Let d = -25019/90 - -278. Let v(j) be the third derivative of 0 + 1/27*j**3 - d*j**5 + 1/54*j**4 + 3*j**2 + 0*j. Suppose v(o) = 0. What is o?
-1/3, 1
Let g be 2 - (0 - (-1 - -1)). Determine q so that -q**4 - 6*q**2 + 0*q**4 - 3 + g - 4*q - 4*q**3 = 0.
-1
Let d(k) be the first derivative of -1 - 4/3*k**3 + 0*k + 1/2*k**2. Find z such that d(z) = 0.
0, 1/4
Let r(l) be the third derivative of l**8/336 - l**7/105 + l**6/120 - 6*l**2. Suppose r(n) = 0. Calculate n.
0, 1
Let s(w) be the second derivative of w**6/15 - 3*w**5/10 + w**4/6 + w**3 - 2*w**2 + 12*w. Factor s(m).
2*(m - 2)*(m - 1)**2*(m + 1)
Let y(f) be the third derivative of -f**8/672 - f**7/420 + f**6/40 - f**5/60 - 5*f**4/48 + f**3/4 - 14*f**2. Factor y(c).
-(c - 1)**3*(c + 1)*(c + 3)/2
Let i(k) = -k**2 + 2*k + 8. Let y(j) = j**2 - j + 1. Let b(d) = i(d) - 3*y(d). Let l(n) = -n**2 + n + 1. Let m(q) = -b(q) + 5*l(q). Let m(a) = 0. What is a?
0
Factor 5*c**5 + c**2 - 11*c**2 - 6*c**3 + 0*c**2 - 9*c**3.
5*c**2*(c - 2)*(c + 1)**2
Let w(x) be the first derivative of -2*x**3/3 - 4*x**2 - 8*x - 3. Suppose w(g) = 0. Calculate g.
-2
Let s(i) = -4*i**5 + 4*i**4 - 6*i**3 + i**2 - 5. Let w(u) = -u**5 + u**4 - u**3 - 1. Let g(o) = -s(o) + 5*w(o). Factor g(h).
-h**2*(h - 1)**2*(h + 1)
Let g(o) be the second derivative of o**4/48 + 5*o**3/12 + 25*o**2/8 + 6*o. Factor g(v).
(v + 5)**2/4
Let o be (2 - 36/44) + 2/(-11). Suppose -o + 1/2*d**2 + 1/2*d = 0. Calculate d.
-2, 1
Let p(s) = 2*s**2 - 1 + 1. Let u be p(-1). Factor 58*i**3 + 362*i**3 - 686*i**5 + 7*i + 9*i - 98*i**4 - 152*i**u.
-2*i*(i + 1)*(7*i - 2)**3
Let s(f) = -f**2 + 6*f - 5. Let c be s(4). Let i(r) = -r**2 + 12*r + 15. Let p be i(13). Solve -t**4 + p*t + c*t**2 + 4*t**3 + t**2 + t**2 + 2*t**4 = 0.
-2, -1, 0
Factor 10*u**4 + 35*u**3 + 25*u**3 + 300*u + 125 - 5*u**4 + 230*u**2.
5*(u + 1)**2*(u + 5)**2
Let u be (-234)/(-57) + 12/(-114). Let a(w) be the first derivative of -4/5*w + w**2 - 8/15*w**3 + 1/10*w**u + 2. Let a(p) = 0. What is p?
1, 2
Let q(m) = m**2 + 2*m + 2. Let c(y) = y + 10. Let w be c(-12). Let s be q(w). Find o, given that o**s + 0*o - o + 1 + 0 - o = 0.
1
Let v(s) be the third derivative of s**5/20 + s**4/4 + s**3/2 + 12*s**2. Solve v(i) = 0 for i.
-1
Let g = 11/24 - 1/8. Let s be 5 + (-10)/2*36/60. