*(l + 1)**3
Let s(n) be the first derivative of n**6/30 - 3*n**5/25 + n**4/20 + n**3/5 - n**2/5 + 8. Factor s(x).
x*(x - 2)*(x - 1)**2*(x + 1)/5
Factor -2/15*z**5 + 0*z - 10/3*z**3 + 4/3*z**4 + 0 + 0*z**2.
-2*z**3*(z - 5)**2/15
Let t(p) be the first derivative of 0*p - 1/3*p**2 - 4 - 2/9*p**3 + 2/15*p**5 + 1/6*p**4. Factor t(i).
2*i*(i - 1)*(i + 1)**2/3
Let o(l) be the first derivative of l**4/36 + l**3/6 + l**2/3 - l - 4. Let m(p) be the first derivative of o(p). Factor m(t).
(t + 1)*(t + 2)/3
Let q(k) be the second derivative of 0*k**2 + 4*k + 1/10*k**5 + 0 + 0*k**3 + 1/6*k**4. Factor q(s).
2*s**2*(s + 1)
Suppose 2*y = -5 + 9. Find u such that 0 - 2/3*u**5 - 4/3*u**y + 2/3*u**3 + 0*u + 4/3*u**4 = 0.
-1, 0, 1, 2
Let o(g) be the second derivative of g**6/20 - g**5/20 + 5*g**2/2 - 3*g. Let h(l) be the first derivative of o(l). Factor h(z).
3*z**2*(2*z - 1)
Let u(h) be the first derivative of h**4/18 + 2*h**3/27 - 2*h**2/9 - 8. Let u(c) = 0. Calculate c.
-2, 0, 1
Let c(d) = 9*d**2 - 3*d. Let j(t) = -t + 3*t + 6*t**2 - 10*t**2. Let m(r) = r - 8. Let u be m(6). Let y(a) = u*c(a) - 5*j(a). Suppose y(k) = 0. Calculate k.
0, 2
Let i(s) be the second derivative of -22*s**7/35 + 41*s**6/50 + 3*s**5/20 - s**4/10 + 7*s. Find y such that i(y) = 0.
-1/4, 0, 2/11, 1
Suppose -10 = -4*a + i, 5*a - 2*i = -0*i + 14. Factor 6*x**4 - 6*x + 6*x**3 + 2*x**2 - 5*x**a - 2*x**4 - x**4.
3*x*(x - 1)*(x + 1)*(x + 2)
Find l such that 9/4 + 1/4*l**2 - 3/2*l = 0.
3
Let s(k) be the first derivative of 6 + 45/2*k**4 + 10/3*k**3 + 0*k**5 - 5*k**2 - 2*k - 36*k**6. Determine a so that s(a) = 0.
-1/3, 1/2
Let c be 2 + (0 - 0) - -1. Suppose -2*m + 4*u = -20, u + 0*u = -c*m + 9. Factor -1/3*o**m + 1/3*o**2 - 1/3*o + 1/3*o**3 + 0.
-o*(o - 1)**2*(o + 1)/3
Let q(a) be the first derivative of 2/27*a**3 + 32/9*a + 7 - 8/9*a**2. Factor q(n).
2*(n - 4)**2/9
Let y = -18 + 20. Suppose 3*m + 4 = 5*b, y*m - 1 = 3*b - 3. Solve -1/6*s**4 - 1/6*s**m + 0 + 0*s + 1/3*s**3 = 0.
0, 1
What is l in 0*l**2 - 2*l + 2*l**3 - 7*l**4 + 1 - 1 + 7*l**2 = 0?
-1, 0, 2/7, 1
Let n(x) = 54*x**3 - 126*x**2 - 63*x - 3. Let k(w) = -w**3 + w**2 - w - 1. Let d(m) = 6*k(m) + n(m). Factor d(p).
3*(p - 3)*(4*p + 1)**2
Let t(k) = -k**3 - k**2 + 3*k - 3. Let m = -3 - -2. Let z(o) be the first derivative of o**2/2 - o - 4. Let d(b) = m*t(b) + 3*z(b). Solve d(g) = 0 for g.
-1, 0
Let y(v) be the second derivative of 1/20*v**5 - 1/12*v**4 + 1/30*v**6 + 0 - 1/42*v**7 + 3*v + 0*v**3 + 0*v**2. Factor y(b).
-b**2*(b - 1)**2*(b + 1)
Let h(x) = -x**3 - 5*x**2 + 5*x - 4. Let i be h(-6). Let j = 69 + -65. Factor 5/2*z + j*z**2 + 1/2 + i*z**3.
(z + 1)*(2*z + 1)**2/2
Suppose 5 = 4*g + 3*w, -3*g + 8 - 3 = w. Let -t**4 + 2/3 - 5/3*t**3 + 1/3*t**g + 5/3*t = 0. Calculate t.
