e second derivative of k(m). Factor w(f).
-2*(f - 1)**2*(4*f + 1)/9
Let m = 54 + -50. Determine s, given that -s**2 - s + s**m + 0 + 1/4*s**5 + 3/4*s**3 = 0.
-2, -1, 0, 1
Let h(r) be the first derivative of 4*r**5/5 - 4*r**3/3 + 15. Suppose h(p) = 0. What is p?
-1, 0, 1
Let l be 2/42*(-27)/(-63). Let s = 87/539 + l. Let -18/11*v**2 - 4/11*v**4 + 10/11*v + 14/11*v**3 - s = 0. Calculate v.
1/2, 1
Factor 6*t**2 + 12*t - 2*t**2 - 22 - 6*t**2 + 4.
-2*(t - 3)**2
Let p be 3/21 - 60/(-21). Factor 8/3*d**2 + 4/3 + 10/3*d + 2/3*d**p.
2*(d + 1)**2*(d + 2)/3
Suppose 0 = 8*v - 9*v + 4. Let 2/3*z**v + 1/3*z - 5/3*z**3 + z**2 - 1/3 = 0. What is z?
-1/2, 1
Let x(s) be the second derivative of -s**9/10584 - s**8/2940 - s**7/2940 + s**3/2 - 2*s. Let y(g) be the second derivative of x(g). Find p such that y(p) = 0.
-1, 0
Let f(j) be the first derivative of -2*j**5/95 - 3*j**4/38 - 4*j**3/57 - 16. Find a such that f(a) = 0.
-2, -1, 0
Factor -4/25*g**2 + 4/25 + 2/5*g**3 - 2/5*g.
2*(g - 1)*(g + 1)*(5*g - 2)/25
Let w(i) = -4*i**3 - 2*i**2 + 6*i - 4. Let p be -2*(2 + 3/6). Let s(g) = 9*g**3 + 5*g**2 - 12*g + 8. Let f(n) = p*w(n) - 2*s(n). Factor f(a).
2*(a - 1)**2*(a + 2)
Let g = -3/20 - -801/140. Solve -17/7*z**4 - 37/7*z**3 - 20/7*z - 4/7 - 3/7*z**5 - g*z**2 = 0.
-2, -1, -2/3
Let f(h) be the second derivative of -h**7/168 + 7*h**6/240 - h**5/20 - h**4/6 - 7*h. Let w(g) be the third derivative of f(g). Factor w(q).
-3*(q - 1)*(5*q - 2)
Let p = 53/279 - -1/31. Let j(k) = k - 2. Let h be j(4). Factor -p*r**h + 2/9*r - 2/9*r**3 + 2/9.
-2*(r - 1)*(r + 1)**2/9
Factor 5*q**3 - 6*q + 15*q**2 + 4*q**3 + 12*q**3.
3*q*(q + 1)*(7*q - 2)
Let v(z) be the second derivative of 0 + 0*z**2 - 1/20*z**5 + z + 1/6*z**4 - 1/6*z**3. Solve v(m) = 0.
0, 1
Suppose 2 = -5*y - 3. Let n(j) = j**2 + 6*j + 5. Let u(g) = g + g - 1 - 3*g. Let v(r) = y*n(r) - 5*u(r). Find t such that v(t) = 0.
-1, 0
Let a be (-8)/(-7)*42/(-18) - -3. Factor 0*l - a*l**2 - 1/3*l**4 + 0 - 2/3*l**3.
-l**2*(l + 1)**2/3
Let k(a) = a**4 - a**3 - 3*a + 3. Let o(q) = q**3 + q - 1. Let d(t) = -k(t) - 3*o(t). Find n, given that d(n) = 0.
-2, 0
Factor 15/4*c + 3/2 - 3/4*c**3 + 9/4*c**2 - 3/4*c**4.
-3*(c - 2)*(c + 1)**3/4
Let y(z) be the second derivative of -z**7/126 - z**6/45 - z**5/60 + 8*z. Find n, given that y(n) = 0.
-1, 0
Let k(a) be the first derivative of a**6/60 - a**5/40 + 3*a - 3. Let x(s) be the first derivative of k(s). Determine y so that x(y) = 0.
0, 1
Let f(c) be the first derivative of -3 + 1/4*c**4 + 0*c**2 + 0*c + 1/5*c**5 - 1/6*c**6 - 1/3*c**3. Determine l, given that f(l) = 0.
-1, 0, 1
Let q(z) be the third derivative of z**6/160 + z**5/40 - z**4/32 - z**3/4 - 21*z**2. Find s such that q(s) = 0.
-2, -1, 1
Let g(k) be the second derivative of k**7/1120 + k**6/288 + k**5/480 - k**4/96 - k**3/2 - k. Let s(x) be the second derivative of g(x). Factor s(q).
