) = 0.
-2, 1
Factor 1/3*f**3 - 1/3*f**2 + 4/3 - 4/3*f.
(f - 2)*(f - 1)*(f + 2)/3
Let k = -3 - -7. Determine n so that -2*n**k + 10*n**3 + 0*n**3 + n - 6*n**2 + 7*n - 10*n**2 = 0.
0, 1, 2
Let q(g) be the third derivative of -1/110*g**5 - 1/1155*g**7 + 0 + g**2 + 0*g**3 + 0*g - 1/132*g**4 - 1/220*g**6. Factor q(p).
-2*p*(p + 1)**3/11
Let o(q) = -7*q**5 - 9*q**4 + 3*q**3 + 73*q**2 - 102*q + 30. Let f(d) = -d**5 + d**3 - d - 1. Let m(v) = 6*f(v) - o(v). Solve m(x) = 0 for x.
-6, 1
Suppose 12*r - 59*r**2 + 0 + 0 + 55*r**2 = 0. Calculate r.
0, 3
Factor -20/3*w + 8/3 - 28/3*w**2.
-4*(w + 1)*(7*w - 2)/3
Let 3*g**3 + 1536 + 799*g + 206*g**2 - 223*g - 134*g**2 = 0. What is g?
-8
Let z(x) = x**2 + x - 2. Let v be z(-2). Factor -1/4*h**2 + v - 1/4*h.
-h*(h + 1)/4
Let x be (-3 - (-2)/96) + 3. Let u(s) be the second derivative of -1/24*s**3 + s + 0 + 1/80*s**5 - x*s**4 + 1/8*s**2. Factor u(w).
(w - 1)**2*(w + 1)/4
Solve 2/9 - 4/9*w - 14/9*w**2 - 8/9*w**3 = 0 for w.
-1, 1/4
Determine g, given that -1/2 - 2/3*g - 1/6*g**2 = 0.
-3, -1
Let h be ((-4)/(-600))/((-1)/(15/(-6))). Let m(k) be the third derivative of -1/6*k**3 + 0 + 0*k - 3*k**2 - h*k**5 + 1/12*k**4. Let m(t) = 0. Calculate t.
1
Let a(l) = -13*l**2 + 29*l - 1. Let w(k) = -6*k**2 + 15*k. Let x(o) = -3*a(o) + 5*w(o). Factor x(t).
3*(t - 1)*(3*t - 1)
Let r = -90 + 54. Let b be (-1 + -3)*18/r. Determine h, given that 0 - 1/3*h**3 + 0*h - 2/3*h**b = 0.
-2, 0
Let l be 4/(-15)*(-3 - (-273)/112). Let g(m) be the second derivative of 3*m + 0 + 1/12*m**4 + 0*m**3 + 0*m**2 + l*m**5. Let g(v) = 0. What is v?
-1/3, 0
Let v be (-8)/7*21/(-6). Factor 3*y**4 + y**3 + y**3 - 7*y**2 + 2*y + 0*y**v.
y*(y - 1)*(y + 2)*(3*y - 1)
Factor 0 + 0*p + 3/2*p**5 - 5/2*p**4 + 1/2*p**3 + 1/2*p**2.
p**2*(p - 1)**2*(3*p + 1)/2
Let r = -1 - -4. Suppose 0*x**4 - 4*x**4 - 8*x**r + 2*x**4 + 3*x**2 + 8*x**5 - x**2 = 0. What is x?
-1, 0, 1/4, 1
Let g be ((-194)/(-12) - 2)*30/75. Determine p, given that -5/3*p**3 - 4/3 - g*p**2 - 16/3*p = 0.
-2, -1, -2/5
Let m(s) be the first derivative of -s**6/1260 + s**5/210 - s**4/84 - s**3 - 2. Let i(k) be the third derivative of m(k). Factor i(c).
-2*(c - 1)**2/7
Solve 0 - 2/3*o**2 - 2*o = 0.
-3, 0
Factor -3/2*r**2 - 3*r + 9/2.
-3*(r - 1)*(r + 3)/2
Let u(c) be the second derivative of 4*c**2 + 5/2*c**5 + 15/2*c**4 + 8*c**3 + 0 + c. Determine r, given that u(r) = 0.
-1, -2/5
Let v(z) be the third derivative of 1/105*z**7 + 3*z**2 - 1/30*z**5 + 0 + 0*z**3 + 0*z + 1/60*z**6 - 1/12*z**4. Factor v(p).
2*p*(p - 1)*(p + 1)**2
Suppose -3*k + 4 - 1 = 3*w, k - 5 = -2*w. Let h be -1 - (-13 + (k - -3)). Factor r - 3*r**3 + 0*r**3 - 16*r - h*r**2 - 6.
