. What is q?
-1, 0
Let f(s) be the first derivative of 0*s**2 + 0*s + 1/3*s**6 - 7 - 1/2*s**4 + 2/3*s**3 - 2/5*s**5. Factor f(r).
2*r**2*(r - 1)**2*(r + 1)
Find r, given that -60/11*r**4 - 24/11*r + 0 - 136/11*r**2 + 50/11*r**5 - 222/11*r**3 = 0.
-1, -2/5, 0, 3
Let o = 2/4035 - -447/2690. Factor 1/6*z**2 - 1/3 + o*z.
(z - 1)*(z + 2)/6
Let j = -1517 - -1519. Let g(k) be the second derivative of -1/18*k**4 - 2/3*k**j + 1/3*k**3 + 0 + k. Factor g(z).
-2*(z - 2)*(z - 1)/3
Let t(o) be the third derivative of o**7/2100 - o**6/150 - o**5/20 + o**4/6 + 4*o**2. Let i(a) be the second derivative of t(a). Let i(m) = 0. Calculate m.
-1, 5
Find w such that 1/3*w**4 + w**2 - 4/3*w - 4/3 + 4/3*w**3 = 0.
-2, -1, 1
Factor 128/5*h - 8/5*h**3 - 2/5*h**2 + 32/5.
-2*(h - 4)*(h + 4)*(4*h + 1)/5
Let a(c) be the second derivative of -c**7/168 - 5*c**6/72 - 7*c**5/24 - 5*c**4/8 - c**3/6 + 12*c. Let b(l) be the second derivative of a(l). Factor b(j).
-5*(j + 1)**2*(j + 3)
Let b = 85/2196 - 2/183. Let t(j) be the second derivative of -2/3*j**2 + 1/6*j**3 + 0 - j + b*j**4. Factor t(s).
(s - 1)*(s + 4)/3
Let l(q) be the second derivative of -q**4/4 + 14*q**3 + 97*q. Suppose l(t) = 0. Calculate t.
0, 28
Let n be 17 + 242/(-33) + 5. Let k(a) be the first derivative of 14*a**4 + 0*a + 4*a**2 - n*a**3 - 10. Solve k(x) = 0.
0, 2/7, 1/2
Let n = 172 + -176. Let o(d) = 4*d + 19. Let w be o(n). Let -3/2*j**5 + 0*j**2 + 0*j + 3/2*j**4 + 3*j**w + 0 = 0. What is j?
-1, 0, 2
Let x(k) be the second derivative of k**5/4 - 85*k**4/12 + 455*k**3/6 - 735*k**2/2 + 4*k - 19. Suppose x(w) = 0. What is w?
3, 7
Factor -166375/7 - 165/7*y**2 - 9075/7*y - 1/7*y**3.
-(y + 55)**3/7
Suppose -5*n + j = 53, n + 54 = -3*n - 5*j. Let s = -7 - n. Factor s*t + 3*t**2 - 6 - 4*t + t - 4*t.
3*(t - 2)*(t + 1)
Let l(j) be the third derivative of -j**11/997920 + j**10/226800 - j**9/181440 + j**5/5 + 18*j**2. Let h(o) be the third derivative of l(o). Factor h(p).
-p**3*(p - 1)**2/3
Let p(q) = -2*q**2 - 77*q - 84. Let n(r) = 10*r**2 + 384*r + 416. Let s(y) = 6*n(y) + 28*p(y). Find b such that s(b) = 0.
-36, -1
Let r(o) be the first derivative of 2*o**5/5 + 13*o**4/2 - 28*o**3/3 - 152. Factor r(j).
2*j**2*(j - 1)*(j + 14)
Suppose 11*m + 16 = 60. Let d(z) be the second derivative of 0 + 1/3*z**2 + 1/18*z**m - 2/9*z**3 + 5*z. Factor d(o).
2*(o - 1)**2/3
What is j in -4/11*j**3 - 158/11*j**2 + 800/11 - 1520/11*j = 0?
-20, 1/2
Suppose 11 = 10*g - 39. Find d, given that -12*d**4 + 20*d**2 + 5*d**3 - 8*d**4 + 16*d**g - 17*d**3 - 4*d = 0.
-1, 0, 1/4, 1
Let l be (-376)/32 - (-24 - -12). Let c(q) be the third derivative of 0*q + 0 + 1/10*q**5 - 3/16*q**4 - l*q**3 - 9*q**2. Factor c(g).
3*(g - 1)*(4*g + 1)/2
Let w(u) = 4*u - 32. Let r be w(9). Factor 10 + 1 + 5 - 46*y - 4*y**r + 16*y**3 - 12*y**2 + 30*y.
-4*(y - 2)**2*(y - 1)*(y + 1)
Let d(x) = -46*x - 690. Let h be d(-15). Factor h + 1/3*i**2 + 8/3*i.
i*(i + 8)/3
Let o = -29 - -33. Determine 