 + 0 + 2/5*c**2.
2*c**2*(c + 1)/5
Suppose 4*g + 2 = 2*b - 0, 2*g + b - 1 = 0. Let x = 2 + -5/3. Suppose -x*u**2 + g*u + 0 = 0. Calculate u.
0
Let r be (1 + -2)/(-1)*2. Factor -b**3 + 0*b**2 + r*b**2 + 0*b**5 - 2*b**4 + b**5.
b**2*(b - 2)*(b - 1)*(b + 1)
Let m(r) = r**3 + 5*r**2 - r - 1. Let o be m(-5). Determine q, given that 3*q**3 - q + 6 - 8 + o*q**2 + 0*q**2 - 4*q = 0.
-2, -1/3, 1
Let z(u) = 10*u**4 - 5*u**2 - 5*u + 5. Let s(f) = 11*f**4 - 4*f**2 - 6*f + 5. Let y(n) = -5*s(n) + 6*z(n). Find g such that y(g) = 0.
-1, 1
Let b be 6/(-15) + (-104)/(-10). Suppose -5*g = -3*u + 1, 4*u + 4*g - 2 - b = 0. Let -4/5*p + 2/5*p**u + 0 = 0. What is p?
0, 2
Let f(h) be the second derivative of -h**4/60 + h**3/15 - h**2/10 + 2*h. Factor f(v).
-(v - 1)**2/5
Factor 0 - 2/5*t - 6/5*t**3 - 6/5*t**2 - 2/5*t**4.
-2*t*(t + 1)**3/5
Suppose -3*y - 6 = 0, -5*y + 2*y = -4*q + 22. Let k be 110/(-6)*q/(-30). Factor 2/3*s**5 - 2*s**2 - k*s**4 + 10/3*s**3 + 4/9*s + 0.
2*s*(s - 1)**3*(3*s - 2)/9
Suppose -2*u - 3*l + 1718 = 0, -3*u - 2*l = -0*u - 2572. Let v = u + -7672/9. Factor 0*j - 2/9*j**4 + 0*j**3 - v + 16/9*j**2.
-2*(j - 2)**2*(j + 2)**2/9
Let r(g) be the first derivative of 1/6*g**3 - 1/24*g**4 - 1/4*g**2 - 5 + 1/6*g. Solve r(l) = 0 for l.
1
Let f(x) be the third derivative of -5*x**8/2856 + x**7/105 - 7*x**6/340 + 11*x**5/510 - x**4/102 - 5*x**2 + 7*x. Solve f(s) = 0 for s.
0, 2/5, 1
Suppose 0 = 9*z + 2*z - 44. Let n(f) be the second derivative of 2*f + 8/9*f**3 + 17/36*f**z + 1/12*f**5 + 0 + 2/3*f**2. Factor n(h).
(h + 1)*(h + 2)*(5*h + 2)/3
Suppose -5*m = 3*k - 25, k = 3*m - 3*k + 14. Solve -8*g - 8*g**2 - 3*g**4 - 1 - 22*g**3 + 29*g**m + 11*g**4 + 2 = 0 for g.
1/4, 1/2, 1
Factor 11/3*s**3 + 7/3*s**5 + 0*s + 0 + 16/3*s**4 + 2/3*s**2.
s**2*(s + 1)**2*(7*s + 2)/3
Factor 0*q**3 + 1 - 8/3*q - 1/3*q**4 + 2*q**2.
-(q - 1)**3*(q + 3)/3
Let z(g) be the first derivative of -g**4/12 - g**3/9 + g**2/6 + g/3 - 35. Factor z(u).
-(u - 1)*(u + 1)**2/3
Suppose 7*i = 12*i + 280. Let r be ((-28)/(-6))/(i/(-42)). Factor -s**3 - s**4 + 4*s**2 - r*s + 1 + 1/2*s**5.
(s - 1)**4*(s + 2)/2
Let j(p) = -p. Let d be (-4)/10 + (-115)/25. Let o be j(d). Find x such that -3*x**2 + 0*x - x**4 - o*x + 4*x + 0*x**3 - 3*x**3 = 0.
-1, 0
Let g = 19/6 + -5/3. Suppose 4*l = 3*k + 23, -2*k + 7*k - 5 = -2*l. Factor -3/2*i - 1/2 + g*i**4 + i**3 - i**2 + 1/2*i**l.
(i - 1)*(i + 1)**4/2
Let y(g) = 32*g**3 + 60*g**2 + 18*g - 7. Let h(p) = 31*p**3 + 60*p**2 + 19*p - 6. Let s(k) = -3*h(k) + 4*y(k). What is u in s(u) = 0?
-1, 2/7
Let z = 7/3 + -13/6. Let h(q) be the second derivative of -q + 0 + 2/3*q**3 + q**2 + z*q**4. Suppose h(f) = 0. Calculate f.