(q + 1)**2*(3*q - 1)/4
Suppose -5*l = -12 - 3. Let g be l/(-30) + (-3)/(-5). Factor -g*m**2 - 1/2 + m.
-(m - 1)**2/2
Let g(t) be the second derivative of -t**3/6 - 4*t**2 - t. Let q be g(-10). Factor -6*o + 6*o**q - o**3 + 3*o**3 - 2*o**3 - 2*o**3 + 2.
-2*(o - 1)**3
Let m(r) = r + 1 + 3 + 1. Let v be m(-5). Factor -2/5*y**4 + 0*y**3 + v*y**2 + 2/5*y**5 + 0*y + 0.
2*y**4*(y - 1)/5
Let k(y) be the second derivative of -1/11*y**2 + 2/33*y**3 + 0 - 2*y - 1/66*y**4. Determine f, given that k(f) = 0.
1
Suppose 2 = 15*x - 12*x - 4*m, -3*m - 5 = -4*x. Determine v, given that 3/7*v**x + 1/7*v**3 + 3/7*v + 1/7 = 0.
-1
Let s(q) be the first derivative of 2/3*q + 11/6*q**4 - 1 - 2*q**3 - 8/15*q**5 + 1/3*q**2. Let s(d) = 0. Calculate d.
-1/4, 1
Let v = -34 - -133. Let m be 12/(-14)*(-308)/v. Find u such that 2/3 - 2/3*u**2 - 8/3*u + m*u**3 = 0.
-1, 1/4, 1
Let a(o) be the first derivative of 49*o**6/135 + 7*o**5/30 - 4*o**4/9 + 4*o**3/27 - 2*o - 6. Let l(i) be the first derivative of a(i). Factor l(m).
2*m*(m + 1)*(7*m - 2)**2/9
Let w be 24/10 - 6/15. Suppose -w*i + 0*i = 0. Factor 4*j + i + 2*j**4 + 2*j**3 - 2 - 6*j**3.
2*(j - 1)**3*(j + 1)
What is d in -414*d**3 + 4*d**4 + 411*d**3 - d**4 = 0?
0, 1
Let s(j) = -6*j**2 + 8*j + 1. Suppose -l + 2*l = 6. Let a(p) = p**2 - p - 1. Let o(g) = l*a(g) + 2*s(g). Factor o(u).
-2*(u - 1)*(3*u - 2)
Let t(h) be the first derivative of 3/2*h**2 + 3 - 9/2*h - 1/6*h**3. Factor t(i).
-(i - 3)**2/2
Let g(w) be the first derivative of -w**3/15 - 4*w**2/5 - 16*w/5 + 3. What is h in g(h) = 0?
-4
Let u(k) be the second derivative of -k**5/80 - k**4/12 - 5*k**3/24 - k**2/4 + k. Factor u(i).
-(i + 1)**2*(i + 2)/4
Let k = -8741/11 - -795. Solve -6/11 + 2/11*n**2 - k*n = 0.
-1, 3
Suppose -4*v + 88 = -3*b, -4*v - 5*b = -2*b - 112. Let -75*m**3 + v*m**2 + 12*m - 40*m**5 - 95*m**5 + 246*m**4 - 73*m**2 = 0. Calculate m.
-2/5, 0, 2/9, 1
Suppose -4*z = 5*w + 15, -5*z + 2*w = -z - 6. Let r be (5/(15/(-6)))/(-9). Factor r*c + z + 2/3*c**3 + 2/3*c**2 + 2/9*c**4.
2*c*(c + 1)**3/9
Let t be (-2 + 0)*((-7)/2 + 2). Let m(i) be the second derivative of 1/6*i**2 - 1/9*i**t + 0 + 1/36*i**4 + 2*i. Let m(x) = 0. What is x?
1
Determine o so that 0*o + 0 + 2/9*o**2 + 2/9*o**3 = 0.
-1, 0
Let i = 80/11 - 538/77. Let o = -941/7 + 135. Suppose -i*w**2 + 0*w + o*w**3 + 0 - 2/7*w**4 = 0. Calculate w.
0, 1
Let c(q) be the first derivative of q**4/20 + 6*q**3/5 + 54*q**2/5 + 216*q/5 + 1. Factor c(d).
(d + 6)**3/5
Let u(v) be the third derivative of 4*v**8/21 - 16*v**7/35 - 7*v**6/30 + 23*v**5/15 - 3*v**4/2 + 2*v**3/3 - 17*v**2. Determine h so that u(h) = 0.
-1, 1/4, 1
Suppose 5*k + p + 75 = -p, 2*p - 61 = 3*k. Let m = -15 - k. Find i, given that -2/3*i**m + 2/3*i - 2/3*i**4 - 14/9*i**3 + 4/9 = 0.
