, 0
Let c(a) be the third derivative of -3*a**6/80 - a**5/40 - 8*a**2. Factor c(b).
-3*b**2*(3*b + 1)/2
Let t(g) be the first derivative of -g**4/72 - g**3/18 - g**2/12 - 2*g + 2. Let k(r) be the first derivative of t(r). Factor k(s).
-(s + 1)**2/6
Factor -412*m + 409*m + 3*m**2 - 6*m**2.
-3*m*(m + 1)
Find q, given that -q**4 + 0*q + 5/4*q**3 + 1/4*q**5 + 0 - 1/2*q**2 = 0.
0, 1, 2
Let k(g) be the second derivative of g**7/5040 - g**6/480 + g**5/120 + 7*g**4/12 - 7*g. Let t(r) be the third derivative of k(r). Factor t(z).
(z - 2)*(z - 1)/2
Let c be (-24)/(-12)*(2 + -1). Let m(q) be the second derivative of 0 + 1/4*q**c + q + 1/8*q**3 + 1/48*q**4. Factor m(j).
(j + 1)*(j + 2)/4
Solve -2 - 7/2*m**2 + 15/4*m**3 - 7*m = 0.
-2/3, -2/5, 2
Let t(h) be the third derivative of -h**7/280 - h**6/80 - h**5/80 + 7*h**2. Suppose t(x) = 0. Calculate x.
-1, 0
Factor -6/5 + 27/5*o - 21/5*o**2.
-3*(o - 1)*(7*o - 2)/5
Let r = 0 + 2. Let a = r + 0. Factor 5*h**a - 4*h**5 + 3*h**5 + 4*h**4 - 6*h**3 + 0*h**3 - h**2 - h.
-h*(h - 1)**4
Let z be (1/(-3))/(1/(-9)). Factor -z*i + 4*i**2 - 3 + i**3 + 2 + 3 + 8*i.
(i + 1)**2*(i + 2)
Let d(b) be the first derivative of b**9/7560 - b**8/4200 - b**7/2100 + b**6/900 + 2*b**3/3 - 1. Let n(r) be the third derivative of d(r). Factor n(g).
2*g**2*(g - 1)**2*(g + 1)/5
Let h(b) be the second derivative of b**5/210 + b**4/42 + b**3/21 - 3*b**2/2 - 2*b. Let j(x) be the first derivative of h(x). What is v in j(v) = 0?
-1
Let b be 2/(-5) - 108/(-70). Let t = 23/14 - b. Suppose 1/4*j + 1/2*j**2 - t - 1/4*j**3 = 0. Calculate j.
-1, 1, 2
Let g(f) = -f**3 + 11*f**2 - 20*f + 18. Let x be g(9). Factor x*t**3 + 0*t + 0 + 1/2*t**5 + 0*t**2 + 1/2*t**4.
t**4*(t + 1)/2
Let r = 11 - 31. Let u = -16 - r. Solve 2/3*d**2 + 0 + 1/3*d**u + 0*d - d**3 = 0 for d.
0, 1, 2
Let r = 18/5 - 499/140. Let q(o) be the second derivative of 0*o**2 + 3/8*o**5 + 0 + r*o**7 + 2*o + 1/6*o**3 + 11/60*o**6 + 3/8*o**4. Solve q(z) = 0.
-1, -2/3, 0
Find w, given that -1/3*w**4 + 0*w**2 - 2/3*w**3 + 0*w + 1/3*w**5 + 0 = 0.
-1, 0, 2
Suppose 2 = -4*v - 0*v - 2*m, 5*v - 5*m - 35 = 0. Let x(b) = -2*b**3 + b**2 - 1. Let p be x(-1). Factor -p*y**2 - v + 3*y + 3*y - 2*y.
-2*(y - 1)**2
Let i(o) be the third derivative of -2/5*o**5 - 1/168*o**8 - 13/60*o**6 + 0*o**3 + 0*o - 2/35*o**7 - 6*o**2 + 0 - 1/3*o**4. Solve i(c) = 0.
-2, -1, 0
Let m be (44/(-1))/((-10)/20). Let s = m + -349/4. Determine r, given that 9/4*r - 3/2 - s*r**2 = 0.
1, 2
Let s(z) be the first derivative of 2/15*z**5 + 0*z + 2/3*z**3 + 7 + 23/18*z**4 + 1/9*z**2 - 4/3*z**6. Determine y, given that s(y) = 0.
-1/3, -1/4, 0, 1
Let g(t) be the third derivative of t**9/6048 - t**8/1680 + t**3/3 + 4*t**2. Let u(y) be the first derivative of g(y). Determine z so that u(z) = 0.
0, 2
Suppose -8 + 20 = 4*s. Factor -t**2 + 0*t**2 - 3 - t + s.
