m**2. Let u(i) be the second derivative of h(i). Factor u(v).
v**2*(v - 1)*(v + 1)/2
Suppose 440*i + 99 = 473*i. Factor 16/3*a - 4/3 - 8*a**2 + 16/3*a**i - 4/3*a**4.
-4*(a - 1)**4/3
Let b = 13906 + -13903. Solve 2*k**2 - 6*k - b*k**4 + 9/2*k**3 + 1/2*k**5 + 0 = 0.
-1, 0, 2, 3
Suppose 0*i - i = -y - 1, 3*y - i = 3. Factor 9*q**2 - 3*q**2 + 3*q**4 - 6*q**4 + y*q**3 + q**3.
-3*q**2*(q - 2)*(q + 1)
Let v be (-4 - -1)/(6 - (-45)/(-6)). Let m(h) = 12*h**2 - 183*h + 117. Let d(g) = -g**2 + 14*g - 9. Let s(n) = v*m(n) + 27*d(n). Factor s(x).
-3*(x - 3)*(x - 1)
Let z = 2412 - 2410. Factor 2/5*b**3 - 2/5*b - 1/5 + 0*b**z + 1/5*b**4.
(b - 1)*(b + 1)**3/5
Suppose -3*c + 5 = 3*b - 16, b - 4 = 0. Determine v, given that 0*v - 21/4*v**2 + 9/4*v**4 - 3/4*v**c + 3 + 3/4*v**5 = 0.
-2, -1, 1
Suppose 2*v = 5*c + v - 25, 4*v + 25 = 5*c. Solve 3*r**3 - 4*r**c + 16*r**4 - 19*r**3 - 22*r**4 - 14*r**4 = 0 for r.
-4, -1, 0
Let g = 11 + -1. Let a = g - -11. Factor -26 + 55 - a - 28*b**3 - 12*b - 48*b**2.
-4*(b + 1)**2*(7*b - 2)
Solve -4/5*z - 4/5*z**3 + 0 - 8/5*z**2 = 0.
-1, 0
Suppose -3*o - 1 = -10. Let p be 7*(1 - 30/42). Suppose -o*m**p - 16*m + 18*m**3 + 16*m = 0. Calculate m.
0, 1/6
Let a(s) be the second derivative of 5/3*s**4 + 0 + 21*s + 8/3*s**3 - 2*s**2. Factor a(x).
4*(x + 1)*(5*x - 1)
Let w(d) be the first derivative of d**4/4 + 5*d**3/14 - 3*d**2/7 + 10*d - 11. Let u(k) be the first derivative of w(k). Factor u(t).
3*(t + 1)*(7*t - 2)/7
Suppose -2*d + 3*f + 4 = 1, -7 = -4*d + 5*f. Let b = -1177/28 + 303/7. Suppose -b*z**2 + d*z - 1 = 0. What is z?
2/5, 2
Let m be ((-2)/(-2))/(7/14). Let -52*c - 36*c - 11*c**m + 4*c - 15*c**3 + 24 + 77*c**2 = 0. What is c?
2/5, 2
Let b = -3 - -7. Suppose -b*c + 4*s - 3*s + 10 = 0, 0 = -4*c - 2*s + 4. Let w**3 + 2*w**3 + 3 - 4*w - 4*w**2 + w + w**c = 0. What is w?
-1, 1
Suppose -4*f + 21*q = 17*q - 24, -2*q = f + 3. Find k, given that 3/7*k**5 - 3*k - 6/7*k**f + 6/7 - 6/7*k**4 + 24/7*k**2 = 0.
-2, 1
Find l, given that 17/2 + 9*l + 1/2*l**2 = 0.
-17, -1
Let p(b) = 2*b**2 - 144*b + 2596. Let j(t) = 2*t**2 - 144*t + 2595. Let m(k) = 4*j(k) - 3*p(k). What is a in m(a) = 0?
36
Let q(g) be the second derivative of g**7/77 + 13*g**6/165 + 3*g**5/110 - g**4/2 - 10*g**3/33 + 24*g**2/11 + 10*g - 26. Find i such that q(i) = 0.
-3, -2, -4/3, 1
Let y(n) be the third derivative of n**6/900 - n**5/75 - n**4/20 + 14*n**3/45 - 2*n**2 + 242. Factor y(j).
2*(j - 7)*(j - 1)*(j + 2)/15
Suppose 27*z - 42 = 12. Let b(c) be the second derivative of 1/4*c**4 + 0 + 0*c**3 - 3/2*c**z - 2*c. Find i, given that b(i) = 0.
-1, 1
Let h(s) = s**5 - 9*s**4 + 52*s**3 - 6*s**2 - 48*s + 5. Let o(r) = 8*r**4 - 52*r**3 + 4*r**2 + 48*r - 4. Let w(j) = -4*h(j) - 5*o(j). What is n in w(n) = 0?