-1
Let w(c) be the third derivative of c**9/108 - c**8/14 + 6*c**7/35 - 4*c**6/45 - c**3/3 - 4*c**2. Let z(m) be the first derivative of w(m). Factor z(o).
4*o**2*(o - 2)**2*(7*o - 2)
Let s be (-6)/8*(0 + (-14)/21). Let 0 + s*v**2 + v = 0. What is v?
-2, 0
Let i be 46/10 + 8/20. Factor q**2 - 4*q**2 + i*q**2 - 10*q + 4*q + 4.
2*(q - 2)*(q - 1)
Let y(l) = l**3 + 8*l**2 + 7*l. Let c be y(-7). Let j(t) be the first derivative of -2*t**2 + c*t - 2*t**5 - 1 + t**4 + 10/3*t**3. Let j(x) = 0. Calculate x.
-1, 0, 2/5, 1
Let f(v) = -v**3 + 7*v**2 - 25*v + 5. Let u(r) = 5*r**2 + 3*r - 3*r**2 + 2 - 11*r. Let n(k) = 4*f(k) - 14*u(k). Find m such that n(m) = 0.
-2, 1
Suppose -8*o - 2/3*o**3 + 16/3 + 4*o**2 = 0. Calculate o.
2
Factor 14*y + 1/2*y**5 + 25/2*y**3 - 4 - 19*y**2 - 4*y**4.
(y - 2)**3*(y - 1)**2/2
Factor 24*i + 5*i**2 - 5*i**2 + 3*i**2 + 48 + 0*i**2.
3*(i + 4)**2
Let r(a) be the second derivative of 0 + 2*a - 1/10*a**5 - 1/7*a**3 + 2/7*a**4 - 2/7*a**2. Factor r(j).
-2*(j - 1)**2*(7*j + 2)/7
Determine s so that 3*s**4 - s - 4*s**5 + s + s**5 = 0.
0, 1
Let l be 2 - (-1 + 3 - 6). Suppose 2*k = -2 + l. Find z such that 2/5*z**3 + 0 - 4/5*z**4 + 2/5*z**5 + 0*z + 0*z**k = 0.
0, 1
Let r(g) be the second derivative of 0 + 2/3*g**3 - 5*g - 2*g**2 - 1/12*g**4. Factor r(v).
-(v - 2)**2
Let w(s) be the second derivative of -s**4/4 - s**3 - 3*s**2/2 - 19*s + 1. Factor w(j).
-3*(j + 1)**2
Let d(c) = -3*c**4 - 29*c**3 - 19*c**2 - 3*c. Let z(y) = -8*y**4 - 72*y**3 - 48*y**2 - 8*y. Let h(r) = -12*d(r) + 5*z(r). Factor h(u).
-4*u*(u + 1)**3
Let j(g) = -3*g**3 - g**2 - 5*g + 5. Suppose 4*s + 2 + 22 = 0. Let f(u) = -2*u**3 - 3*u + 3. Let t(m) = s*j(m) + 10*f(m). Determine w, given that t(w) = 0.
0, 3
Suppose -1/2*b**3 - 4*b + 7/2*b**2 - 8 = 0. Calculate b.
-1, 4
Let s(l) = -l**2 - 11*l - 8. Let w be s(-10). Factor -2/3*p + 2/3*p**w + 0.
2*p*(p - 1)/3
Let i(o) be the second derivative of o**7/6300 - o**4/4 + 2*o. Let z(h) be the third derivative of i(h). Determine v, given that z(v) = 0.
0
Let z(i) be the second derivative of i**9/1512 + i**8/420 + i**7/420 - 7*i**3/6 + 7*i. Let m(g) be the second derivative of z(g). Factor m(b).
2*b**3*(b + 1)**2
Let y(p) = -4*p**3 - p**2 + p + 1. Let d be y(-1). Let j be 3 - d*(-3)/(-9). Solve 5 + s**j + s - 5 = 0.
-1, 0
Let k = 209 + -626/3. Solve k*a**2 - 1/3 + 0*a = 0 for a.
-1, 1
Suppose -24 = -5*c + 16. Let k = c - 3. Let f**3 + 2*f - 4 - k*f**3 + 0 + 2*f**3 + 4*f**2 = 0. What is f?
-1, 1, 2
Let j = 35 + -35. Let m(v) be the second derivative of -1/15*v**3 + 1/50*v**5 - 1/30*v**4 - 3*v + j + 1/5*v**2. Factor m(q).
2*(q - 1)**2*(q + 1)/5
Let m(y) = 5*y - 27. Let g be m(6). Let o(u) be the second derivative of 4*u + 1/5*u**2 + 0 + 2/15*u**g + 1/30*u**4. Factor o(j).
2*(j + 1)**2/5
Factor o**2 - 47*o**3 + 46*o**3 + 0*o**2.
