 2)*(q - 1)**2/3
Let l(q) be the first derivative of q**8/5040 + q**7/2520 + 2*q**3/3 + 3. Let z(v) be the third derivative of l(v). Solve z(i) = 0.
-1, 0
Suppose -5*w + 6 = -4. Find k, given that -k**w - 1/5*k**3 - 4/5 - 8/5*k = 0.
-2, -1
Suppose 3*u - 6 = -0*u. Factor 0*l**3 - 2*l**3 + 4*l**3 - l**u + 8*l**4.
l**2*(2*l + 1)*(4*l - 1)
Let w(k) = -k**5 + k**3 + 1. Let q(x) = -16*x**5 + 12*x**4 - 16*x**3 + 20*x**2 + 20. Let r(a) = q(a) - 20*w(a). Suppose r(p) = 0. What is p?
-5, 0, 1
Let v(o) = o**2 + 4*o - 2. Let h be v(-5). Suppose 2*l - 21 + 6 = h*q, 5*q + 3 = -4*l. Find a such that 0 + 0*a + 1/2*a**4 + 1/2*a**2 + a**l = 0.
-1, 0
Let d = 6 - -1. Suppose 2*p = d*p. Factor 5*a**4 + 0 + 1/2*a**2 - 9/4*a**5 - 13/4*a**3 + p*a.
-a**2*(a - 1)**2*(9*a - 2)/4
Let w(f) = -2*f - 11. Let p be w(-6). Let n be (1 - 3)*p/(-3). Factor n*z**2 + 4/3 - 2*z.
2*(z - 2)*(z - 1)/3
Determine y, given that -1/4*y**3 + 1/4*y**2 + 3/4 + 5/4*y = 0.
-1, 3
Suppose -2*b = 2*b - g - 53, -4*g + 22 = 2*b. Let m = b - 10. Find h such that h**2 + 4*h**m + 2*h**2 - h**3 = 0.
-1, 0
Let j = -16 + 11. Let r(v) = v**3 + 5*v**2 - v - 3. Let z be r(j). Factor -1/3*d**4 + 1/3*d**z + 0 - 1/3*d + 1/3*d**3.
-d*(d - 1)**2*(d + 1)/3
Let f(a) be the second derivative of 0 + 1/5*a**3 - 9/10*a**2 - 1/60*a**4 - 3*a. Suppose f(t) = 0. What is t?
3
Suppose -3 = -3*b + 3. Let j(z) be the third derivative of 0*z**5 + 0*z**4 + 0*z + 0*z**3 + 1/30*z**6 + 0 - z**b + 5/48*z**8 + 4/35*z**7. Factor j(g).
g**3*(5*g + 2)*(7*g + 2)
Let b(n) be the second derivative of 3*n**5/5 - 7*n**4/4 - n**3 + 6*n. Solve b(c) = 0.
-1/4, 0, 2
Let p(i) be the second derivative of -9*i**5/110 + 10*i**4/33 - 13*i**3/33 + 2*i**2/11 - 37*i. Suppose p(z) = 0. Calculate z.
2/9, 1
Let m(r) = -4*r**5 - r**4 - 3*r**3 + r**2 + r - 3. Let f(b) = -b**5 - b**4 - b**3 + b**2 - 1. Let a(y) = -3*f(y) + m(y). Suppose a(w) = 0. What is w?
-1, 0, 1
Let p(h) = -2*h**3 - h**2. Let r be p(-1). Let z(m) = m**2 + 1. Let f(n) = -n**3 - 2*n**2 - 2*n + 1. Let g(w) = r*z(w) - f(w). Factor g(q).
q*(q + 1)*(q + 2)
Let c(r) be the third derivative of r**5/60 + r**4/8 - 2*r**3/3 + 25*r**2 + 1. Solve c(i) = 0.
-4, 1
Let w(u) = -3*u - 3. Let g be w(-2). Let y(x) be the first derivative of 4/27*x**g + 0*x + 1/18*x**4 + 1/9*x**2 + 3. Let y(t) = 0. Calculate t.
-1, 0
Let z(f) be the third derivative of f**7/70 + f**6/8 + 9*f**5/20 + 7*f**4/8 + f**3 + 8*f**2. Factor z(l).
3*(l + 1)**3*(l + 2)
Let u(y) be the first derivative of y**6/12 - 2*y**5/5 + 3*y**4/4 - 2*y**3/3 + y**2/4 + 2. Let u(o) = 0. Calculate o.
0, 1
Let a(f) be the third derivative of f**8/784 + 3*f**7/490 - f**6/280 - 3*f**5/140 - 7*f**2. Determine m so that a(m) = 0.
