 - 2/9*k**5.
-2*(k + 1)**2*(k + 2)**3/9
Let n be -2*(-3)/48*2. Determine z, given that 1/4*z**3 - n*z + 0 + 0*z**2 = 0.
-1, 0, 1
Let c(y) be the second derivative of -5*y + 0 + 0*y**4 - 3/140*y**5 + 0*y**2 + 0*y**3. Determine m, given that c(m) = 0.
0
Factor -21/2*p - 6*p**2 - 3 + 6*p**3.
3*(p - 2)*(2*p + 1)**2/2
Find n, given that -3/2*n**4 - 4*n**2 + 7/2*n**3 + 9/4*n + 1/4*n**5 - 1/2 = 0.
1, 2
Let r be 8/(-40) - (-17)/(-15). Let i = -7/6 - r. Factor -1/6*b + i*b**2 + 0.
b*(b - 1)/6
Let l be 3 + 1 + -2 + (-14)/9. Solve l*h**2 - 2/9*h + 2/9*h**3 - 4/9 = 0.
-2, -1, 1
Let t = -14 + 22. Suppose -p - p + 4 - t*p + 6*p**2 = 0. What is p?
2/3, 1
Let b be (-8)/(36/(-24)*(-8)/(-6)). Factor -2/5*r**5 + 4/5*r**2 - 2/5*r**b - 2/5 + 4/5*r**3 - 2/5*r.
-2*(r - 1)**2*(r + 1)**3/5
Suppose 6 + 6 = 6*c. Let r(d) be the second derivative of 0 + 1/50*d**5 + 8/15*d**3 + 4/5*d**c + d + 1/6*d**4. Factor r(q).
2*(q + 1)*(q + 2)**2/5
Let c(a) be the second derivative of -a**4/48 + a**3/8 + a**2/2 - 10*a. Factor c(y).
-(y - 4)*(y + 1)/4
Determine k, given that 5*k + 3/2 + 25/6*k**2 = 0.
-3/5
Let n(h) be the third derivative of h**8/2520 + h**7/315 + h**6/108 + h**5/90 - 2*h**3/3 + 5*h**2. Let a(l) be the first derivative of n(l). Solve a(c) = 0.
-2, -1, 0
Let q(n) be the second derivative of n**7/63 + n**6/9 + 3*n**5/10 + 7*n**4/18 + 2*n**3/9 + 11*n. Factor q(b).
2*b*(b + 1)**3*(b + 2)/3
Let k(t) be the first derivative of -2*t - 2 - 1/4*t**2 - 1/48*t**4 - 1/8*t**3. Let a(y) be the first derivative of k(y). What is h in a(h) = 0?
-2, -1
What is l in -19*l**3 - 19*l + 35*l**5 - l - 6*l**3 + 10*l**5 + 60*l**4 - 60*l**2 = 0?
-1, -2/3, 0, 1
Let v = -3175/9 - -353. Suppose 0 = -2*n + 3*n. Factor v*g - 2/9*g**2 + n.
-2*g*(g - 1)/9
Let h = 5 - 2. Factor -14 + 16 - 2*p**2 + 2*p - p**h - p**3.
-2*(p - 1)*(p + 1)**2
Factor 0*c**2 - c**4 + 1/5*c**5 + 6/5*c**3 + 0*c + 0.
c**3*(c - 3)*(c - 2)/5
Let f(b) be the third derivative of -b**6/60 - b**5/3 + 3*b**2 - 6*b. Suppose f(c) = 0. What is c?
-10, 0
Suppose 6 = -c + 3*c. Let i be (-6)/(-4) + -2 + 1. Suppose -a**4 + i*a - 3*a**2 + 1 - 7/2*a**c = 0. Calculate a.
-2, -1, 1/2
Let t = -59 + -86. Let a be 1 + -4 - t/15. Factor -2/3 - 20/3*z**3 - a*z**2 - 10/3*z - 2/3*z**5 - 10/3*z**4.
-2*(z + 1)**5/3
Let i(q) be the third derivative of -q**7/2520 + q**6/360 - q**5/120 - q**4/12 + 3*q**2. Let l(b) be the second derivative of i(b). Solve l(d) = 0 for d.
1
Let i be (((-11)/(-30))/11)/2. Let s(b) be the third derivative of -b**2 + i*b**6 + 1/30*b**5 + 0*b + 0*b**3 + 0 + 0*b**4. Solve s(j) = 0.
-1, 0
Let n = 362 + -1084/3. Factor 1/3*d**4 + 0*d**2 - n*d**3 + 0*d + 0.
d**3*(d - 2)/3
Let p be 3/(-2) - 132/(-24). Let q = -2 + 7. Factor 2*z + 2*z**4 - 2*z**q - 6*z**p + 4*z**2 - z**5 + z**5.