-4, -1, 0, 1, 3
Let d(j) = -5*j + 40. Let i be d(8). Let w(h) be the third derivative of -1/8*h**4 + i*h - h**3 + 3/20*h**5 + 0 + 7*h**2. Suppose w(k) = 0. Calculate k.
-2/3, 1
Let k(o) be the third derivative of -o**5/330 - 14*o**4/11 - 2352*o**3/11 - 3*o**2 - 63*o. Let k(f) = 0. What is f?
-84
Let l(u) be the first derivative of -3*u**5/10 - 15*u**4/8 - 9*u**3/2 - 21*u**2/4 - 3*u + 28. Factor l(i).
-3*(i + 1)**3*(i + 2)/2
Let y(l) be the third derivative of 0*l - 1/4*l**3 + 3/32*l**4 + 1/16*l**5 - 33*l**2 + 0. Solve y(n) = 0.
-1, 2/5
Suppose 3*k + 4 - 1 = 3*a, 4*k = -3*a + 24. Determine r so that k*r**3 + 16 - 12*r**2 - 2*r**3 - 3*r**3 + 4*r**4 + 16*r - 6*r**3 = 0.
-1, 2
Let k be (2/(-4))/((-17)/102). Suppose -12 = -3*l, -k*l - 13 = -2*s - 3*s. Factor 0*a**s - 5*a**2 + a**2 - 3*a**5 + 2*a**5 + 3*a**4.
-a**2*(a - 2)**2*(a + 1)
Let i(r) be the third derivative of -7*r**2 - 3/20*r**5 + r**3 + 1/8*r**4 - 1/40*r**6 + 0*r + 1/70*r**7 + 0. Factor i(p).
3*(p - 2)*(p - 1)*(p + 1)**2
Factor -105125 - 5*k**2 - 481*k - 654*k - 315*k.
-5*(k + 145)**2
Let l(n) be the second derivative of -n**9/1512 - n**8/840 + n**7/420 + n**6/180 - n**3/3 + 5*n. Let x(k) be the second derivative of l(k). Factor x(b).
-2*b**2*(b - 1)*(b + 1)**2
Let x(f) = 21*f**2 - 41*f + 1. Let l be x(2). Let -8/5*u - 162/5*u**l + 0 - 72/5*u**2 = 0. What is u?
-2/9, 0
Suppose -3 = -5*r + 4*r. Factor 323 - 2*d**r - 323.
-2*d**3
Suppose 27*w = 104*w. Solve 3/4*j - 3/4*j**3 + 0*j**2 + w = 0 for j.
-1, 0, 1
Factor 17/3*i**2 - 1/6*i**3 - 182/3*i + 196.
-(i - 14)**2*(i - 6)/6
Let r(f) be the first derivative of f**4/28 + f**3 + 39*f**2/14 + 19*f/7 + 224. Find z such that r(z) = 0.
-19, -1
Let g be ((-4)/(-6))/(-14 - 1183/(-78)). Determine k, given that 10/7*k + 2/7*k**4 - 2/7*k**3 - g - 6/7*k**2 = 0.
-2, 1
Suppose -4*w = -15 - 5. Find u such that 4*u**5 + 0*u**w + 0 + 8*u**2 - 16*u**4 + 16*u**3 - 3 - 20*u + 11 = 0.
-1, 1, 2
Let i(l) be the second derivative of 2*l**7/7 - 5*l**6/2 + 87*l**5/10 - 61*l**4/4 + 14*l**3 - 6*l**2 - 105*l. Determine z, given that i(z) = 0.
1/4, 1, 2
Let c(p) be the first derivative of -p**5/10 - p**4/2 - 2*p**3/3 - p - 9. Let j(n) be the first derivative of c(n). Find b such that j(b) = 0.
-2, -1, 0
Factor 0 + 0*o**2 + 0*o - 2*o**3 + 8*o**4 - 7/2*o**5.
-o**3*(o - 2)*(7*o - 2)/2
Let d be ((-32)/(-21))/((-115)/(-805)). Solve 0 + 0*j - 49/3*j**5 + 77/3*j**4 + 4/3*j**2 - d*j**3 = 0.
0, 2/7, 1
Suppose 14*w - 77 = 7*w. Solve 4 - 18*o**2 + 3*o - w*o**3 + 2 + 9*o**5 + 12*o**4 + 2*o**3 - 3*o**3 = 0 for o.
-1, 2/3, 1
Let f(q) be the third derivative of -q**6/120 + 23*q**5/60 + 11*q**2. Factor f(z).
-z**2*(z - 23)
Let r(h) = 64*h**2 - 82*h - 26. Let i(t) = 13*t**2 - 16*t - 5. Let g(n) = 11*i(n) - 2*r(n). Factor g(v).