-1, -2/3, 1
Let a(b) be the third derivative of b**6/600 - b**4/120 - 6*b**2. Suppose a(t) = 0. What is t?
-1, 0, 1
Let i(a) = 54*a - 162. Let c be i(3). What is t in -4/5*t**3 + c + 4/5*t**2 + 8/5*t = 0?
-1, 0, 2
Let p = -139/3 - -47. What is c in p*c + 0 + 0*c**2 - 2/3*c**3 = 0?
-1, 0, 1
Let q(x) = -12 + 8*x**3 - 2*x - 5*x**4 - 6*x**2 + 11 + 0*x. Let d(k) = 9*k**4 - 15*k**3 + 11*k**2 + 4*k + 2. Let t(j) = 6*d(j) + 11*q(j). Factor t(r).
-(r - 1)*(r + 1)**3
Solve -6*u**4 - u**4 + 3*u**2 + 4*u**4 = 0 for u.
-1, 0, 1
Let q(g) be the first derivative of 3*g**5/5 + 9*g**4/4 + 2*g**3 + 3. Determine z so that q(z) = 0.
-2, -1, 0
Suppose 3*l + 2*n - n = 45, -17 = -l - n. Suppose 5*z - 1 = l. Suppose -1/4*v**z + 0*v**2 + 0*v - 1/4*v**4 + 0 = 0. What is v?
-1, 0
Let h = 149/795 - -2/159. Let r(q) be the first derivative of -4/15*q**3 + 2/5*q + 1/15*q**6 + 2/25*q**5 + 1 - h*q**4 + 1/5*q**2. Solve r(g) = 0.
-1, 1
Let p(t) = -1. Let b(l) = 4*l**3 - 124*l**2 + 896*l + 1004. Let u(z) = -b(z) + 20*p(z). Factor u(k).
-4*(k - 16)**2*(k + 1)
Let z(b) be the third derivative of -1/448*b**8 - 1/70*b**7 + 0*b**4 + 0*b - 1/40*b**5 + 0 + 0*b**3 - 1/32*b**6 + 4*b**2. Determine s so that z(s) = 0.
-2, -1, 0
Determine f, given that -4/7*f**3 + 0 - 4/7*f**2 + 4/7*f**4 + 4/7*f = 0.
-1, 0, 1
Let o(s) be the first derivative of -1/5*s**5 + 1/3*s**3 - 3 - 1/2*s**4 + 0*s + s**2. Solve o(c) = 0 for c.
-2, -1, 0, 1
Find z such that -48/7*z**4 + 0 + 16/7*z**5 + 4/7*z + 52/7*z**3 - 24/7*z**2 = 0.
0, 1/2, 1
Let w(h) be the first derivative of -2*h**3/33 + h**2/11 + 2. Determine r so that w(r) = 0.
0, 1
Let v(s) be the first derivative of s**5/5 + 3*s**4/2 + 4*s**3 + 4*s**2 + 1. What is j in v(j) = 0?
-2, 0
Let q(u) = -u**2 - 5*u. Let k be q(-5). Solve -8 - h**2 + k*h**2 - h**2 - 8*h = 0 for h.
-2
Let y(l) be the first derivative of 1 + 1/300*l**6 + 1/60*l**4 + 0*l**3 + 1/75*l**5 + 0*l + l**2. Let t(i) be the second derivative of y(i). Factor t(f).
2*f*(f + 1)**2/5
Suppose 0*p - p = p. Factor -2/5*t**2 - 2/5*t + p.
-2*t*(t + 1)/5
Let b(d) be the first derivative of -2*d**5/35 + d**4/14 + 2*d**3/21 - d**2/7 + 7. Find t, given that b(t) = 0.
-1, 0, 1
Let c(u) be the second derivative of 11/100*u**5 + 0 - 2/15*u**3 + 2/15*u**4 + 5*u + 0*u**2 - 1/10*u**6. Find j such that c(j) = 0.
-2/3, 0, 2/5, 1
Let c(n) be the first derivative of 1/4*n**3 + 3/8*n**2 - 3/4*n - 1 - 3/16*n**4. Factor c(w).
-3*(w - 1)**2*(w + 1)/4
Let r(t) be the third derivative of 2*t**7/105 + t**6/15 - t**5/5 - 11*t**2. Factor r(g).
4*g**2*(g - 1)*(g + 3)
Suppose -3*x - 18 = 3*q, 3*q + 2*x = 7*x - 34. Let n be 60/(-8)*q/10. Suppose 3*g**2 - g**2 + 2*g**2 - n*g**2 = 0. What is g?
0
Factor -5*p**3 + 9*p**2 - 6*p**2 + 3*p**3 + 4*p - p**2.
