. Let f = b + -36. Factor 32/3*x + 0 - f*x**4 + 98/3*x**5 + 176/3*x**3 + 64*x**2.
2*x*(x - 2)**2*(7*x + 2)**2/3
Suppose 6*r = 9*r + 11*r. Factor -5/2*b**3 + r + 1/2*b**2 + 2*b**4 + 0*b.
b**2*(b - 1)*(4*b - 1)/2
Let h(v) be the second derivative of -v**8/3360 + v**7/420 - v**6/180 - v**4/4 - 3*v. Let g(m) be the third derivative of h(m). Find f such that g(f) = 0.
0, 1, 2
Let o(c) be the second derivative of 10*c**7/21 - 2*c**6/5 - 23*c**5/20 + 7*c**4/6 + c**3/2 - c**2 + 25*c. Determine k, given that o(k) = 0.
-1, -2/5, 1/2, 1
Let u(h) = h**2 - 5. Let c be u(3). Let s(b) be the third derivative of -b**2 - 1/210*b**5 + 0 + 0*b - 1/42*b**c + 0*b**3. Factor s(t).
-2*t*(t + 2)/7
Let y(f) be the third derivative of f**7/735 + f**6/420 - 4*f**2. Let y(c) = 0. Calculate c.
-1, 0
Let f = 42 - 40. Let r(a) be the third derivative of -1/6*a**3 - 1/60*a**5 + 0 - a**f - 1/12*a**4 + 0*a. Find t, given that r(t) = 0.
-1
Suppose 6*t = 138 - 126. Factor -1 + 1/3*x**t + 2/3*x.
(x - 1)*(x + 3)/3
Let k(l) = -12*l**2 + 9*l - 27. Let n(u) = -u**2 - 1. Let p(t) = k(t) - 15*n(t). Factor p(y).
3*(y - 1)*(y + 4)
Suppose -2*x = -3*h + 14, 4*x = 2*h - 15 - 5. Let u = 0 + 5. Solve 4*g**3 + g**5 + g**5 - 5*g**h + 4*g**2 - u*g**4 = 0 for g.
0, 1/2, 1
Let x(m) = 2*m**4 - 4*m**3 + 2*m**2 + 5*m + 5. Let o(v) = v**4 - 2*v**3 + v**2 + 3*v + 3. Let c(q) = -5*o(q) + 3*x(q). Factor c(b).
b**2*(b - 1)**2
Let t be 0/(-21)*(-1)/2. Suppose -j + 15 = -t*j + 5*i, -2*j - 4*i + 12 = 0. Factor -1/2*k**5 + 1/2*k**3 + 0*k + 0*k**4 + 0*k**2 + j.
-k**3*(k - 1)*(k + 1)/2
Let l(y) be the second derivative of y**7/168 - y**6/240 - 3*y**2/2 + 2*y. Let f(g) be the first derivative of l(g). What is p in f(p) = 0?
0, 2/5
Factor -2*d + 0 + 8/7*d**3 - 54/7*d**2.
2*d*(d - 7)*(4*d + 1)/7
Let g(f) be the first derivative of -f**5/80 + 3*f - 2. Let i(s) be the first derivative of g(s). Determine k so that i(k) = 0.
0
Let w(f) be the first derivative of -1/2*f**2 + 1/24*f**4 - 2 - f - 1/12*f**3. Let j(c) be the first derivative of w(c). Suppose j(a) = 0. Calculate a.
-1, 2
Let z(j) = 6*j**5 - 9*j**4 + 6*j**2 + 1. Let r(p) = 25*p**5 - 37*p**4 + p**3 + 23*p**2 + p + 5. Let t(a) = -4*r(a) + 18*z(a). Factor t(g).
2*(g - 1)**3*(g + 1)*(4*g + 1)
Suppose -2*t + 6 = -0. Factor -146 + 146 + 4*m**2 - 2*m**t - 2*m**4.
-2*m**2*(m - 1)*(m + 2)
Suppose -7*x + 3*o = -2*x + 9, x + o + 5 = 0. Let s(z) = -z**3 - 2*z**2 + z - 3. Let g be s(x). Factor 8/9*t - 8/9*t**g + 2/9*t**4 + 2/3*t**2 - 8/9.
2*(t - 2)**2*(t - 1)*(t + 1)/9
Suppose 0 + 2*z**2 + 0*z**3 - 2/3*z**4 - 4/3*z = 0. What is z?
-2, 0, 1
Let f(v) be the third derivative of -3*v**7/490 + v**6/56 - v**5/70 + 23*v**2. Factor f(u).
