- 2*i**3 + 2*i**4.
-2*i**3*(i + 1)
Let x(y) be the third derivative of -2*y**7/35 - y**6/15 + y**5/5 + y**4/3 - 6*y**2. Find p such that x(p) = 0.
-1, -2/3, 0, 1
Let k(o) = o**2 + 10*o + 12. Let r be k(-9). Let l(u) = -u + 3. Let a be l(r). Solve -2/7*d**3 - 4/7*d**4 + 0*d - 2/7*d**5 + 0 + a*d**2 = 0.
-1, 0
Factor -2/9*p**2 - 4*p - 18.
-2*(p + 9)**2/9
Let w(y) = -5*y + 57. Let v be w(11). Factor 0*q**3 + 1/2*q**5 + q**v - q**4 + 0 - 1/2*q.
q*(q - 1)**3*(q + 1)/2
Let i(k) = -6*k**4 - 3*k**3 + 3*k**2 + 3*k. Let y(x) = 17*x**4 + 8*x**3 - 10*x**2 - 8*x + 1. Let u(r) = 8*i(r) + 3*y(r). Suppose u(h) = 0. Calculate h.
-1, 1
Solve 27/2*d - 1 + 29/2*d**2 = 0.
-1, 2/29
Let f = 2524/7 + -360. Let 18/7*p**2 + 0 + f*p + 24/7*p**3 + 10/7*p**4 = 0. What is p?
-1, -2/5, 0
Let s(o) be the first derivative of o**4/28 + 2*o**3/21 - o**2/14 - 2*o/7 - 11. Solve s(z) = 0.
-2, -1, 1
Let q(t) be the first derivative of -1/3*t**2 + 4/3*t - 2/9*t**3 + 3. Factor q(p).
-2*(p - 1)*(p + 2)/3
Let y(k) be the first derivative of k**6/3 + 4*k**5/5 - 3*k**4/2 - 16*k**3/3 - 4*k**2 - 11. Suppose y(o) = 0. What is o?
-2, -1, 0, 2
Let q = 0 + 2. Factor 2*o**5 + 0*o**4 + q*o**5 - 2*o**3 + 7*o**4.
o**3*(o + 2)*(4*o - 1)
Let i(q) = 5*q**2. Suppose 0*x = x + 1. Let j be i(x). Solve t**3 - t**2 + j*t**3 + 4*t**3 + 5*t**2 = 0 for t.
-2/5, 0
Let z be 1 + -4 - (-49)/7. Factor -u - 1 + 2*u**2 - u**5 + u**z + 2*u**3 + 0*u**4 - 2*u**4 + 0*u**3.
-(u - 1)**2*(u + 1)**3
Let x(i) be the first derivative of -i**5/60 + i**2 + i - 2. Let r(z) be the first derivative of x(z). Let a(u) be the first derivative of r(u). Factor a(y).
-y**2
Let i = 185 - 182. Find p such that -4/3 + 10/3*p - 8/3*p**2 + 2/3*p**i = 0.
1, 2
Let j = 2/3611718689 + -105086567012530/67513857453477. Let s = -2/2077 - j. Factor 2/3*z**2 - s*z + 4/9.
2*(z - 2)*(3*z - 1)/9
Let w(p) be the second derivative of p**7/360 + p**6/144 - p**5/60 + p**4/4 - p. Let b(g) be the third derivative of w(g). Suppose b(i) = 0. What is i?
-1, 2/7
Let c(i) = 240*i**3 + 111*i**2 - 273*i - 177. Let j(b) = 15*b**3 + 7*b**2 - 17*b - 11. Let z(o) = 2*c(o) - 33*j(o). Suppose z(s) = 0. What is s?
-1, -3/5, 1
Let z(n) = 2*n + 0*n - 2 + 5 + 3. Let p be z(5). Let -p*b**4 + 2*b**2 + 2*b**2 + 4*b**5 + 2*b**3 + 6*b**5 = 0. Calculate b.
-2/5, 0, 1
Suppose 2*l + 5*a = -21, -5*l - 11 = 5*a + 4. Suppose l*i = 3*i. Solve i + 1/2*y**4 - 1/2*y**2 - 1/2*y + 1/2*y**3 = 0.
-1, 0, 1
Let t(m) be the first derivative of 1/9*m**3 + 0*m**2 + 0*m - 1/15*m**5 + 0*m**4 - 3. Suppose t(n) = 0. What is n?
-1, 0, 1
Suppose -10 = -4*p + s + 12, 3*p = 3*s + 12. Suppose -2*n = -5*n + p. Factor 3 - 3 + n*w**2 - 2.
2*(w - 1)*(w + 1)
Let f(x) = -3*x**4 - 23*x**3 - 28*x**2 + 20*x + 38. Let z(t) = 5*t**4 + 45*t**3 + 55*t**2 - 40*t - 75. Let q(j) = -5*f(j) - 2*z(j). Factor q(u).