-3*(r + 1)**2*(r + 2)
Let m(s) = -3*s**4 - 9*s**3 - 12*s**2 - 3*s - 3. Let l(j) = j**3 + j**2 + j - 1. Let r(h) = -3*l(h) + m(h). Solve r(u) = 0 for u.
-2, -1, 0
Let a(f) = f**3 - 5*f**2 + 2*f - 4. Let c be a(5). Let 9*y**3 + 2*y**2 - y**3 - 6*y**4 + c*y**3 + 30*y**4 = 0. What is y?
-1/3, -1/4, 0
Let d(z) = z**2 - 4*z + 5. Let w be d(4). Factor 0*p**2 + p**2 + p**w - p**4 + p - p - p**3.
p**2*(p - 1)**2*(p + 1)
Let k = 5 + -3. Suppose 17 = k*t - 0*t + 3*s, 0 = -2*t + 4*s - 4. Let 6*g + t + g**2 + g**2 + 0*g**2 = 0. What is g?
-2, -1
Suppose 0 = 5*w - w - 36. Let r(x) = -x**3 - 5*x**2 + 11*x - 15. Let q be r(-7). Factor -w*a**3 - q - 18*a - 39/2*a**2 - 3/2*a**4.
-3*(a + 1)**2*(a + 2)**2/2
Let z(j) = -7*j**2 - 8*j - 6. Let y(g) = g**2 + 2*g + 1. Let r(w) = -6*y(w) - z(w). Let r(f) = 0. Calculate f.
0, 4
Factor -4 - 35*u**2 - 22*u - 25/2*u**3.
-(u + 2)*(5*u + 2)**2/2
Let c(j) = 8 - 14*j + 2*j**3 - 8*j**2 + 4*j**3 + 2*j. Let i(b) = 6*b**3 - 9*b**2 - 13*b + 9. Let d(k) = 7*c(k) - 6*i(k). Factor d(s).
2*(s - 1)*(s + 1)*(3*s - 1)
Let h be 72/(-54) - (1 + -3). Suppose v - h - 1/3*v**2 = 0. Calculate v.
1, 2
Let m be (0 + 1 - 2) + 46. Let d = m + -43. Factor -14/3*w**d + 4/3 + 10/3*w.
-2*(w - 1)*(7*w + 2)/3
Solve -17*d**2 - 6*d - 12*d**3 + 3*d**4 - 7*d**2 + 9*d**2 - 6*d**4 = 0.
-2, -1, 0
Suppose -7*o = -6*o. Suppose -5*r - r = o. Solve r*y + 2/3*y**2 + 0 = 0 for y.
0
Factor 0 - 4/5*t**2 + 8/5*t.
-4*t*(t - 2)/5
Let x(s) be the first derivative of -s**6/720 + s**5/360 + s**4/144 - s**3/36 - s**2 - 4. Let g(w) be the second derivative of x(w). Factor g(p).
-(p - 1)**2*(p + 1)/6
Let d(k) be the second derivative of k**7/210 + k**6/72 + k**5/120 + k**3/3 - 6*k. Let z(t) be the second derivative of d(t). Find c, given that z(c) = 0.
-1, -1/4, 0
Let n(r) be the third derivative of r**10/252000 - r**9/75600 + r**8/100800 - r**5/12 - 2*r**2. Let z(w) be the third derivative of n(w). Factor z(p).
p**2*(p - 1)*(3*p - 1)/5
Let i(c) = -c + 4. Let b be i(3). Factor -b + 8*m**3 - m**4 + 2*m + 2 - 10*m**3.
-(m - 1)*(m + 1)**3
Let m(t) be the second derivative of -t**8/560 + t**7/630 + t**4/3 + 3*t. Let f(q) be the third derivative of m(q). Solve f(o) = 0 for o.
0, 1/3
Let p(g) be the third derivative of -g**7/42 + g**6/12 + g**5/12 - 5*g**4/12 - 15*g**2. Find w such that p(w) = 0.
-1, 0, 1, 2
Let q(k) be the first derivative of -k**5/40 - k**4/16 - k**2 - 3. Let z(m) be the second derivative of q(m). Factor z(h).
-3*h*(h + 1)/2
Suppose 5*j = -h + 11 - 31, 5*h - 10 = -3*j. Let x(m) be the third derivative of -4*m**2 + 0 + 1/3*m**3 + 0*m**4 - 1/30*m**h + 0*m. Let x(l) = 0. What is l?
-1, 1
Let d be -11 - 1053/(-90) - (-2)/(-10). Let y = 1 - -1. Factor -p + 0*p**y + d*p**4 + p**3 - 1/2.
(p - 1)*(p + 1)**3/2
Suppose -5*t = -0*t - 15. Let c be (4/(-30))/(t/(-5)). Factor -c + 4/9*x + 2/3*x**2.