-1, 2/3
Let i be (125/(-100))/(12/(-16)). Factor -4/3*m**2 - i*m - 2/3 - 1/3*m**3.
-(m + 1)**2*(m + 2)/3
Let h(a) be the third derivative of 7*a**2 + 0 + 1/56*a**8 + 0*a - 2/3*a**3 - 1/5*a**5 + 1/15*a**6 - 7/12*a**4 + 8/105*a**7. Let h(v) = 0. What is v?
-1, -2/3, 1
Factor -2*i + 4/5*i**2 + 4/5.
2*(i - 2)*(2*i - 1)/5
Let c(i) = -4*i**3 - 3*i**2 - 4. Let z(l) = 9*l**3 + 6*l**2 - l + 9. Let r(t) = -14*c(t) - 6*z(t). Factor r(y).
2*(y + 1)**3
Let y(b) = b + 12. Let f be y(-9). Solve -u**4 - f*u**3 - 3*u**2 - u - 4 + 4 = 0 for u.
-1, 0
Let t = 5 - 23. Let q = t + 18. Find i, given that -4/9*i**3 + 2/9*i**2 + q + 4/9*i - 2/9*i**4 = 0.
-2, -1, 0, 1
Let p(b) be the second derivative of b**6/6 + b**5/2 + 5*b**4/12 - 3*b. Suppose p(s) = 0. Calculate s.
-1, 0
What is p in 959*p**2 + 16 - 272*p + 180*p**2 + 17*p**2 = 0?
2/17
Let p(d) = d**2 + 4*d + 1. Let m be p(-5). Determine f, given that 4 + 2 + 5 + 3*f**2 - 8 + m*f = 0.
-1
Let t(s) = -s**3 + s**2 - 3*s - 1. Let i(w) = w**3 + 3*w**2 + 3*w. Let h be i(-2). Let q(j) = -j**2 - 1. Let a(n) = h*t(n) + 4*q(n). Let a(g) = 0. What is g?
1
Let n(r) = -r**3 + 3*r**2 - 2*r + 2. Let k be n(2). Factor -o**k + o**4 - 1/3*o + 0 + 1/3*o**3.
o*(o - 1)*(o + 1)*(3*o + 1)/3
Let q(d) be the second derivative of 1/20*d**5 - 1/14*d**7 + 0*d**4 + 0*d**2 + 2*d + 1/15*d**6 + 0 + 0*d**3. Let q(k) = 0. What is k?
-1/3, 0, 1
Let c(f) = -f**5 + f**2 + f. Let z(g) = g**2 - 5*g**2 - 3*g**3 + 0*g**4 + g**2 - 3*g**4 + g**5 - 2*g. Let t(m) = -4*c(m) - 2*z(m). Let t(o) = 0. Calculate o.
-1, 0
Let u(q) be the second derivative of -q**6/105 + q**5/70 + 6*q. Factor u(t).
-2*t**3*(t - 1)/7
Suppose -i + 1 + 2 = 0. Let v(l) be the second derivative of 49/66*l**4 - 4/11*l**2 - 4/33*l**3 + 49/110*l**5 - i*l + 0. Let v(g) = 0. Calculate g.
-1, -2/7, 2/7
Let u(f) be the second derivative of f**4/16 - 3*f**2/2 + 9*f. Factor u(n).
3*(n - 2)*(n + 2)/4
Let l(d) be the second derivative of d**9/98280 + d**8/21840 - d**6/2340 - d**5/780 + d**4/4 - d. Let b(s) be the third derivative of l(s). Factor b(j).
2*(j - 1)*(j + 1)**3/13
Let d(q) = -1 + 2*q - 2*q**2 - 3*q**2 + 3*q**2 + 52*q**3. Let h be d(1). Factor 12*r**5 - 6*r**3 + h*r**3 - 22*r**4 + 15*r**3 - 12*r**2 - 29*r**4.
3*r**2*(r - 2)**2*(4*r - 1)
Let n(o) be the first derivative of o**7/280 - o**6/120 - 4*o**3/3 + 6. Let f(g) be the third derivative of n(g). Factor f(z).
3*z**2*(z - 1)
Let h(r) = -r**3 + 12*r**2 - 9*r + 12. Let g(m) = m + 1. Let q(s) = 3*g(s) - h(s). Let k be q(11). Factor 2/3*z**k + 0 + 1/3*z + 1/3*z**3.
z*(z + 1)**2/3
Suppose -11*c**4 + c + 17*c**4 - 3*c**5 + 2*c - 6*c**2 = 0. What is c?
-1, 0, 1
Let o be 10/12 - 31/