5*(u - 1)*(u + 2)**3
Factor 6*z**2 + 6*z - 2*z**2 - 12 + 2*z.
4*(z - 1)*(z + 3)
Let d(j) be the second derivative of 3*j - 1/20*j**4 + 0 + 0*j**2 - 1/10*j**3. Find t such that d(t) = 0.
-1, 0
Let b be ((-15)/3)/(2/10). Let i = 25 + b. Find p, given that 0*p + 0*p**2 - 2/11*p**3 + i = 0.
0
Let d = 19/29 + 1/87. Find q such that 2/3*q**3 + 0*q**2 - d*q + 0 = 0.
-1, 0, 1
Let p(r) = r**2 + r + 1. Let q(b) = 2*b**2 + 12*b + 7. Let y(d) = 3*p(d) + q(d). Determine i, given that y(i) = 0.
-2, -1
Let d(l) be the second derivative of -2*l**7/35 - 13*l**6/75 + l**5/25 + 7*l**4/30 - 2*l**3/15 - l. Let d(z) = 0. What is z?
-2, -1, 0, 1/3, 1/2
Suppose -6*k - 11 = -41. Suppose -i + k = 2*h, 0 = i - 1. Factor 0 - 3*n**h + 3/2*n**3 + 3/2*n.
3*n*(n - 1)**2/2
Let z(i) be the first derivative of i**4/2 + 2*i**3 + 3*i**2 + 2*i - 15. Solve z(c) = 0 for c.
-1
Let r(l) be the first derivative of 1 + 2/3*l**2 + 1/6*l**4 + 2/3*l**3 + 0*l. Let r(j) = 0. Calculate j.
-2, -1, 0
Let l(a) be the third derivative of -a**7/105 + a**6/30 - a**4/6 + a**3/3 + 3*a**2. Factor l(p).
-2*(p - 1)**3*(p + 1)
Suppose d = 2*o - 2, -d + 3*d = -2*o + 14. Suppose 3*j - d*j = -4. Factor 3*h - 11*h**5 + 0*h**2 + 33*h**j - 19*h**3 + 3*h**2 - 8*h**3 - h**5.
-3*h*(h - 1)**3*(4*h + 1)
Let f(u) be the second derivative of u**5/5 - 2*u**4/3 + 2*u**3/3 - 17*u. Solve f(o) = 0.
0, 1
Let t be 111/(-3780)*34 + 1. Let g(k) be the third derivative of 0*k + 0*k**6 + 1/18*k**3 + 0*k**4 + t*k**7 - 3*k**2 + 0 - 1/90*k**5. Factor g(v).
(v - 1)**2*(v + 1)**2/3
Let h(y) = 5*y**2 - 5*y + 6 + 8*y**3 + y**3 - 8*y**3. Let z be h(-6). Factor z - 6/7*l**4 + 2/7*l**5 + 6/7*l**3 - 2/7*l**2 + 0*l.
2*l**2*(l - 1)**3/7
Determine f so that 5*f**2 - 3*f**3 - 4*f**2 + 2*f**2 + 3*f + 0*f**2 - 3 = 0.
-1, 1
Let v = -44 - -47. Factor 0 - 2/7*k**v - 2/7*k - 4/7*k**2.
-2*k*(k + 1)**2/7
Suppose -3*x - 4*l = 6, 0*x = -x - l - 3. Let v be x/12*1*2. Let d(s) = 4*s**2 + 3*s - 1. Let z(m) = m**2 + m. Let k(p) = v*d(p) + 3*z(p). Factor k(t).
-(t - 1)*(t + 1)
Let t = -1/12 + 1/3. Let 0 - 3/4*q**3 - q**2 - t*q = 0. Calculate q.
-1, -1/3, 0
Find w, given that 0 + 4/3*w**3 + 0*w - 1/3*w**2 - w**4 = 0.
0, 1/3, 1
Let i = -55 + 60. Factor -1/4*m**3 + 1/4*m**2 + 0*m + 1/4*m**i + 0 - 1/4*m**4.
m**2*(m - 1)**2*(m + 1)/4
Let z(x) = -x**4 + x**2 + x + 1. Suppose 2*s = 7 - 3. Let j(f) = -4*f**4 + 5*f**2 + 3*f + 2. Let n = -7 - -1. Let g(a) = n*z(a) + s*j(a). Factor g(r).
-2*(r - 1)**2*(r + 1)**2
Factor -1/2*i + 0 + 1/4*i**3 + 1/4*i**2.
i*(i - 1)*(i + 2)/4
Let t(s) be the first derivative of 2*s**5/25 + s**4/10 - 2*s**3/15 - s**2/5 - 10. Determine p so that t(p) = 0.
-1, 0, 1
Let r(n) be the first derivative of -n**4/10 + 2*n**3/15 + n**2/5 - 2*n/5 + 7. Find k such that r(k) = 0.