-2*z*(z - 1)*(z + 1)**3
Suppose 6 = -v - v, 3*o + v - 24 = 0. Let f = 11 - 8. Factor 4*b**2 + o*b**3 + f*b**2 + 3*b**4 + 2*b**2 - 2*b + 5*b.
3*b*(b + 1)**3
Let w(a) be the second derivative of -a**6/10 + 3*a**4/4 - a**3 + 11*a. Factor w(v).
-3*v*(v - 1)**2*(v + 2)
Find o such that 0 - 1/6*o**2 - 1/3*o**3 + 0*o - 1/6*o**4 = 0.
-1, 0
Let g(o) be the first derivative of 1/3*o + 1/9*o**3 - 1 - 1/3*o**2. Factor g(u).
(u - 1)**2/3
Let c(z) be the first derivative of 20*z**5/7 - 10*z**4/7 + 4*z**3/21 + 2. Factor c(k).
4*k**2*(5*k - 1)**2/7
Find q such that 3*q**5 + 0*q - 6*q**3 - 2*q + 4*q + q = 0.
-1, 0, 1
Let v(g) be the first derivative of g**6/720 + g**5/30 + g**4/3 - 8*g**3/3 + 4. Let r(c) be the third derivative of v(c). Suppose r(x) = 0. Calculate x.
-4
Let g(r) = r**4 + 9*r**3 + 6*r**2 - 6*r - 4. Let i(z) = -8*z**3 - 6*z**2 + 6*z + 4. Let t(f) = 6*g(f) + 5*i(f). What is o in t(o) = 0?
-1, 2/3
Let s = 194/105 - 9/5. Let u(r) be the second derivative of 0*r**5 - 1/3*r**3 + s*r**7 - 1/3*r**4 + 2*r + 0*r**2 + 2/15*r**6 + 0. Factor u(l).
2*l*(l - 1)*(l + 1)**3
Let h = 15 + -12. Factor h + 2*i + 4*i**2 - 3 + 3*i**3 - i**3.
2*i*(i + 1)**2
Let o be -2 - 4*(-1 + 0). Suppose o*k = k + 4. Factor 2*y**3 + 5*y**k - y**4 - 2*y**4.
2*y**3*(y + 1)
Let h = 429 + -427. Factor 11*w**h + 9/2 + 1/2*w**4 + 4*w**3 + 12*w.
(w + 1)**2*(w + 3)**2/2
Let z be 132/90 + 6/5 + -2. Factor 0 + 1/3*j**3 - z*j**2 + 1/3*j.
j*(j - 1)**2/3
Let t = 18 - 15. Factor n + n**2 - 2*n + 0*n**2 + 5*n**t + 3*n**4.
n*(n + 1)**2*(3*n - 1)
Suppose 2*w - 12 = -6. Let s(h) be the first derivative of 0*h + 2/5*h**2 + 2 - 14/25*h**5 + 2/5*h**w - 3/10*h**4 - 1/5*h**6. Let s(m) = 0. Calculate m.
-1, 0, 2/3
Suppose r - 3*a + 5 + 10 = 0, 4*a = 4*r + 36. Let g be 48/18 - (-4)/r. Factor -3 - 4*d - d**g - 2 + 1.
-(d + 2)**2
Let f(o) be the third derivative of -o**7/1365 - o**6/65 - 9*o**5/65 - 9*o**4/13 - 27*o**3/13 - 3*o**2 - 4*o. Find t such that f(t) = 0.
-3
Suppose -c + 9 = 4. Let o(a) be the second derivative of -1/48*a**4 - a + 1/120*a**6 + 0*a**3 + 0*a**c + 0*a**2 + 0. Factor o(p).
p**2*(p - 1)*(p + 1)/4
Let i = 1 - 7. Let j be (i/(-27) + 0)/1. Factor -j*w**3 - 4/9*w**2 - 2/9*w + 0.
-2*w*(w + 1)**2/9
Let a(h) be the second derivative of h**5/80 - h**4/16 + 2*h**2 - 4*h. Let s(y) be the first derivative of a(y). Factor s(b).
3*b*(b - 2)/4
Let d(u) be the third derivative of 1/12*u**4 + 0*u**3 + 3/20*u**5 + 3*u**2 + 1/12*u**6 + 0*u + 0. Factor d(f).
f*(2*f + 1)*(5*f + 2)
Let r be (0 - -1)/(15 - 3). Let x(o) be the second derivative of -o + r*o**4 + 0 - 1/3*o**3 + 1/2*o**2. Determine c so that x(c) = 0.
1
Let o(s) = -3*s**2 + 3*s**2 - 2*s + s**2 + s**2 - 5 + 5*s**3. Let m(c) = -6*c**3 - 2*c**2 + 2*c + 6. Let q(i) = -3*m(i) - 4*o(i). Factor q(t).