-t*(t + 1)
Factor -16/5*l - 24/5*l**2 - 4/5*l**4 + 4*l**3 + 32/5.
-4*(l - 2)**3*(l + 1)/5
Let f(l) = l**3 + 4*l**2 + 3*l. Let r be f(-2). Suppose r*t = -3*a + 10, 5*t - 7 = -5*a + 18. Factor a*m**3 + 0*m - 2*m + 2*m**3.
2*m*(m - 1)*(m + 1)
Let l(d) be the third derivative of -d**10/75600 + d**9/18900 - d**8/16800 + d**4/8 - 4*d**2. Let p(w) be the second derivative of l(w). Factor p(a).
-2*a**3*(a - 1)**2/5
Let y be -2 - ((2 - 5) + -1). Suppose -4 = s + 3*o - 6*o, -5*s = -4*o - 2. What is v in 11 + 85*v**y - 9 + 128*v**3 + 24*v + 11*v**s = 0?
-1/4
Let h be 142/270 - 16/(-216) - 0. Factor -768/5*f - 768/5 - 288/5*f**2 - h*f**4 - 48/5*f**3.
-3*(f + 4)**4/5
Suppose 0 = -q + 2*q. Let a(s) be the first derivative of -2 - 3*s - 3*s**2 + q*s**2 - s**3 + 0. Factor a(k).
-3*(k + 1)**2
Let t(n) = n + 10. Let z be t(-6). Find x, given that 0*x - 4*x**2 - 6*x**3 + z*x**3 - 2*x = 0.
-1, 0
Factor -2*t**3 - 2*t + 4*t - 1 - 6*t + 0 - 5*t**2.
-(t + 1)**2*(2*t + 1)
Let q = -69 + 69. Let h(t) be the third derivative of 0 + q*t - 1/24*t**3 + 1/120*t**6 + 1/24*t**4 - 1/840*t**7 - 2*t**2 - 1/40*t**5. Factor h(i).
-(i - 1)**4/4
Let z(g) be the first derivative of g**3/27 - 2*g**2/3 + 4*g + 24. Factor z(a).
(a - 6)**2/9
Let i(h) = 9*h**2 + 5. Let c(p) = -4*p**2 - 2. Let s(o) = 5*c(o) + 2*i(o). Solve s(f) = 0.
0
Let f be 58/14 - (-3)/(-21). Let n(l) be the third derivative of 0 + 0*l**3 - 2/105*l**5 - 2*l**2 - 1/420*l**6 + 0*l - 1/21*l**f. Factor n(u).
-2*u*(u + 2)**2/7
Let h(u) be the second derivative of -u**5/4 - 11*u**4/6 - 4*u**3/3 + 3*u. Factor h(n).
-n*(n + 4)*(5*n + 2)
Factor -2/7*j**3 - 6/7*j**4 + 0*j**2 + 0*j + 0 + 8/7*j**5.
2*j**3*(j - 1)*(4*j + 1)/7
Factor -1/3*t - 2/3*t**2 + 1/3 - 1/3*t**5 + 2/3*t**3 + 1/3*t**4.
-(t - 1)**3*(t + 1)**2/3
Let t(c) be the third derivative of -1/9*c**3 + 1/24*c**4 + 0 - 1/180*c**5 + c**2 + 0*c. Factor t(d).
-(d - 2)*(d - 1)/3
Solve 4/13*n**2 - 6/13 - 10/13*n - 2/13*n**5 + 2/13*n**4 + 12/13*n**3 = 0.
-1, 1, 3
Let q(m) = 7*m**4 + 12*m**3 - 39*m**2 + 23*m. Let x(s) = -8*s**4 - 12*s**3 + 40*s**2 - 24*s. Let a(t) = -4*q(t) - 3*x(t). Let a(n) = 0. Calculate n.
-5, 0, 1
Let u(y) be the first derivative of -5*y**6/6 + 2*y**5 - 5*y**4/4 - 62. Determine r, given that u(r) = 0.
0, 1
Suppose -20 = -5*n, -12 = v - 4*n + 3*n. Let m be (-8)/(-3) + v/12. Factor 7*l**2 - 2*l**2 + 3*l**m + 56*l**3 + 98*l**4.
2*l**2*(7*l + 2)**2
Let k = 109/7340 + 2/1101. Let b(g) be the third derivative of 0*g + 1/75*g**5 + 1/840*g**8 + 0 + 0*g**6 - 2*g**2 - k*g**4 + 0*g**3 - 2/525*g**7. Factor b(z).
2*z*(z - 1)**3*(z + 1)/5
Suppose 4*b - 330 = -2*i, -3*i - 3*b + 483 = -0*b. Let f = i - 779/5. Factor -2/5*c**3 - f*c**2 - 6/5*c - 2/5.
