 10082. Let m(h) = 14*h**2 + 260*h + 10082. Let r(l) = 7*m(l) + 6*u(l). Factor r(g).
2*(g + 71)**2
Let y(z) = 30*z**3 - 24*z**2 - 10*z + 1. Let u(a) = -a**3 + a + 1. Let f(w) = 6*u(w) + 2*y(w). Factor f(c).
2*(c - 1)*(3*c - 1)*(9*c + 4)
Let x(d) = 273*d - 8724. Let q be x(32). Factor q - 2/3*v**3 - 14*v + 16/3*v**2.
-2*(v - 3)**2*(v - 2)/3
Solve 0 + 5/4*i**3 - 155/4*i + 75/2*i**2 = 0 for i.
-31, 0, 1
Let q = 249 - 261. Let m be 4*2/(q/(-9)). Let -2/3*b**2 - m + 4*b = 0. What is b?
3
Suppose a = -5*t - 0*a - 35, a - 21 = 3*t. Let g = 11 + t. Factor -2 + f**2 + g - 3 + 0.
(f - 1)*(f + 1)
Factor 0 + 4/7*p + 16/7*p**2.
4*p*(4*p + 1)/7
Suppose -4*s = -3*s + 5*y + 23, -3*s = 5*y + 19. Factor -4*n**2 + 14*n**2 - 4*n**4 - 6*n**s.
-4*n**2*(n - 1)*(n + 1)
Let f(y) be the first derivative of y**4 - 1352/3*y - 320/9*y**3 + 1118/3*y**2 - 21. Suppose f(h) = 0. Calculate h.
2/3, 13
Let o(n) be the first derivative of -n**5/36 + 5*n**4/72 + 5*n**3/9 - 2*n**2 - 12. Let s(d) be the second derivative of o(d). What is f in s(f) = 0?
-1, 2
Factor 68/7 + 64/7*v - 4/7*v**2.
-4*(v - 17)*(v + 1)/7
Let m(x) be the first derivative of x**3/15 + 109*x**2/10 + 323. Factor m(p).
p*(p + 109)/5
Factor 60*a**3 - 26*a**4 - 6*a**4 - 121*a**2 - 64*a + 4*a**5 + 153*a**2.
4*a*(a - 4)**2*(a - 1)*(a + 1)
Let i(k) be the third derivative of -k**7/70 + 11*k**6/40 - 19*k**5/20 + 9*k**4/8 - 2*k**2 + 36*k. Factor i(p).
-3*p*(p - 9)*(p - 1)**2
Let v(t) = t**2 + 6*t + 9. Let k be v(-3). Let y(x) be the first derivative of k*x**2 + 0*x + 4/5*x**5 - 1/2*x**4 + 0*x**3 - 5 - 1/3*x**6. Factor y(f).
-2*f**3*(f - 1)**2
Let s be 342/798 + (-9)/21. Factor 0*k - 2/3*k**5 + s*k**3 + 0 - 2/3*k**4 + 0*k**2.
-2*k**4*(k + 1)/3
Let s(u) = u**3 - 4*u**2 + 5*u - 3. Let r be s(3). Factor 11*j**r + 0*j**3 + j**4 - j**5 + 3*j**4 - 116*j**2 + 122*j**2.
-j**2*(j - 6)*(j + 1)**2
Find n such that 2/3*n**3 + 8*n**2 - 8 - 2/3*n = 0.
-12, -1, 1
Let o(h) be the third derivative of h**5/20 + 161*h**4/2 + 51842*h**3 - 568*h**2. What is q in o(q) = 0?
-322
Let b(r) be the first derivative of -3*r**5/5 + 15*r**4/2 - 21*r**3 - 6*r**2 + 84*r - 459. Find t such that b(t) = 0.
-1, 2, 7
Let m(b) = -b**4 - b**3 + b - 1. Let a(z) = -36 + 9*z**4 - 70*z**2 - 26*z**3 - 89*z + 15*z**3 - 15*z**2. Let w(u) = -a(u) + 6*m(u). Find q such that w(q) = 0.
-1, -2/3, 3
Let a(z) be the second derivative of -148225*z**4/3 - 3080*z**3/3 - 8*z**2 - 52*z - 8. Solve a(r) = 0.
-2/385
Let n(o) = -o**2 + 11*o + 10. Let w(u) = u + 1. Let j(l) = n(l) - 4*w(l). Let c be j(7). Solve 6*y - c*y**2 + 3*y**3 - 3*y + 0*y = 0.
0, 1
Let p(k) be the third derivative of -k**6/150 + 4*k**5/25 + k**4/30 - 8*k**3/5 - 2*k**2 + 100. Factor p(f).
-4*(f - 12)*(f - 1)*(f + 1)/5
Determine g so that -3/2 - 5/8*g - 1/8*g**3 + 3/4*g**2 = 0.
