)
Suppose -13*a = -18*a. Let j(l) be the second derivative of -2/15*l**3 + a + 1/30*l**4 - 3*l + 0*l**2. Factor j(u).
2*u*(u - 2)/5
Let j = 9 - 5. Suppose -4*z - 4*k = 8, 5*z - 8 = j*k + 18. Factor -5/2*g**z + 1/2*g**3 - 3/2 + 7/2*g.
(g - 3)*(g - 1)**2/2
Let f(c) be the second derivative of -c**7/40 - c**6/24 + c**5/20 - c**3/3 + 3*c. Let b(r) be the second derivative of f(r). Let b(q) = 0. Calculate q.
-1, 0, 2/7
Let n(t) be the second derivative of t**7/15 + t**6/12 - t**5/15 + t**2/2 + 4*t. Let v(l) be the first derivative of n(l). Let v(m) = 0. What is m?
-1, 0, 2/7
Let n = 16/9 - 23/18. Factor 0*p + 0 + p**3 - n*p**2 - 1/2*p**4.
-p**2*(p - 1)**2/2
Let g(q) = -q**3 + 4*q**2 + 3*q - 4. Let p be g(3). Let h = p - 13. Factor -h - 1/4*o**2 + o.
-(o - 2)**2/4
Let s(k) = -2*k**3 - 36*k**2 + 40*k + 41. Let x be s(-19). Let j be (-2)/(-3) - (-2)/(-3). Determine r so that 0*r - 1/3 - 1/3*r**4 + j*r**x + 2/3*r**2 = 0.
-1, 1
Let u(l) = -22*l**4 - 12*l**3 + 10*l. Let s(t) = -7*t**4 - 4*t**3 + 3*t. Let p(n) = 10*s(n) - 3*u(n). Let p(m) = 0. Calculate m.
-1, 0
Let t = -1949/75 + 26. Let q(c) be the second derivative of 0*c**2 - 1/50*c**5 + 0 + 0*c**3 + 0*c**4 - c + t*c**6. Let q(k) = 0. Calculate k.
0, 1
Let g be ((-1)/(-4)*0)/(-1). Suppose g*r + 2*r = 0. Factor r*c + 0 - 1/2*c**3 + 1/2*c**2.
-c**2*(c - 1)/2
What is r in 5*r**3 - 6*r**2 + 20 - 10 - 5*r - 4*r**2 = 0?
-1, 1, 2
Let l(x) = -x**3 - x**2 + 9*x - 9. Let n(w) = 2*w - 2. Let g(f) = 2*l(f) - 9*n(f). What is b in g(b) = 0?
-1, 0
What is p in 15*p**3 - 81 + 0*p**2 + 5*p**4 + 1/2*p**5 - 135/2*p = 0?
-3, 2
Suppose -4*v + v - 99 = 0. Let a = v - -35. Determine u, given that 0 + 4/5*u - 2/5*u**a = 0.
0, 2
Suppose -6/7 - 15/7*p - 6/7*p**2 + 3/7*p**5 + 12/7*p**4 + 12/7*p**3 = 0. What is p?
-2, -1, 1
Let -64/7*b - 32/7*b**2 - 4/7*b**5 + 32/7*b**3 + 4/7*b**4 + 64/7 = 0. Calculate b.
-2, 1, 2
Let m be (-3)/(-1) + -4 - -4. What is i in 3*i**2 - 3*i - 5*i**2 + i**m + 4*i = 0?
0, 1
Let b = 229/4 + -57. Find m such that b*m + 0 + 1/4*m**2 = 0.
-1, 0
Let c = 4/99 - -29/99. Factor 0 - c*f + 2/3*f**2 - 1/3*f**3.
-f*(f - 1)**2/3
Determine l so that 0*l - 1/3*l**2 + 0 + 1/3*l**4 + 0*l**3 = 0.
-1, 0, 1
Let a(c) be the second derivative of 0 + 1/24*c**4 - c + 1/12*c**3 + 1/120*c**5 + 1/2*c**2. Let x(j) be the first derivative of a(j). Let x(n) = 0. What is n?
-1
Let t(h) be the first derivative of h**7/945 - h**5/135 + h**3/27 - h**2/2 - 1. Let w(x) be the second derivative of t(x). Find m, given that w(m) = 0.
-1, 1
Suppose -23 = -3*u - 5. Let z = u + -3. Factor -8*k + 5 - z*k**2 + 3 + 5*k**2.
2*(k - 2)**2
Let h be (9/243*-2)/((-3)/9). Determine a, given that 0*a + 4/9*a**3 + 0 + h*a**4 - 2/9*a**5 + 0*a**2 = 0.