2*(x + 1)*(3*x - 1)/9
Let z be 3 + -3 + 3 + -1. Let r = 2/719 - -715/1438. Factor 0*t + 1/2*t**3 + 0 + r*t**z.
t**2*(t + 1)/2
Let a(y) be the third derivative of -1/945*y**7 + 1/45*y**6 - 1/5*y**5 + 0*y + y**4 + 0 - 3*y**3 - 4*y**2. Factor a(k).
-2*(k - 3)**4/9
Let w be (2 + 2)*(-15)/12. Let r be 24/10 - (-2)/w. Factor 0*t**r - 9*t**4 + 8*t**4 + t**2.
-t**2*(t - 1)*(t + 1)
Let p(r) be the third derivative of r**6/240 + r**5/40 + r**4/16 + r**3/12 - 6*r**2. Suppose p(w) = 0. Calculate w.
-1
Let n(k) = k**4 + k**3 + k - 1. Let a(q) = -q**5 + 9*q**3 + 12*q**2 + q - 1. Let b(o) = -a(o) + n(o). Determine s, given that b(s) = 0.
-2, 0, 3
Suppose 2*g = 16 - 8. Let -4/7*n**2 + 6/7*n**g - 2/7*n**5 - 4/7*n**3 + 6/7*n - 2/7 = 0. What is n?
-1, 1
Let v(y) = -y - 6. Let w be v(-8). Let z be (5 - 4) + w/(-4). Factor -2*a**2 + z*a + 0.
-a*(4*a - 1)/2
Let y(i) = 2*i + 22. Let h be y(-10). Let n(d) be the third derivative of 1/30*d**5 - 2*d**h + 2/105*d**7 - 1/20*d**6 + 0*d**4 + 0*d + 0*d**3 + 0. Factor n(s).
2*s**2*(s - 1)*(2*s - 1)
Let t(o) be the second derivative of -o**4/4 - o**3/2 + 3*o**2 - 14*o. Factor t(c).
-3*(c - 1)*(c + 2)
Let a(k) be the third derivative of -k**6/120 + k**5/10 - k**4/2 + 4*k**3/3 - 5*k**2. Suppose a(z) = 0. What is z?
2
Let u(g) be the third derivative of -g**5/90 - g**4/3 - 4*g**3 - 11*g**2. Factor u(f).
-2*(f + 6)**2/3
Let b(o) be the second derivative of -1/110*o**5 - 1/33*o**4 + 2*o + 0 - 1/33*o**3 + 0*o**2. Factor b(i).
-2*i*(i + 1)**2/11
Let q be (12/8)/((-6)/(-4)). Let v = q + -1. Suppose -1/2*g - g**4 + v*g**3 + 1/2*g**5 + g**2 + 0 = 0. Calculate g.
-1, 0, 1
Let a(y) = -y**2. Let w(t) = 6*t**2 - 2. Let j(i) = 4*a(i) + w(i). Factor j(d).
2*(d - 1)*(d + 1)
Let x(v) be the third derivative of v**6/24 - 5*v**4/6 - 8*v**2. Solve x(z) = 0.
-2, 0, 2
Let l be (40/16)/(1/(-2)). Let s be 1/(l/(225/(-10))). Factor s + 1/2*f**2 - 3*f.
(f - 3)**2/2
Let k(n) be the third derivative of -2*n**7/525 - 17*n**6/600 - 2*n**5/25 - 13*n**4/120 - n**3/15 + 7*n**2. Let k(g) = 0. Calculate g.
-2, -1, -1/4
Factor 15*y**2 + 9*y + y + 2*y**4 - 7*y**4.
-5*y*(y - 2)*(y + 1)**2
Let w(b) be the second derivative of 0*b**2 + 2*b - 1/70*b**5 + 0 - 2/21*b**3 - 1/14*b**4. Solve w(h) = 0 for h.
-2, -1, 0
Let r be ((-2)/3)/(((-35)/(-21))/(-5)). Let 8/3 - 16/3*t - 2/3*t**3 + 10/3*t**r = 0. What is t?
1, 2
Let q(i) be the third derivative of -4*i**5/45 - i**4/9 - i**3/18 - 5*i**2. Factor q(x).
-(4*x + 1)**2/3
Determine a so that -1/4 - 1/4*a + 1/4*a**2 + 1/4*a**3 = 0.
-1, 1
Suppose -156*n**2 + 2*n**5 + 2*n + 156*n**2 - 4*n**3 = 0. Calculate n.
-1, 0, 1
Let q = -21 - -25. Let o be 5/20 + 54/40. Solve -2*y**2 + 0 + 2/5*y - o*y**5 + 2*y**q + 6/5*y**3 = 0 for y.
-1, 0, 1/4, 1
Let r(d) be the first derivative of 2*d**3/15 - 2