-3*u**2*(u - 1)*(3*u - 2)/7
Let p(u) = 2*u**2 + 6*u + 2. Let b be p(-3). Let r(c) be the second derivative of -2/7*c**3 - 1/7*c**b - 3/14*c**4 + 0 - 2*c. Factor r(o).
-2*(3*o + 1)**2/7
Let s(d) be the second derivative of 3*d**5/20 + 5*d**4/4 - 7*d**3 + 8*d. Find n such that s(n) = 0.
-7, 0, 2
Let k(d) be the third derivative of -d**5/150 - d**4/60 + d**2. Factor k(c).
-2*c*(c + 1)/5
Suppose 0 = -10*g + 12*g - 1124. Let n = g + -2792/5. Solve -4/5 - 8/5*y**3 + n*y - 6/5*y**2 = 0.
-2, 1/4, 1
Let t(f) be the third derivative of -f**6/200 - f**5/100 + f**4/40 + f**3/10 + 8*f**2. Find l such that t(l) = 0.
-1, 1
Let y be 1 - (-3)/(5 - 2). Factor g + 7*g - 3*g + 2*g**3 - y - 6*g**2 + g.
2*(g - 1)**3
Let r(z) be the second derivative of z**5/60 - z**3/6 + 2*z**2 + z. Let q(m) be the first derivative of r(m). Suppose q(g) = 0. What is g?
-1, 1
Let v be (-5)/(180/64) + 2. Let -44/9*i**3 - v*i + 0 + 16/3*i**4 + 16/9*i**2 - 2*i**5 = 0. What is i?
0, 1/3, 1
Let n(s) be the second derivative of 14*s**6/15 - s**5 - 3*s**4 + 10*s**3/3 + 4*s**2 + 18*s. Factor n(d).
4*(d - 1)**2*(d + 1)*(7*d + 2)
Suppose 5*m - 2*k = 14, 3*m + 6 - 3 = 5*k. Factor a**2 - m*a**2 + 0*a + 9*a - 3*a.
-3*a*(a - 2)
Let n(j) = 9*j**2 + 10*j + 9. Let d(b) = 8*b**2 + 10*b + 8. Let x(q) = -4*d(q) + 3*n(q). What is t in x(t) = 0?
-1
Let u = 4 - 5/2. Find z such that -3/2*z - 3/2 + u*z**2 + 3/2*z**3 = 0.
-1, 1
Let s = 10 - 5. Suppose -48*c**5 + c**2 - 6*c**4 + 3*c + 45*c**s + 5*c**2 = 0. Calculate c.
-1, 0, 1
Let i(n) be the third derivative of -n**5/40 + 9*n**4/16 + 4*n**2 + 10*n. Factor i(g).
-3*g*(g - 9)/2
Solve 4*q - 14/5*q**2 - 22/5*q**3 + 16/5 - 2/5*q**4 + 2/5*q**5 = 0.
-2, -1, 1, 4
Let p(f) = f**3 - 3*f**2 + f + 2. Let c be p(3). Let -5*r**5 + 24*r**3 + 9*r**4 - 4*r**5 - 18*r**c - 12*r**2 = 0. What is r?
-1, 0, 2/3
Let g(n) be the first derivative of n**4/8 + n**3/3 + n**2/4 - 9. Factor g(u).
u*(u + 1)**2/2
Suppose 0*q - 3*q - 12 = -3*h, -9 = 3*q. Let w be -5*h/(-3 + 2). Suppose 2*l**4 + 14/3*l**3 - 4/3*l + 0 - 2*l**2 - 10/3*l**w = 0. Calculate l.
-1, -2/5, 0, 1
Let d be (1/(-2))/((-28)/32). Let a be (0 - -1)/((-7)/(-2)). Factor 2/7*k**5 + d*k**2 - a + 2/7*k - 4/7*k**3 - 2/7*k**4.
2*(k - 1)**3*(k + 1)**2/7
Let d(x) be the first derivative of -2 - 1/180*x**5 - 1/72*x**4 - 3/2*x**2 + 0*x**3 + 0*x. Let y(n) be the second derivative of d(n). Find c such that y(c) = 0.
-1, 0
Let r(s) be the first derivative of 2*s**3/3 - 5*s**2 - 12*s - 37. Let r(p) = 0. What is p?
-1, 6
Let x(s) be the second derivative of -s**8/420 - s**7/210 + s**6/90 + s**5/30 - 5*s**3/6 - 3*s. Let q(k) be the second derivative of x(k). Factor q(o).
-4*o*(o - 1)*(o + 1)**2
Let x(b) be the first derivative of b**4/2 + 8*b**3 - b**2 - 24*b - 59. Factor x(o).
2*(o - 1)*(o + 1)*(o + 12)
Let m be 4 - ((-1 - -1) + 150/39). Factor 8/13*s - m - 2/13*s**4 - 12/13*s**2 + 8/13*s**3.