3*(v - 1)*(5*v + 1)
Let p(g) = g**5 - g**2 + g + 1. Let o(t) = -4*t**5 + 109*t**4 - 3886*t**3 + 42553*t**2 + 97196*t + 50650. Let d(h) = -5*o(h) - 15*p(h). Solve d(x) = 0.
-1, 37
Let 316*a**4 - 113*a**2 - 103*a**4 + 1088*a**3 - 544*a + 160 + 18*a**5 - 63*a**2 + 397*a**4 + 32*a**5 = 0. Calculate a.
-10, -2, -1, 2/5
Let w(t) be the third derivative of t**8/6720 - t**7/420 - t**6/48 + t**5/20 - 11*t**2. Let o(h) be the third derivative of w(h). Factor o(c).
3*(c - 5)*(c + 1)
Suppose 3/4*h**3 - 2*h - 23/4*h**2 + 0 = 0. What is h?
-1/3, 0, 8
Let q be ((-4)/(-10) + 0)/((-1)/60). Let z = q - -26. Suppose -1/5 - 1/5*u**4 + 1/5*u + 2/5*u**z + 1/5*u**5 - 2/5*u**3 = 0. Calculate u.
-1, 1
Let q(u) = -5*u - 6. Let f be q(-3). Suppose -f*b + 18 = -3*b. Suppose 2*x + 3*x - x**4 - 7 - x**b + 3*x**2 + 9 = 0. Calculate x.
-1, 2
Let b(f) = 15*f**3 - 49*f**2 + 15*f + 101. Let w(k) = -3*k**3 + 10*k**2 - 3*k - 20. Let u = -43 - -54. Let r(t) = u*w(t) + 2*b(t). Factor r(n).
-3*(n - 3)*(n - 2)*(n + 1)
Let y be 1 - ((-2)/1 - -1). Suppose 5*q + 292 = -y*p + 6*p, 16 = -4*q. Factor 2*d**3 + p*d - 26*d + 12*d + 18*d**2 + 54.
2*(d + 3)**3
Let p = -70119/5 + 14024. Factor -9/5 + 8/5*m + p*m**2.
(m - 1)*(m + 9)/5
Let a be 10/(-8)*-46 - -2. Let v = a + -59. Solve -v*s**3 + 0 - s**2 + 0*s = 0.
-2, 0
Factor -13*m**2 + 10*m**2 + 62500 - 296*m + 973*m + 323*m + 7*m**2.
4*(m + 125)**2
Let u be 0 - (-144)/56 - (1 + 1). Factor -20/7*n + 36/7*n**3 + u + 12/7*n**2.
4*(n + 1)*(3*n - 1)**2/7
Let p(s) be the first derivative of -1/3*s**3 - 1 + 0*s**2 + s. Factor p(b).
-(b - 1)*(b + 1)
Let q(x) be the first derivative of x**3/12 + 109*x**2/2 + 11881*x + 1006. Factor q(g).
(g + 218)**2/4
Factor -4*b**4 + 26*b**3 - 4*b**4 - 20*b**2 - 50*b**3 + 4*b**4.
-4*b**2*(b + 1)*(b + 5)
Let f(y) be the third derivative of -y**8/2184 + 4*y**7/1365 + y**6/195 - 8*y**5/195 + 3*y**2 + 34. Determine n so that f(n) = 0.
-2, 0, 2, 4
Let g(b) be the first derivative of 4*b**5/5 + 68*b**4 + 2312*b**3 + 39304*b**2 + 334084*b + 84. Suppose g(o) = 0. What is o?
-17
Suppose -58 = 2*a - 66. Solve v + 0 + 15/2*v**a + 5*v**2 + 37/4*v**3 + 9/4*v**5 = 0.
-1, -2/3, 0
Let p(j) be the third derivative of j**6/480 + j**5/240 - j**4/48 - 58*j**2. Suppose p(d) = 0. What is d?
-2, 0, 1
Let u be (5 - 6)/(25/(-50)). Find m such that 8*m**u + 32*m + 2/3*m**3 + 128/3 = 0.
-4
Let z(o) be the first derivative of -3/4*o**4 - 5*o**3 - 17/2*o**2 + 1/5*o**5 - 6*o - 31. Suppose z(j) = 0. Calculate j.
-1, 6
Factor 5*m**4 + 44549*m - 14*m**3 + 70*m**2 - 44469*m - 75 - 66*m**3.
5*(m - 15)*(m - 1)**2*(m + 1)
Let x be ((-177)/(-18) - 8) + 1/6. Let w(g) be the first derivative of 75/7*g + 1/7*g**3 + 15/7*g**x + 12. Factor w(b).
3*(b + 5)**2/7
Let r(p) be the first derivative of -p**3 - 9*p**2/2 