-1, 1
Let u(q) = -q. Let w be u(-2). Let x be w/(-21)*(-1 + -8). Factor x*b - 2/7 - 6/7*b**2 + 2/7*b**3.
2*(b - 1)**3/7
Suppose 52 = 26*r - 52. Factor 1/2 - o**r - 5/4*o + o**3 + 1/2*o**2 + 1/4*o**5.
(o - 2)*(o - 1)**3*(o + 1)/4
Suppose 5*v + 3*f = 2*v + 21, -3*v - 7 = -4*f. Factor 1 + 18*s - 19*s - v + s**2.
(s - 2)*(s + 1)
Let g = 203 + -292. Let p = g + 449/5. Factor -28/5*z**3 - 18/5*z - 32/5*z**2 - 2/5*z**5 - p - 12/5*z**4.
-2*(z + 1)**4*(z + 2)/5
Factor 8/3*l + 1/3*l**4 - 4/3 - 2/3*l**3 - l**2.
(l - 2)*(l - 1)**2*(l + 2)/3
Let u = 12 - 10. Let t = 5 - u. Find y such that t*y**4 - 9*y**3 + 9*y**2 - 4*y**4 + 4*y**4 - 3*y = 0.
0, 1
Suppose -i = -4*i - 5*z + 31, 30 = 5*i + 4*z. Factor 4*r**3 + 2*r**i - 4*r**3 - 2*r**3.
-2*r**2*(r - 1)
Let l be ((-64)/24)/2*1/(-6). Factor -4/9*t**2 + 2/9*t**4 + 0 + 0*t - l*t**3.
2*t**2*(t - 2)*(t + 1)/9
Let o be 6/(-9)*-1*3. Let x(n) be the first derivative of 2 + 0*n - 7/4*n**4 + n**o + 5/6*n**6 - n**3 + 3/5*n**5. What is a in x(a) = 0?
-1, 0, 2/5, 1
Let f = -1 - 2. Let p be ((-12)/f*1)/1. Factor -2*u**2 + u**4 + 1 + 4*u**4 - p*u**4.
(u - 1)**2*(u + 1)**2
Let t(r) = r**2 + 5*r + 4. Let s(p) = -p. Let m(o) = -2*o**2 + 2*o + 2. Let u be m(2). Suppose 3*j + 9 - 3 = 0. Let x(b) = j*s(b) + u*t(b). Factor x(z).
-2*(z + 2)**2
What is h in -2*h**2 + 30 + h**3 - 30 + 3*h**2 = 0?
-1, 0
Solve 3*c + 0*c**2 + 15*c - 3*c**2 - 12*c = 0 for c.
0, 2
Let y = -726/7 - -104. Factor 4/7*o**2 - y*o - 2/7.
2*(o - 1)*(2*o + 1)/7
Let i be (-4)/(-10)*(-25)/(-11). Let w = 51/44 - i. Factor -1/2 - w*a + 1/4*a**2.
(a - 2)*(a + 1)/4
Let d = -11 - -17. Suppose -5*l + d = -4. Let 1/3*h**l + 1/3*h - 2/3 = 0. What is h?
-2, 1
Suppose 0 = -3*l + l - 4*s - 6, 3*l - 5*s - 24 = 0. Suppose l*h + 8 = 20. Factor -4*w - 11*w**2 + 13*w**2 + h*w + w**4 + 3*w**3.
w**2*(w + 1)*(w + 2)
Let v be (-20)/(-6)*(-54)/(-45). Suppose 2 = 2*k, 5*k = 3*y + v*k + 1. Factor 2/5*z**3 - 2/5*z**2 + 0*z + y.
2*z**2*(z - 1)/5
Suppose -5*d + 0*d - 4*b - 20 = 0, -3*d - 4*b = 20. Suppose d*n - 2/5*n**2 + 0 = 0. Calculate n.
0
Let h be (-57)/(-27) - (-2)/(-18). Let d(l) be the second derivative of -2*l + 0*l**h + 0*l**3 + 0 + 0*l**4 + 1/90*l**6 + 1/60*l**5. What is w in d(w) = 0?
-1, 0
Suppose 5*m = 12*m. Factor 0 - 1/5*r**4 + 0*r + m*r**3 + 0*r**2.
-r**4/5
Suppose -4*w = -2*w - 4*w. Factor -1/2*g**3 + 0*g**2 + 0*g + w.
-g**3/2
Let x be (-5 + 5)/(-1) - (-2)/6. Factor -2/3*v + v**2 - x.
(v - 1)*(3*v + 1)/3
Let l(r) be the third derivative of -r**5/120 + r**4/12 - r**3/3 - 7*r**2. Find y, given that l(y) = 0.
2
Suppose -8/5*x**2 - 24/5*x**3 + 6/5*x**5 + 2/5*x**4 + 0 + 0*x = 0. What is x?
-2, -1/3, 0, 2
Let m(d) = d**3 - 10*d**2 - d + 12. Let s be m(10). Let 2/7*b**s + 2/7*b - 4/