-1, 3, 4
Suppose -21*q + 18*q = 201. Let z = q + 70. Factor -4/5 + 4*g + 7/5*g**z - 23/5*g**2.
(g - 2)*(g - 1)*(7*g - 2)/5
Let c(m) be the second derivative of m**7/105 + m**6/15 + 2*m**5/15 + 11*m**2 - 24*m. Let b(v) be the first derivative of c(v). Factor b(h).
2*h**2*(h + 2)**2
Let z = 1775 - 1772. Suppose -12 = -2*t + 4*p, 4*t + 5*p = -t. Factor 2/3*k**4 + 8/3*k**z + t*k**2 - 8/3*k - 8/3.
2*(k - 1)*(k + 1)*(k + 2)**2/3
Let f = 1805/129 + 286340/387. Let t = f + -753. Factor -2/9 - t*g**3 - 8/9*g - 4/3*g**2 - 2/9*g**4.
-2*(g + 1)**4/9
Suppose 9 = -5*u - y + 24, -2*y = u - 3. Let i(c) be the second derivative of 1/21*c**u + 0 + 0*c**2 + 1/14*c**4 - 2*c + 1/35*c**5. Suppose i(v) = 0. What is v?
-1, -1/2, 0
Suppose -5 = 3*u - 14. Factor 0*h**3 - h**3 + 2*h**2 + 5*h**u - 2*h**3.
2*h**2*(h + 1)
Let o(r) be the third derivative of -r**6/420 + r**5/105 + r**4/4 + 6*r**3/7 - 17*r**2. Suppose o(y) = 0. What is y?
-3, -1, 6
Let a(l) be the second derivative of -l**6/6 - l**5 - 5*l**4/12 + 5*l**3 - 89*l. What is y in a(y) = 0?
-3, -2, 0, 1
Let d(a) be the third derivative of 0*a + 0*a**3 + 1/15*a**5 - 18*a**2 + 0 + 1/60*a**6 - 2/3*a**4. Let d(g) = 0. Calculate g.
-4, 0, 2
Suppose -165 - 75 = -6*l. Find o, given that -33*o**4 + 8*o**3 + 8*o**2 + 75*o**4 - l*o**4 = 0.
-2, 0
Solve -3*n**5 + 159*n**2 + 117*n**3 + 66*n + 352*n**4 - 166*n**4 - 165*n**4 = 0 for n.
-2, -1, 0, 11
Let j = 239/134 + -19/67. Factor -3/8*l**2 - 9/8 - j*l.
-3*(l + 1)*(l + 3)/8
Let n(y) = 9*y**4 - 66*y**3 + 348*y**2 - 654*y + 379. Let d(z) = 55*z**4 - 395*z**3 + 2090*z**2 - 3925*z + 2275. Let o(i) = -4*d(i) + 25*n(i). Factor o(l).
5*(l - 5)**2*(l - 3)*(l - 1)
Suppose 6 = 5*j - f, -3*j - f - 4 + 14 = 0. Let t(q) be the first derivative of 0*q - 1/15*q**3 + 0*q**j + 12. Suppose t(n) = 0. Calculate n.
0
Let -4*o**4 + 37*o**2 - 11*o**3 - 9*o**3 - 61*o**2 = 0. What is o?
-3, -2, 0
Factor 11 + 9 + c**4 + 9*c - 20 - c**3 - 8*c - c**2.
c*(c - 1)**2*(c + 1)
Let p(t) be the first derivative of t**4/36 - t**2/6 + t - 16. Let o(f) be the first derivative of p(f). Factor o(u).
(u - 1)*(u + 1)/3
Find x such that 3 - 5*x + x**2 + 0*x**2 - 2*x**2 + 2 + 9 = 0.
-7, 2
Let i(z) be the first derivative of z**6/6 - 6*z**5/5 - 7*z**4/4 + 139. Factor i(q).
q**3*(q - 7)*(q + 1)
Let k = -8 - -10. Let b be 2 + (147/14)/(-7). Solve 1/2*h**k - h + b = 0 for h.
1
Let h be ((-5)/(-195)*-6)/(-1). Solve h*t**3 + 8/13*t**2 + 10/13*t + 4/13 = 0.
-2, -1
Let m be 1*2*(8 + (-209)/22). Let v be 1 + 2 + m/(-3). Suppose 0*k + 2/9*k**v - 2/9*k**3 - 2/9*k**2 + 2/9*k**5 + 0 = 0. What is k?
-1, 0, 1
Let t(n) be the first derivative of 47 + 7/2*n**2 - 1/6*n**3 - 49/2*n. Factor t(u).
-(u - 7)**2/2
Let l(o) = o**2 - 48*o - 89. Let b(y) = 11*y + 30 + 2*y - 9*y + 12*y. Let k(q) = 7*b(q) + 2*l(q). Solve k(i) = 0.