-1, 0, 2
Let g(s) be the second derivative of -s**9/30240 + s**7/5040 + s**4/3 - s. Let q(x) be the third derivative of g(x). Factor q(k).
-k**2*(k - 1)*(k + 1)/2
Let x(j) = -10*j**3 - 30*j**2 - 44*j - 24. Let l(i) = 4*i**3 + 5 - 4*i**3 + 9*i + 6*i**2 + 2*i**3. Let o(s) = 14*l(s) + 3*x(s). Factor o(n).
-2*(n + 1)**3
Let z(m) be the first derivative of m**4/2 + m**3/3 - m**2/2 + 6. Solve z(o) = 0.
-1, 0, 1/2
Let l = -30059/60 + 501. Let m(i) be the third derivative of 2*i**2 + 0*i**3 - 1/105*i**7 + 0*i + 0*i**5 + 0*i**4 - l*i**6 + 0. Determine z so that m(z) = 0.
-1, 0
Let t(z) be the third derivative of -z**8/112 + z**6/40 - 4*z**2. Factor t(w).
-3*w**3*(w - 1)*(w + 1)
Let -3 + 46*c**2 - 54*c**2 + 3 - 8*c**3 - 2*c**4 = 0. What is c?
-2, 0
Let p(x) = -2*x**2 + 10*x - 12. Let t(h) = 6*h**2 - 29*h + 37. Let s(l) = 14*p(l) + 4*t(l). Factor s(v).
-4*(v - 5)*(v - 1)
Let f(m) = -m**2 - 1. Let t(y) = -7 - 7 - 2*y**3 + 4*y**3 - 12*y**2 + 2. Suppose 5*x + 0*x - 5 = 0. Let g(k) = x*t(k) - 12*f(k). What is d in g(d) = 0?
0
Let u(n) be the third derivative of 0*n + 0*n**4 + 0 + 3*n**2 + 1/120*n**6 + 1/210*n**7 + 0*n**3 + 0*n**5. What is d in u(d) = 0?
-1, 0
Let u = -19 + 24. Let g = 5 - u. Determine j so that -1/2*j + 1/2*j**2 + g = 0.
0, 1
Let q(v) be the first derivative of 0*v + 0*v**4 - 1/60*v**5 + 0*v**2 - 3 + 1/180*v**6 + v**3. Let c(f) be the third derivative of q(f). Solve c(i) = 0 for i.
0, 1
Let d be 47/15 + (-1 - (-65)/75). Factor 1/3*u**d + 0 + 2/3*u**2 + 0*u.
u**2*(u + 2)/3
Suppose -134 - 1 = -5*c. Let b be 2/((-3 - c)/(-3)). Find t such that 0 - 1/5*t**2 + 1/5*t**4 - 1/5*t**3 + b*t = 0.
-1, 0, 1
Suppose 2*t - y = -1, t - 4*t + 1 = y. Suppose a - 4 = -4*v + 1, -3*v = t. Suppose i**3 + 2*i**5 - i**2 - 4*i**3 - 3*i**4 - 3*i**a = 0. What is i?
-1, 0
Let y(a) be the second derivative of -a**6/15 + a**4/2 - 2*a**3/3 + 16*a. Suppose y(z) = 0. Calculate z.
-2, 0, 1
Let k(g) = -6*g**2 + 13*g - 21. Let p(v) = v**2 - v + 1. Let w(d) = -k(d) - 5*p(d). Factor w(n).
(n - 4)**2
Let w be 2 + 1*(-1 - -3). Solve 2*q**2 - w*q**3 - q + q + q + 5*q**3 = 0.
-1, 0
Let i = -470321/72 + 55681/8. Let j = i - 427. What is t in 8/9*t - j - 2/9*t**2 = 0?
2
Suppose -3*h + 11 = 8*b - 3*b, -5*h - 4*b = -14. Suppose -h*n = n - 9. Solve -1/4*i + 1/2*i**n + 0 - 1/4*i**2 = 0 for i.
-1/2, 0, 1
Let i(p) be the first derivative of -1000*p**6/21 - 680*p**5/7 - 215*p**4/7 + 482*p**3/21 - 4*p**2 + 2*p/7 + 8. Factor i(t).
-2*(t + 1)**2*(10*t - 1)**3/7
Let r = -11 + 15. Suppose 6*n = 4*n + r. Determine v, given that -4/9*v + 0 - 10/9*v**n + 10/9*v**4 - 2/9*v**3 + 2/3*v**5 = 0.
-1, -2/3, 0, 1
Let i(l) be the first derivative of l**5/12 - 7*l**4/36 + l**3/9 - 2*l - 3. Let n(y) be the first derivative of i(y). Factor n(h).
h*(h - 1)*(5*h - 2)/3
Let b(t) be the first derivative of -t**6/5 - 4*t**5/5 - 7*t**4/6 - 2*t**3/3 + 4*t - 1. Let v(i) be the first derivative of b(i). Factor v(f).
