*(7*n - 2)/4
Let p = 1/230 + 917/690. Factor -2*b + 10/3*b**2 - p.
2*(b - 1)*(5*b + 2)/3
Let v(c) be the second derivative of 0*c**4 + 0*c**2 + 3/10*c**5 - 1/15*c**6 + 0 - 4/3*c**3 + 6*c. Determine b, given that v(b) = 0.
-1, 0, 2
Let o(q) be the third derivative of q**7/140 - q**6/80 - 12*q**2. Factor o(y).
3*y**3*(y - 1)/2
Let d(x) = 3*x**4 + 5*x**3 + 7*x**2 - 5*x - 5. Let n(w) = 4*w**4 + 7*w**3 + 10*w**2 - 7*w - 7. Let m(a) = -7*d(a) + 5*n(a). Solve m(y) = 0.
-1, 0, 1
Let x = 899/48 + -56/3. Let w(t) be the second derivative of 0*t**2 + 3*t + x*t**4 + 0 - 1/12*t**3 - 1/80*t**5. Factor w(y).
-y*(y - 2)*(y - 1)/4
Let l(z) = 2*z**2 - 20*z. Let s be l(10). Let o(k) be the second derivative of s - 3/2*k**2 + 1/4*k**4 - 2*k**3 + 3*k + 3/5*k**5. Factor o(g).
3*(g - 1)*(g + 1)*(4*g + 1)
Let r be ((-1)/(-12))/(0 - 6/(-24)). Solve z + z**2 + 1/3 + r*z**3 = 0 for z.
-1
Let q(u) be the third derivative of u**6/240 - u**4/48 - 10*u**2. Factor q(l).
l*(l - 1)*(l + 1)/2
Let s(v) = 2*v**3 - 4*v**2 - 5*v + 4. Let d(z) = 4*z**3 - 8*z**2 - 9*z + 8. Let y(l) = -3*d(l) + 5*s(l). Factor y(w).
-2*(w - 2)*(w - 1)*(w + 1)
Let x(l) be the first derivative of 0*l**2 - 2/5*l - 2/25*l**5 + 0*l**4 + 4/15*l**3 + 3. Determine y so that x(y) = 0.
-1, 1
Let b = 2/155 + 151/310. Suppose 1/2*n**2 - b + 0*n = 0. What is n?
-1, 1
Let s(g) be the first derivative of -g**6/21 + 12*g**5/35 - 9*g**4/14 + 8*g**3/21 - 25. Factor s(h).
-2*h**2*(h - 4)*(h - 1)**2/7
Let i(w) be the second derivative of 1/8*w**3 + 0 - 1/80*w**5 - 1/4*w**2 + 0*w**4 + 3*w. Factor i(b).
-(b - 1)**2*(b + 2)/4
Let s(x) be the second derivative of x**8/840 + x**7/420 - x**6/180 - x**5/60 - x**3/6 + 2*x. Let g(f) be the second derivative of s(f). Factor g(h).
2*h*(h - 1)*(h + 1)**2
Factor -5/6*y**3 + 1/3*y**2 + 2/3*y**4 + 0 - 1/6*y**5 + 0*y.
-y**2*(y - 2)*(y - 1)**2/6
Determine z so that -2/3*z**4 - 14/3*z**3 - 10*z**2 + 0 - 6*z = 0.
-3, -1, 0
Let l(w) be the first derivative of -2 + 1/50*w**5 + 2*w + 1/3*w**3 - 2/15*w**4 - 2/5*w**2. Let p(v) be the first derivative of l(v). Factor p(x).
2*(x - 2)*(x - 1)**2/5
Let j(m) be the second derivative of m**10/60480 + m**9/15120 - m**7/2520 - m**6/1440 + m**4/12 + 2*m. Let b(h) be the third derivative of j(h). Factor b(l).
l*(l - 1)*(l + 1)**3/2
Determine b, given that 1/4*b**2 + 0 + b = 0.
-4, 0
Let p(q) be the second derivative of -q**6/420 + q**5/105 + q**4/84 - 2*q**3/21 + 7*q**2/2 + 7*q. Let o(w) be the first derivative of p(w). Factor o(t).
-2*(t - 2)*(t - 1)*(t + 1)/7
Let 6/5*s**2 - 6/5*s**3 + 3/5*s + 3/5*s**5 - 3/5 - 3/5*s**4 = 0. What is s?
-1, 1
Let a(w) be the third derivative of w**8/1008 + w**7/315 + w**6/360 - 18*w**2. Let a(v) = 0. Calculate v.
-1, 0
Let y(c) = -c**2 - c. Suppose 0 = 2*d - 7 - 1. Let r(a) = -6*a**2 - 4*a. Let x(z) = d*y(z) - r(z). Solve x(f) = 0 for f.