-3, -1, 0, 1
Let r(h) be the third derivative of h**9/6048 - h**8/7560 - h**7/1890 - h**5/30 - 2*h**2. Let b(l) be the third derivative of r(l). Factor b(c).
2*c*(3*c - 2)*(5*c + 2)/3
Let l(z) be the second derivative of -z**5/4 + z**4/3 - 2*z**3/15 - 4*z. Factor l(i).
-i*(5*i - 2)**2/5
Let h be 294/(-77) + (-6 - -10). Let 0 + h*x**2 + 0*x + 0*x**3 - 2/11*x**4 = 0. Calculate x.
-1, 0, 1
Suppose -5*c + 3*x - 8*x = 35, -3*c + 5*x = 13. Let b(i) = -i**3 - i**2 - i - 1. Let d(k) = -5*k**3 - 10*k**2 - k - 8. Let l(p) = c*b(p) + d(p). Factor l(q).
(q - 2)*(q - 1)**2
Factor o**3 + o**2 - 2*o**2 - 4*o**4 - 3*o**2 - 9*o**3.
-4*o**2*(o + 1)**2
Let s = 5/34 - -6/17. Let t = 141/2 - 69. Factor 1/2 + t*c**2 + 3/2*c + s*c**3.
(c + 1)**3/2
Let q(a) be the third derivative of a**10/75600 + a**9/30240 + a**5/60 - 3*a**2. Let f(w) be the third derivative of q(w). Find z, given that f(z) = 0.
-1, 0
Let b(a) = -a + 5. Let f be b(5). Let w(x) be the first derivative of f*x - 2 + 0*x**3 - 1/2*x**2 + 1/4*x**4. Suppose w(v) = 0. What is v?
-1, 0, 1
Let r(z) be the third derivative of z**9/18144 - z**8/3360 + z**7/1680 - z**6/2160 - 7*z**3/6 - 3*z**2. Let n(t) be the first derivative of r(t). Factor n(a).
a**2*(a - 1)**3/6
Let r = -19 - -19. Suppose 3*z = 4*t - 14, -7 = -2*z + z - t. Factor -1/2*g**z - g + r.
-g*(g + 2)/2
Factor -f**4 + 0*f**2 + 12*f**2 + 9*f**4 - 36*f**3 + 7*f**4.
3*f**2*(f - 2)*(5*f - 2)
Let w = 7267/42 - 173. Let j(r) be the second derivative of 2/7*r**2 - w*r**4 + 0 + r - 1/21*r**3. Solve j(d) = 0 for d.
-2, 1
Let h(l) be the first derivative of -l**6/9 + 4*l**5/15 + 10*l**4/3 - 16*l**3/9 - 128*l**2/3 - 256*l/3 - 27. Factor h(m).
-2*(m - 4)**2*(m + 2)**3/3
Suppose 2*o = o + 2. Let r(u) be the first derivative of 0*u - 2/15*u**5 + 0*u**o + 1/3*u**4 - 2/9*u**3 + 1. Factor r(p).
-2*p**2*(p - 1)**2/3
Let l = 62/335 - -1/67. Factor -1/5*t**5 - l*t + 0*t**4 + 2/5*t**3 + 0*t**2 + 0.
-t*(t - 1)**2*(t + 1)**2/5
Let n(s) = s**3 - s**2 - 2. Let r be n(2). Let m = -2/29 + 33/58. Suppose 0 - 1/4*z + m*z**r + 1/4*z**5 + 0*z**3 - 1/2*z**4 = 0. Calculate z.
-1, 0, 1
Let f(y) be the first derivative of y**5/80 - y**4/8 - 7*y**2/2 + 7. Let k(z) be the second derivative of f(z). Suppose k(s) = 0. What is s?
0, 4
Factor 5*a - 9*a - 10*a**4 - 2*a**5 - 18*a**3 - 1 - 14*a**2 + 1.
-2*a*(a + 1)**3*(a + 2)
Let q(d) = 18*d**2 + 12*d - 23. Let r(u) = -6*u**2 - 4*u + 8. Suppose 6 = 4*y - 3*y. Let a(b) = y*q(b) + 17*r(b). Factor a(k).
2*(k + 1)*(3*k - 1)
Suppose -x = 5*q + 270, 3*q - 4*x = 29 - 191. Let w be 16/18 - (-12)/q. Factor -w*d - 10/9*d**2 + 4/9.
-2*(d + 1)*(5*d - 2)/9
Let k(a) be the third derivative of a**6/280 + 3*a**5/140 - 11*a**2. Factor k(g).
3*g**2*(g + 3)/7
Suppose -2*q + 18 = -3*r - q, -5*q = 4*r + 5. Let k(d) = d**2 + 5*d + 3. Let x be k(r). Solve -2*s + s**2 + x - 2*s + 1 = 0.