-2*(c + 1)**3/5
Let q(t) be the third derivative of 0*t - 1/8*t**4 + 0 - 1/6*t**3 - 3*t**2 - 1/20*t**5 - 1/120*t**6. Factor q(n).
-(n + 1)**3
Let s = 13 + -8. Let w = -39 - -45. Factor -1 - 3*q**2 - w*q - s - 3*q.
-3*(q + 1)*(q + 2)
Let g = 205/3 - 1639/24. Let u(z) be the third derivative of 0 + 0*z - g*z**4 + 2*z**2 + 0*z**5 + 0*z**3 + 1/120*z**6. Determine i so that u(i) = 0.
-1, 0, 1
Let p(m) be the second derivative of -m**5/70 + m**4/14 - m**3/7 + m**2/7 - 15*m. Factor p(z).
-2*(z - 1)**3/7
Let t(q) be the second derivative of -1/1260*q**6 + 0*q**2 + 0*q**4 + 2*q + 0 - 1/6*q**3 + 1/420*q**5. Let y(o) be the second derivative of t(o). Factor y(v).
-2*v*(v - 1)/7
Suppose -3*s - 2*v - 2*v = 2, -5*v - 6 = 2*s. Let h be s + (-3 - 1)/(-4). Solve -2/5*w**2 + 2/5*w + 0 + 2/5*w**4 - 2/5*w**h = 0 for w.
-1, 0, 1
Let p(g) be the third derivative of 1/120*g**6 + 1/10*g**5 + 1/2*g**4 + 8*g**2 + 0*g + 4/3*g**3 + 0. What is y in p(y) = 0?
-2
Solve -3/5 + 3/5*v**3 + 9/5*v - 9/5*v**2 = 0 for v.
1
Let i(z) be the second derivative of 0 - 1/27*z**6 + 1/27*z**3 + 3*z + 0*z**2 - 4/189*z**7 + 1/30*z**5 + 5/54*z**4. Find k, given that i(k) = 0.
-1, -1/4, 0, 1
Factor 5 - 6 - 4*f**2 + 622*f - 634*f - 7.
-4*(f + 1)*(f + 2)
Let m(f) be the second derivative of f**6/60 - f**5/40 - 4*f. Factor m(u).
u**3*(u - 1)/2
Let x(b) be the second derivative of -b**5/5 + b**4/3 + 14*b. Solve x(y) = 0 for y.
0, 1
Let v be 1/1 + (13 - -2). Let w be v/42 + (-4)/(-14). Factor 0 - w*t**2 + 0*t.
-2*t**2/3
Factor 3/2*p**2 - 3 - 3/2*p.
3*(p - 2)*(p + 1)/2
Let v(l) be the second derivative of -l**4/8 + 2*l. Factor v(u).
-3*u**2/2
Let j(d) = 2*d**3 + 75*d**2 + 372*d + 622. Let w(t) = t**3 + 75*t**2 + 371*t + 621. Let k(a) = -4*j(a) + 3*w(a). Suppose k(b) = 0. Calculate b.
-5
Let o(j) be the first derivative of -1/4*j**5 + 1/4*j**3 + 7/8*j**2 - 5 - 7/16*j**4 + 1/2*j. Determine p so that o(p) = 0.
-1, -2/5, 1
Let u(m) be the first derivative of 12*m**5/35 + 9*m**4/14 + 2*m**3/7 - 33. Factor u(a).
6*a**2*(a + 1)*(2*a + 1)/7
Let r(x) = 0 + x**2 - 1 - 2*x + 6*x. Let a be r(-5). Let -10/7*v**3 + 2*v**5 + 0 - 18/7*v**a + 18/7*v**2 - 4/7*v = 0. Calculate v.
-1, 0, 2/7, 1
Let d = 3 + -1. Suppose -d*p = 3*p - 10. Let 2*i**4 + i**p + 6*i**2 - 4*i**3 - 5*i**2 = 0. What is i?
0, 1
Let z(t) be the second derivative of -t**7/231 + 3*t**5/110 + t**4/33 + 2*t. Let z(x) = 0. Calculate x.
-1, 0, 2
Let o(s) be the first derivative of -s**6/2 - 3*s**5 - 15*s**4/2 - 10*s**3 - 15*s**2/2 - 3*s - 60. Solve o(n) = 0.
-1
Let k(p) be the second derivative of -p**5/80 - p**4/12 - 5*p**3/24 - p**2/4 + 12*p. Determine g, given that k(g) = 0.
-2, -1
Let n(j) be the first derivative of j**4/8 + j**3/3 - 5. Solve n(x) = 0.
-2, 0
Let j(r) be the third