-4
Let i(r) be the first derivative of -5*r**9/4032 + r**8/336 + 3*r**3 - 21. Let b(z) be the third derivative of i(z). Let b(f) = 0. What is f?
0, 4/3
Let b = -67954/9 + 7551. Let y be 2/(-10) - (-116)/180. Let -2/9 - y*u**2 - b*u - 1/9*u**3 = 0. Calculate u.
-2, -1
Let z(l) = -33*l**3 - 60*l**2 - 6*l + 18. Let d(h) = -h**3 + h**2 + 6. Let v(s) = 3*d(s) - z(s). Let v(m) = 0. Calculate m.
-2, -1/10, 0
Let i = 164/495 + -6/55. Let w be 114/270 - (-1)/(-5). Find x such that 0 - i*x**2 - w*x = 0.
-1, 0
Suppose -2*m + 29 + 7 = 0. Let b = -6 + m. Factor -v + 6*v + 9*v**4 - b*v**2 + 6*v**3 - 11*v + 3.
3*(v - 1)*(v + 1)**2*(3*v - 1)
Let c(y) be the first derivative of 2*y**3/15 + 58*y**2/5 + 1682*y/5 - 69. Factor c(n).
2*(n + 29)**2/5
Let l = -391 - -1205/3. Suppose 8*a**2 + 4/3*a**3 + 16*a + l = 0. What is a?
-2
Let n = 313/280 + -26/35. Factor n*f**5 + 15/8*f**4 + 21/8*f**2 + 0 + 3/4*f + 27/8*f**3.
3*f*(f + 1)**3*(f + 2)/8
Factor 2/13*k + 4/13 - 2/13*k**3 - 4/13*k**2.
-2*(k - 1)*(k + 1)*(k + 2)/13
Let b(a) = 3*a**2 + a. Let m be (-12)/(-8) + (-1)/2. Let c be b(m). Factor 0 - 2/7*q**3 + 0*q - 2/7*q**c + 4/7*q**2.
-2*q**2*(q - 1)*(q + 2)/7
Let i(p) = -p**5 + p**4 + 10*p**3 - 10*p**2 - p + 5. Let t(x) = -5*x**5 + 5*x**4 + 40*x**3 - 40*x**2 - 5*x + 20. Let d(w) = 15*i(w) - 4*t(w). Factor d(q).
5*(q - 1)**3*(q + 1)**2
Let m(p) be the second derivative of 0*p**3 + 0*p**2 - 1/35*p**5 + 5/147*p**7 + 0*p**4 + 0 - 12*p + 1/35*p**6. Find h, given that m(h) = 0.
-1, 0, 2/5
Let w(t) = 3*t**4 - 8*t**3 + 13*t**2 + 4*t - 17. Let g(z) = 2*z**4 - z**3 + z**2 - 1. Let j(h) = g(h) - w(h). Solve j(f) = 0 for f.
-1, 2, 4
Let g = 848/85 - 156/17. Let g*p**2 + 0*p - 16/5 = 0. What is p?
-2, 2
Let q be (-1)/4 + ((-1148)/(-112) - 10). Factor -4/13*r + 2/13*r**2 + 2/13*r**3 + q.
2*r*(r - 1)*(r + 2)/13
Solve -24*i - 16*i**3 + 13*i**2 - 9*i**3 + 29*i**3 + 7*i**2 = 0 for i.
-6, 0, 1
Let w(r) = 3*r**3 + 79*r**2 - 2187*r + 19683. Let c(j) = -2*j**3 + j**2. Let q(i) = 6*c(i) + 3*w(i). Factor q(m).
-3*(m - 27)**3
Let u(d) = 2*d**2 - 26*d + 44. Let j(o) = -2*o**2 + 26*o - 44. Let p(a) = 2*j(a) + 3*u(a). Factor p(t).
2*(t - 11)*(t - 2)
Let q = 312 - 312. Let v(r) be the second derivative of 5*r + q*r**2 + 0 + 2/27*r**3 - 1/54*r**4. Let v(x) = 0. What is x?
0, 2
Factor 0*z + 0 + 3/4*z**2 + 1/4*z**4 - z**3.
z**2*(z - 3)*(z - 1)/4
Suppose -1943*m = -1956*m. Suppose 0*c**3 - 1/3*c**2 + 0 + m*c + 1/3*c**4 = 0. What is c?
-1, 0, 1
Let p(a) be the second derivative of a**5/30 - a**4/12 + 2*a**2 - 5*a. Let s(o) be the first derivative of p(o). Find c, given that s(c) = 0.
0, 1
Let z(y) be the second derivative of y**5/70 + y**4/6 + 5*y**3/7 + 9*y**2/7 + 5*y + 2.