-2*p*(p - 2)*(p + 1)
Let y(o) be the first derivative of 0*o + 1/2*o**2 - 1/6*o**3 + 1/10*o**5 + 3 - 1/4*o**4. Find b such that y(b) = 0.
-1, 0, 1, 2
Let r(c) be the second derivative of -c**4/12 - 7*c**3/6 - 3*c**2 - 24*c. Determine a so that r(a) = 0.
-6, -1
Let o = 11 + -8. Suppose -3*q**3 + q**5 - 4*q**4 - o*q**2 + 7*q**4 + 2*q**5 = 0. What is q?
-1, 0, 1
Let b(a) be the third derivative of 8*a**3 + 4*a**2 + 1/20*a**5 + 0 + 0*a + a**4. Suppose b(d) = 0. Calculate d.
-4
Let x be (-11 - (-459)/42)*(0 + -4). Find b such that 6/7*b**2 - 2/7*b**4 - 4/7 - x*b**3 + 2/7*b = 0.
-2, -1, 1
Let z(j) be the second derivative of j**6/90 - 2*j**5/15 + 23*j**4/36 - 14*j**3/9 + 2*j**2 + 5*j + 1. Suppose z(k) = 0. Calculate k.
1, 2, 3
Let t(n) be the second derivative of n**5/80 + n**4/32 - n**3/4 + 7*n**2/2 + 3*n. Let z(o) be the first derivative of t(o). Factor z(g).
3*(g - 1)*(g + 2)/4
Let i(a) be the first derivative of 0*a - 1/5*a**2 + 2/15*a**3 - 3. Suppose i(b) = 0. Calculate b.
0, 1
Let s(m) be the third derivative of -m**7/245 - m**6/42 - 3*m**5/70 - m**4/42 - 9*m**2. Solve s(q) = 0.
-2, -1, -1/3, 0
Let c(x) be the second derivative of x**7/63 - 2*x**6/45 - x**5/10 + x. Find s such that c(s) = 0.
-1, 0, 3
Let h(d) be the third derivative of -d**8/84 + d**6/30 + 21*d**2. Factor h(z).
-4*z**3*(z - 1)*(z + 1)
Let u(v) = v**2 + 4*v - 2. Let n be u(1). Factor 0 + 6*l**n + 1/2*l - 7/2*l**2.
l*(3*l - 1)*(4*l - 1)/2
Suppose -2 = -6*t + 4*t + 2*k, -t - k = 3. Let j be 0 - (-4)/(t - -2). Factor -1/3*w**3 + 1/3*w**j + 0 + 1/3*w**5 + 0*w - 1/3*w**2.
w**2*(w - 1)*(w + 1)**2/3
Solve 7 + 3 - 2 - 10*w + 2*w**2 + 0 = 0.
1, 4
Suppose 0*a - 2 = -a. Let o(u) be the first derivative of -6/5*u**5 + 4*u**a + 0*u + 13/2*u**4 - 2 - 32/3*u**3. Factor o(s).
-2*s*(s - 2)**2*(3*s - 1)
Let w be 8/(-6)*(-6)/4. Suppose -4*o = -3*p + 22, -4 - 8 = 4*p + 5*o. Factor -p*x - x**3 + x**w + 2*x.
-x**2*(x - 1)
Let z = 243 - 243. What is k in 0*k + 0*k**3 + 1/2*k**4 + z - 1/2*k**2 = 0?
-1, 0, 1
Let z(f) be the second derivative of -f**6/24 + 5*f**4/48 + 40*f. Factor z(x).
-5*x**2*(x - 1)*(x + 1)/4
Let f = -1 - -1. Suppose 4*z = -2*z + 12. Let -i**2 - i**2 + f*i**2 - z*i = 0. Calculate i.
-1, 0
Let h(q) be the first derivative of -4*q**2 - 28/3*q**3 + 0*q - 2*q**4 + 12/5*q**5 - 3. Determine x, given that h(x) = 0.
-1, -1/3, 0, 2
Let j(d) = d**3 + d - 1. Let h(w) = -w**3 + 12*w**2 + 8*w + 4. Let g(k) = h(k) + 4*j(k). Let g(n) = 0. Calculate n.
-2, 0
Let o = -20 + 20. Let j(d) be the third derivative of -1/30*d**5 + 0 + 1/36*d**4 + o*d**3 + 0*d - 3*d**2. Find l, given that j(l) = 0.
0, 1/3
Suppose 3*z = -2*u + z - 2, 9 = -u - 5*z. Let r(n) = n - 1. Let d(o) = -o**2 + 6*o - 3. Let p(g) = u*d(g) - 5*r(g). Find s, given that p(s) = 0.
-1, 2
Let j(d) be the t