0
Let d = -6836/5 - -1372. Let x = 101/20 - d. Determine q so that 1/4*q**3 - 1/2*q**2 + x*q + 0 = 0.
0, 1
Let r(d) be the third derivative of 0*d + 0*d**3 + 1/30*d**5 + 1/15*d**6 + d**2 + 0 - 1/6*d**4 - 1/35*d**7. Factor r(f).
-2*f*(f - 1)**2*(3*f + 2)
Let r(x) be the third derivative of -x**7/735 + 2*x**5/105 + 11*x**2. Factor r(g).
-2*g**2*(g - 2)*(g + 2)/7
Let c(b) = -b**5 - 4*b**4 - b**3 - 6*b**2. Let a(j) = j**4 + j**2. Let q(p) = -6*a(p) - c(p). Solve q(s) = 0 for s.
0, 1
Let -4 + 6*j + 2*j + 2*j**2 - 6*j = 0. What is j?
-2, 1
Let d(l) be the first derivative of l**8/5880 - l**6/630 + l**4/84 + 4*l**3/3 - 3. Let c(k) be the third derivative of d(k). Factor c(m).
2*(m - 1)**2*(m + 1)**2/7
Let f(k) = 3*k**2 + 11*k + 13. Let m(s) = -s**2 - 5*s - 7. Let v(h) = 3*f(h) + 5*m(h). Factor v(g).
4*(g + 1)**2
Suppose 6*l**2 + 2*l**5 + 6*l**2 + 2*l**5 + 20*l**4 + 28*l**3 = 0. What is l?
-3, -1, 0
Factor 49/4*x**5 + 0*x + 0 - 63/2*x**4 + 15*x**3 - 2*x**2.
x**2*(x - 2)*(7*x - 2)**2/4
Let s = 36 + -26. Factor 9*o + 21*o**2 - 24*o**2 + s - 9*o**3 - 3*o**4 - 4.
-3*(o - 1)*(o + 1)**2*(o + 2)
Factor 9*g - 39*g - 4*g**3 + 14*g + 18*g**2 + 2*g**2.
-4*g*(g - 4)*(g - 1)
Let y(f) be the first derivative of -9*f**4/16 - 2*f**3 - 13*f**2/8 - f/2 - 5. Solve y(d) = 0.
-2, -1/3
Determine l so that -3/4*l - 3/4*l**2 - 1/4*l**3 - 1/4 = 0.
-1
Let g(b) = -b**3 - 2*b**2 + 2. Let c be g(-2). Factor -2*k**2 - 3*k**3 + c*k**3 + 2*k**3.
k**2*(k - 2)
Let k(u) = 3*u**5 - 2*u**4 + u**3 - 2*u**2 - 2*u. Let f(c) = 7*c**5 - 5*c**4 + 3*c**3 - 5*c**2 - 5*c. Let o(s) = 2*f(s) - 5*k(s). Factor o(n).
-n**3*(n - 1)*(n + 1)
Let f(d) be the second derivative of d**7/14 + d**6/2 + 3*d**5/5 - 12*d. Factor f(z).
3*z**3*(z + 1)*(z + 4)
Let z = 243/2 - 121. Find b, given that -z*b**2 + 0 + 1/2*b = 0.
0, 1
Find q, given that 5/2 - 5*q**2 + 5/2*q**4 + 5*q**3 - 5/2*q - 5/2*q**5 = 0.
-1, 1
Let r be -1 - 2 - -2 - 19. Let x be r/(-175)*(-45)/(-6). Find n, given that 2/7*n**2 - 2/7*n**5 + 0*n - 6/7*n**3 + x*n**4 + 0 = 0.
0, 1
Let m(a) be the second derivative of a**7/105 + 4*a**6/75 + a**5/10 + a**4/15 + 11*a. Factor m(j).
2*j**2*(j + 1)**2*(j + 2)/5
Let o = -193/3 + 66. Let w(d) = -d**3 - 2*d**2 + 3*d. Let r be w(-3). Factor r - o*c**2 + 2/3*c.
-c*(5*c - 2)/3
Factor -8/5*o + 2/5*o**2 + 0.
2*o*(o - 4)/5
Determine j so that 0 + 4/3*j + 2/3*j**3 - 2*j**2 = 0.
0, 1, 2
Let n(t) be the second derivative of -3*t**5/160 - 7*t**4/16 - 25*t**3/16 - 9*t**2/4 - t + 13. Factor n(q).
-3*(q + 1)**2*(q + 12)/8
Let m(s) be the second derivative of s**4/66 + s**3/33 + 5*s. Solve m(n) = 0 for n.