-2*f*(f + 1)**2*(3*f + 2)
Suppose -195 = -2*b - 37. Let k = -709/9 + b. Solve -2/9*i**2 + 2/9*i**4 + k*i**3 - 2/9*i + 0 = 0 for i.
-1, 0, 1
Suppose 0 = -23*k + 3*k + 4*k. Let z(y) be the third derivative of -y**2 + 1/240*y**5 + 0 + 0*y + 0*y**3 + k*y**4. Factor z(b).
b**2/4
Let a = 7 + -14. Let k = 10 + a. Factor -27*b**4 - 2*b**2 - 4*b**3 - 2*b**k + 2*b**2.
-3*b**3*(9*b + 2)
Let k(d) = 6*d**3 + 9*d**2 + 5*d - 8. Let h(f) = 6*f**3 + 9*f**2 + 4*f - 7. Let a(u) = 5*h(u) - 4*k(u). Let a(z) = 0. Calculate z.
-1, 1/2
Let g be (2/(-4))/(2/(-12)). Let h(t) = -t**4 - t**3 + t**2 + t - 3. Let a(c) = 1. Let z(m) = g*a(m) + h(m). What is l in z(l) = 0?
-1, 0, 1
Let j(d) be the third derivative of d**8/14 + 10*d**7/21 + 4*d**6/3 + 2*d**5 + 5*d**4/3 + 2*d**3/3 - 20*d**2. Factor j(m).
4*(m + 1)**4*(6*m + 1)
Let z(m) be the first derivative of -m**3/15 + m/5 - 5. Find v, given that z(v) = 0.
-1, 1
Let h be (4/(-6))/(2/(-15)). Let a**3 - 5 + h + 2*a**2 = 0. What is a?
-2, 0
Let y(s) be the second derivative of -1/15*s**3 + 0*s**2 - 1/30*s**4 + 5*s + 0. Suppose y(m) = 0. Calculate m.
-1, 0
Let w(i) = -i**2 + 4*i + 17. Let f be w(5). Find l such that 0*l - 57*l**2 - 99*l**3 + 3*l - 27*l**4 - f*l = 0.
-3, -1/3, 0
Let f(l) be the third derivative of -l**6/72 - l**5/9 - 5*l**4/72 + 5*l**3/3 - 14*l**2. Find v such that f(v) = 0.
-3, -2, 1
Factor 0 - 1/7*u**4 - 11/7*u**2 + u**3 + 5/7*u.
-u*(u - 5)*(u - 1)**2/7
Let t(v) be the second derivative of -v**4/3 - 2*v**3/3 - 4*v. Factor t(b).
-4*b*(b + 1)
Let i(z) be the first derivative of 27*z**3/4 - 45*z**2/2 + 25*z + 11. Factor i(s).
(9*s - 10)**2/4
Let q(v) = 3*v**5 + 4*v**4 + 9*v**3 + 8*v**2 - 5. Let i(u) = 3*u**5 + 5*u**4 + 9*u**3 + 7*u**2 - 4. Let f(w) = 5*i(w) - 4*q(w). Factor f(r).
3*r**2*(r + 1)**3
Let q(t) be the third derivative of t**6/100 + t**5/15 + 7*t**4/45 + 8*t**3/45 + 9*t**2. Factor q(x).
2*(x + 2)*(3*x + 2)**2/15
Suppose -4*h = -1 - 59. Suppose -2*d - 5*v = -h, 6 = -d + 6*v - 4*v. Factor 5/3*s**2 + 2/3*s + d - 7/3*s**3.
-s*(s - 1)*(7*s + 2)/3
Let j(a) be the third derivative of a**8/840 - 4*a**7/525 - a**6/25 - a**5/75 + 11*a**4/60 + 2*a**3/5 + a**2. Factor j(c).
2*(c - 6)*(c - 1)*(c + 1)**3/5
Suppose 0 = -z + 2*z - m - 45, -185 = -4*z + 3*m. Let l be 2/10 - (-15)/z. What is g in -l*g - 1/2*g**2 + 1 = 0?
-2, 1
Let f(o) be the second derivative of -o**9/30240 - o**8/6720 - o**7/5040 + 5*o**4/12 - 4*o. Let y(v) be the third derivative of f(v). Factor y(i).
-i**2*(i + 1)**2/2
Let r be 6/(30 + 0)*(1 + 1). Let x(t) be the first derivative of -3 + 0*t + 0*t**3 + 0*t**2 - r*t**5 + 0*t**4. Factor x(o).
-2*o**4
Let l(k) be the third deri