-2*(s - 1)**4/13
Let d = 7 - 4. Factor -6*t**d + 4*t**3 + 2*t**3 + t**4 - t**3.
t**3*(t - 1)
Let x = -8 - -10. Let n be 3/9*(6 - 5). Factor -v**3 - v**x - 1/3*v - n*v**4 + 0.
-v*(v + 1)**3/3
Suppose 9 = 3*l - 0. Let p be 12/(-18)*(-1)/l. Let p*q**2 - 4/9*q + 2/9 = 0. Calculate q.
1
Let t be ((-30)/(-20))/((-3)/4). Let q be -14*t/12 + -2. Factor -1/3*s**2 + 0*s - q*s**4 + 2/3*s**3 + 0.
-s**2*(s - 1)**2/3
Let q = 15/8 + -37/24. Let m(z) be the first derivative of 1 + z**2 + 0*z + q*z**3. Determine x so that m(x) = 0.
-2, 0
Let m = -2/317 - -347/4755. Let u(x) be the second derivative of 0*x**2 + 1/75*x**6 - 1/30*x**4 + 1/50*x**5 + 3*x - m*x**3 + 0. Let u(n) = 0. Calculate n.
-1, 0, 1
Let g be 9/(-27) - 11/(-27). Let i(c) be the first derivative of 1/9*c**2 + 0*c - g*c**3 - 1/9*c**4 - 1. Find u such that i(u) = 0.
-1, 0, 1/2
Let k(v) be the first derivative of -1/8*v**4 + 1 - v + 1/2*v**2 - 1/20*v**5 + 1/4*v**3. Find i such that k(i) = 0.
-2, 1
Let h = 15 - 10. Determine q so that -4*q**5 + q + 5*q**5 - 2*q**5 - 2*q**3 + 2*q**h = 0.
-1, 0, 1
Let l be (2 - -2 - 3) + 2. Let k = 110/51 - -20/17. Factor -4/3 + 4/3*j**l + 2/3*j + k*j**2.
2*(j + 1)*(j + 2)*(2*j - 1)/3
Let c(t) be the third derivative of t**7/280 - t**6/120 - t**5/20 + 2*t**3/3 + 2*t**2. Let i(n) be the first derivative of c(n). Let i(s) = 0. Calculate s.
-1, 0, 2
Let o(f) = 4*f**2 + 3*f. Suppose -5*u + 4 = -3*u. Let d(z) = 2*z**2 + 2*z. Let y(q) = u*o(q) - 5*d(q). Find b, given that y(b) = 0.
-2, 0
Let j(p) be the second derivative of 0 - 2*p - 1/1620*p**6 - 1/540*p**5 + 1/54*p**4 + 0*p**2 - 1/3*p**3. Let i(d) be the second derivative of j(d). Factor i(l).
-2*(l - 1)*(l + 2)/9
Let a = -3 + 7. Factor a*c**3 - 12*c - 3 - 9 + 4.
4*(c - 2)*(c + 1)**2
Let r(h) be the second derivative of -1/3*h**3 - 3*h - 2/3*h**2 + 0 + 1/30*h**5 + 0*h**4. Factor r(g).
2*(g - 2)*(g + 1)**2/3
Let b = -23 - -37. Let p be (-99)/(-21) + 4/b. Factor p*c - 4*c + c + 8*c**2.
2*c*(4*c + 1)
Let t(l) be the first derivative of -l**6/1800 - l**5/150 - l**4/30 + 2*l**3/3 + 2. Let o(p) be the third derivative of t(p). Solve o(w) = 0 for w.
-2
Suppose 4*n - 2*n - 10 = -2*a, -5 = 5*a - n. Factor -8*s - 2*s**2 + 0*s**2 - 3 - 5 + a.
-2*(s + 2)**2
Let y = 3 - 68. Let w be ((-104)/y)/((-4)/(-10)). Solve -8/3 + u**w + 11/3*u**3 - 4*u + 2*u**2 = 0 for u.
-2, -2/3, 1
Factor -8/5*r**3 - 8/5 + 6/5*r**2 + 8/5*r + 2/5*r**4.
2*(r - 2)**2*(r - 1)*(r + 1)/5
Let d = 109 - 109. Let r(x) be the first derivative of -1/4*x**6 + 1/8*x**4 + 0*x + 1/3*x**3 + d*x**2 - 2/5*x**5 + 4. Determine u so that r(u) = 0.
-1, 0, 2/3
Let d be 27/9*14/6. Suppose -4*k - 1 = -2*k + 5*z, 4*k - d = -z. Determine o, given that 1/2*o**3 + o**k + 1/2*o + 0 = 0.
-1, 