-1, 0
Suppose -d + 3*d - 10 = 0. Let w(u) be the third derivative of u**2 + 0*u**6 + 1/210*u**7 + 0*u**4 + 0 + 0*u**d + 0*u + 0*u**3. Factor w(m).
m**4
Let i(y) be the first derivative of -y**5/180 - y**4/36 - y**3/18 + y**2/2 - 1. Let c(g) be the second derivative of i(g). Factor c(s).
-(s + 1)**2/3
Factor -3*v**4 + 0*v**4 - 3*v**3 + 0*v**3 + 0*v**3.
-3*v**3*(v + 1)
Suppose 36 = 18*q - 0. Factor -2*p**q - 16/11*p - 6/11*p**3 + 8/11.
-2*(p + 2)**2*(3*p - 1)/11
Let n be 130/18 - 20/90. Solve -3*f**4 - 2*f**2 - 2*f**2 + n*f**4 = 0 for f.
-1, 0, 1
Let r(j) = -9*j**2 + 7*j + 4. Let s(p) = -p**2 - p. Let t(q) = -r(q) - s(q). Factor t(n).
2*(n - 1)*(5*n + 2)
Let x = 15 - 8. Let h(n) be the third derivative of -n**2 - 1/30*n**x + 3/20*n**5 + 0 + 1/24*n**6 - 1/3*n**3 - 5/24*n**4 + 0*n. Factor h(d).
-(d - 1)**2*(d + 1)*(7*d + 2)
Let o(s) = -2*s**3 + 3*s - 3. Let r(c) = -7*c**3 + 11*c - 11. Let n(j) = -22*o(j) + 6*r(j). Factor n(q).
2*q**3
Factor -76*b**3 + 150*b**3 - b**4 - 76*b**3 - b**2.
-b**2*(b + 1)**2
Suppose 0 = -2*j + 5*w + 51 - 18, -5*j + 4*w = -40. Solve -8*c**2 + 2*c**2 - 8*c + 0*c**j + 4*c**3 + 2*c**4 + 8 = 0 for c.
-2, 1
Suppose -17 = -4*b - 5. Let k = -5 - -7. Factor -12*q**k + 0 + 21/2*q**b + 49/2*q**4 + 2*q.
q*(q + 1)*(7*q - 2)**2/2
Find q, given that 4/5*q**2 + 0*q - 6/5*q**3 + 0 - 2*q**4 = 0.
-1, 0, 2/5
Suppose 2*g + 5*y = -8, -5*g + y - 1 + 8 = 0. Suppose -g - 1 = -f. Suppose -5*a - f*a**3 + a**3 - 1 + 2*a - 3*a**2 = 0. What is a?
-1
Factor -2*o - 1/6*o**2 - 11/6.
-(o + 1)*(o + 11)/6
Let i = 16 + -13. Let f(w) be the second derivative of -1/2*w**i + 1/2*w**2 + 1/4*w**4 + 4*w - 1/20*w**5 + 0. Find z such that f(z) = 0.
1
Let t be (18/(-192))/(2/104). Let n = -11/8 - t. Let 5/2*u + n*u**2 - 1 = 0. Calculate u.
-1, 2/7
Let h = -769/5 - -157. Find c such that -h*c**2 - 1/5 - 8/5*c = 0.
-1/4
Suppose -2*s - 2 + 10 = 0. Suppose -4*v + 11 = 2*l - 17, 0 = s*v - 3*l - 8. Factor 0*d**2 + 1/3*d**3 + 0 + 0*d + d**v + 4/3*d**4.
d**3*(d + 1)*(3*d + 1)/3
Let m(f) = f**2 - 3*f + 4. Let z(h) = h - 1. Let b(a) = m(a) + 4*z(a). Solve b(r) = 0 for r.
-1, 0
Let s(y) be the first derivative of -y**9/3024 + y**8/840 - y**6/180 + y**5/120 - 2*y**3/3 + 3. Let d(q) be the third derivative of s(q). Factor d(p).
-p*(p - 1)**3*(p + 1)
Let j = 28 - 111/4. Let y(r) be the first derivative of -1/2*r**2 - 1/3*r**3 + r - 1 + j*r**4. Factor y(h).
(h - 1)**2*(h + 1)
Let y be (-5 - (-1295)/252) + (-2)/(-18). Let j(d) = -d + 10. Let h be j(8). Factor 0 - 1/4*s - y*s**h.
-s*(s + 1)/4
Suppose -4/3*g**4 - 13/6*g**3 + 11/3*g**2 - 1/6*g**5 + 16/3*g - 16/3 = 0. Calculate g.
-4, -2, 1
Suppose 5*h + 4 = 29. Suppose y**5 - 1 + 1 + 3*y**3 - 6*y**4 + 2*y**h = 0. What is y?
0, 1
Let u(l) be the third derivative of l**7/490 - l**6/210 - 13*l**5/420 - l**4/28 - 12*l**2. Let u(g) = 0. Calculate g.
-1, -2/3, 0, 