-o**2*(o - 1)
Let l(o) be the third derivative of o**7/315 + o**6/180 + 2*o**2. Solve l(w) = 0.
-1, 0
Suppose q + 3*d = 6*d - 6, 6 = -4*q + 3*d. Solve q - 2/7*h - 2/7*h**2 = 0.
-1, 0
Let n = 3137/637894 + 3/2038. Let y = n + 2185/939. Factor -o**4 + 0 + y*o**3 + 1/3*o - 5/3*o**2.
-o*(o - 1)**2*(3*o - 1)/3
Let r(i) be the second derivative of 0*i**2 + 1/6*i**3 + 0 + 1/4*i**4 + 4*i + 3/20*i**5 + 1/30*i**6. Determine v, given that r(v) = 0.
-1, 0
Let i(g) be the first derivative of g**7/1120 - g**6/480 + g**3/3 - 3. Let p(j) be the third derivative of i(j). Solve p(c) = 0 for c.
0, 1
Let y = 32/9 - 61/18. Let p(l) be the second derivative of 0*l**3 + 2*l - y*l**4 + 0 + 0*l**2. Let p(r) = 0. What is r?
0
Let i = -108 + 974/9. Factor 2/3*n**3 + 0 + 2/3*n**2 + i*n**4 + 2/9*n.
2*n*(n + 1)**3/9
Let n(s) be the first derivative of 5*s**4/4 - 5. Solve n(q) = 0.
0
Let u(s) be the first derivative of -2*s**3/21 + 2*s**2/7 - 24. Factor u(b).
-2*b*(b - 2)/7
Factor 1/5 + 1/5*n**2 - 2/5*n.
(n - 1)**2/5
Let n = 752 + -3748/5. Suppose -n*u + 18/5 + 2/5*u**2 = 0. What is u?
3
Factor 142 - 142 + 7*b**3 + 3*b + 3*b**5 + 12*b**2 + 12*b**4 + 11*b**3.
3*b*(b + 1)**4
Let u(m) = -9*m**4 + 3*m**3 + 12*m**2 - 9*m - 3. Let z(a) = -9*a**4 + 4*a**3 + 11*a**2 - 8*a - 2. Let j(p) = 2*u(p) - 3*z(p). Factor j(n).
3*n*(n - 1)*(n + 1)*(3*n - 2)
Suppose 2*f - 25 = -3*f, 3*q + 4 = 2*f. Let y(w) be the first derivative of -q + 1/4*w**4 + 5/12*w**3 + 0*w + 1/8*w**2. Solve y(s) = 0 for s.
-1, -1/4, 0
Suppose 15 = 4*c + 4*b - 1, -b = -4. Factor 3/4*n**3 + 1/4*n + c + n**2.
n*(n + 1)*(3*n + 1)/4
Let q = -58 - -60. Let i(u) be the first derivative of 1/4*u - 3/8*u**2 - 1/16*u**4 + 1/4*u**3 + q. Find t such that i(t) = 0.
1
Let k(d) be the first derivative of d**8/6720 - d**7/3360 - d**6/1440 + d**5/480 + d**3 - 2. Let j(m) be the third derivative of k(m). What is t in j(t) = 0?
-1, 0, 1
Let a + 23*a + 98*a**2 + 0 + 2 + 4*a = 0. Calculate a.
-1/7
Let i(m) = m**2 + 0 - 5 + 5 - 3*m. Let u(v) = v**2 - 4*v + 1. Let c(d) = -6*i(d) + 4*u(d). Factor c(n).
-2*(n - 2)*(n + 1)
Suppose -j + 4 = -0. Factor -4*x**2 - 42*x + 42*x + 4*x**j.
4*x**2*(x - 1)*(x + 1)
Suppose -5 = -2*k - 1. Suppose -4*j + 4*y = -20, -2*j + 0*j - 4*y = -4. Find g such that -3*g**3 - 5*g**4 - 2*g**2 + g - 2*g + 7*g**k + j*g**5 = 0.
-1, 0, 1/4, 1
Let q(f) = -f**4 - f**3 - f**2. Let z(r) = 6*r**4 + 9*r**3 + 12*r**2. Let m(x) = -9*q(x) - z(x). Find y, given that m(y) = 0.
-1, 0, 1
Let s(o) = 1. Let u(f) = -f**2 + 2*f + 1. Let r(v) = 2*s(v) + u(v). Factor r(y).
-(y - 3)*(y + 1)
Let g(f) be the first derivative of -3/8*f**4 + 0*f - 1/10*f**5 - 1/3*f**3 + 0*f**2 - 6. Factor g(t).
-t**2*(t + 1)*(t + 2)/2
Let y be 2*((-91)/(-14) + -5). Suppose 0*n - 4/7*n**2 + 2/7*n**y + 0 = 0. Calculate n.
0, 2
Let d(c) be the sec