-2*(t - 1)*(t + 1)**2
Factor 13*t**3 + 3*t**4 + 8*t + 17*t + 48*t**2 - 2*t**4 + 11*t.
t*(t + 1)*(t + 6)**2
Let j be 3/(-9)*2 - (10 - 11). Let b(x) be the first derivative of j*x**6 + 4/5*x**5 + 0*x - 4/3*x**3 - x**2 - 2 + 0*x**4. Determine z so that b(z) = 0.
-1, 0, 1
Let n(t) be the first derivative of 31/6*t**3 + 51/16*t**4 + 1/8*t**6 + t**5 + 2*t - 4 + 9/2*t**2. Find a, given that n(a) = 0.
-2, -1, -2/3
Find u such that 2/7*u + 8/21*u**2 + 0 + 2/21*u**3 = 0.
-3, -1, 0
Let l(q) = -q + 1. Let h(v) = 6*v**2 - 4*v + 2. Let d(n) = -h(n) + 6*l(n). Find p such that d(p) = 0.
-1, 2/3
Let b(r) be the first derivative of 3*r**4/2 + 10*r**3/3 - 2*r**2 + 4. Factor b(t).
2*t*(t + 2)*(3*t - 1)
Let d(z) be the first derivative of -5/14*z**2 - 9 + 4/21*z**3 + 2/7*z - 1/28*z**4. Solve d(m) = 0.
1, 2
Let r(q) = 6*q**2 - 3. Let i(c) = -7*c**2 + c + 2. Let o(h) = -3*i(h) - 4*r(h). Suppose o(b) = 0. What is b?
-2, 1
Let y = -228 + 230. Let -6/11 + 2/11*r - 2/11*r**3 + 6/11*r**y = 0. What is r?
-1, 1, 3
Let c**4 + 90*c**3 + 91*c**3 - 179*c**3 + c**2 = 0. Calculate c.
-1, 0
Let o(m) be the second derivative of m**4/3 - 2*m**3/3 - 16*m. Factor o(q).
4*q*(q - 1)
Let j be 73/52 - (-1 - 90/(-78)). Factor -t + 0 + j*t**3 - 2*t**2.
t*(t - 2)*(5*t + 2)/4
Let n(h) = -h**3 + 4*h**2 + 3*h - 5. Let m be n(4). Let w be 7 - m - 2/(-4). Solve -w*k**2 - 1/2*k**4 - k**3 + 0*k + 0 = 0 for k.
-1, 0
Let l be 0/((0 - 2) + 3). Let t be 15/21 - 1 - (-16)/7. Find i such that -1/2*i + i**3 + 1/2*i**t + l = 0.
-1, 0, 1/2
Let x be -4*(-6 + (-651)/(-112)). Factor -1/2 + x*t - 1/4*t**2.
-(t - 2)*(t - 1)/4
Factor 13*u**4 + 6*u**5 + 9*u**3 + 8*u**5 + 47*u**4 + 7*u**3.
2*u**3*(u + 4)*(7*u + 2)
Let y = -7/20 - -3/4. Let 0 - y*x**2 + 2/5*x = 0. What is x?
0, 1
Suppose l - 2*l = -4*x + 4, 2*x - 2*l = -4. Let g = 1 + x. Factor 4 - 5 + g + 4*z + 2*z**2.
2*(z + 1)**2
Let b(r) be the first derivative of 3/7*r**2 - 2 + 1/14*r**4 - 2/7*r**3 - 2/7*r. Suppose b(d) = 0. Calculate d.
1
Let j(r) be the first derivative of 21*r**4/4 - 16*r**3 + 6*r**2 + 14. Let j(s) = 0. What is s?
0, 2/7, 2
Let j(i) = -10*i**5 + 12*i**4 + 4*i**3 - 8*i**2 + 2*i. Let p(q) = -11*q**5 + 13*q**4 + 3*q**3 - 7*q**2 + 3*q - 1. Let o(g) = -5*j(g) + 4*p(g). Factor o(k).
2*(k - 1)**3*(k + 1)*(3*k + 2)
Let j(m) be the third derivative of -m**10/252000 + m**9/50400 - m**8/33600 - m**5/60 - 3*m**2. Let x(u) be the third derivative of j(u). Factor x(t).
-3*t**2*(t - 1)**2/5
Let s(i) be the third derivative of i**7/105 + i**6/60 + 3*i**2. Factor s(r).
2*r**3*(r + 1)
Let z = -143 - -143. Let p(w) be the second derivative of z + 0*w**3 - 1/20*w**5 + 1/60*w**6 + 0*w**2 + 2*w + 1/24*w**4. Factor p(g).
g**2*(g - 1)**2/2
Let z = 149/3 + -49. Find j such that -2*j - 2*j**2