2
Factor -73*k**2 + 139*k**2 - 71*k**2.
-5*k**2
Suppose 4*t = 1 + 3. Let o(h) be the first derivative of 1/6*h**3 + 1/4*h**2 - t + 0*h. Suppose o(r) = 0. Calculate r.
-1, 0
Let f(a) = 4*a**3 - 3*a**2 + 2*a. Let g(q) = 3*q**3 - 3*q**2 + 2*q. Suppose -5*m + 3 - 18 = 0. Let b(d) = m*g(d) + 2*f(d). Determine c, given that b(c) = 0.
0, 1, 2
Let d(o) be the first derivative of -o**5/25 - o**4/20 + o**3/5 + o**2/2 + 2*o/5 - 15. Factor d(v).
-(v - 2)*(v + 1)**3/5
Let p(l) be the third derivative of -l**7/420 - l**6/48 - l**5/20 + l**4/12 + 2*l**3/3 - 12*l**2. Factor p(j).
-(j - 1)*(j + 2)**3/2
Find l such that 13*l**2 + 11*l - 10*l - 15*l**2 + 11*l = 0.
0, 6
Let d(r) be the third derivative of -r**7/3780 + r**6/1080 + r**4/24 - 7*r**2. Let m(k) be the second derivative of d(k). Find g, given that m(g) = 0.
0, 1
Let a(v) = -v**4 + 4*v**3 - v**2 + 3*v - 3. Let x(r) = -r**4 + 4*r**3 - 2*r**2 + 2*r - 2. Let d(z) = 4*a(z) - 6*x(z). Factor d(h).
2*h**2*(h - 2)**2
Let d(x) = -17*x - 49. Let t be d(-3). Find s, given that 0 + 1/2*s + 0*s**t - 1/2*s**3 = 0.
-1, 0, 1
Solve -8/11 - 14/11*j**2 + 32/11*j = 0.
2/7, 2
Let s be 0 + (1 - 0) + -6. Let z(j) = -j - 2. Let g be z(s). Factor -q**g + 2 + q - 2*q**2 + q**3 - q**3.
-(q - 1)*(q + 1)*(q + 2)
Let t(u) be the third derivative of -u**6/40 + u**5/20 - 9*u**2. Find x, given that t(x) = 0.
0, 1
Let g(l) be the second derivative of l**7/14 + 3*l**6/10 + 3*l**5/10 + 2*l + 9. Factor g(a).
3*a**3*(a + 1)*(a + 2)
Let l = -21 - -21. Suppose -x = -2*n + 3*n, -5*n + 3*x = l. Factor n + 2/7*v**2 - 4/7*v.
2*v*(v - 2)/7
Let i(x) be the third derivative of -x**7/525 - x**6/300 + x**5/75 - 14*x**2. Factor i(p).
-2*p**2*(p - 1)*(p + 2)/5
Suppose -16*a + 20*a - 16 = 0. Suppose -5*w = -10, 6 = -a*k - 0*k + 3*w. Factor 0 + 2/7*y**5 + k*y**2 + 0*y**4 - 2/7*y**3 + 0*y.
2*y**3*(y - 1)*(y + 1)/7
Let k be (-12)/8*12/(-27). Let i(g) be the second derivative of 1/40*g**5 - 3*g + 0 + 5/24*g**4 + k*g**3 + g**2. Determine h so that i(h) = 0.
-2, -1
Factor 3*a + 8 + 6*a - 3 + 1 + 3*a**2.
3*(a + 1)*(a + 2)
Let b = -44/111 - -1667/3552. Let u(l) be the third derivative of 0*l + 0 + b*l**4 - l**2 - 1/12*l**3 + 1/120*l**5 - 7/480*l**6. Factor u(g).
-(g - 1)*(g + 1)*(7*g - 2)/4
Let q = -5/7 - -22/21. Let z(l) = l**3 - l**2 - 12*l + 21. Let x be z(3). Factor q - i - 1/3*i**x + i**2.
-(i - 1)**3/3
Let z(a) = a**3 + a**2. Let p(g) = g**4 - g**3 + 13*g**2 - 7*g + 2. Suppose 12 = -2*b + b. Let x(c) = b*z(c) + 3*p(c). Determine m, given that x(m) = 0.
1, 2
Factor -96/7*d**4 + 0 + 16*d**3 - 38/7*d**2 + 4/7*d.
-2*d*(3*d - 2)*(4*d - 1)**2/7
Suppose l + 5 = 10. Suppose 5*a - 35 = 3*f + 2*f, l*f = 2*a - 29. Factor 0*o**a + 2/5*o**3 - 4/5 - 6/5*o.
2*(o - 2)*(o + 1)**2/5
Let u be 212/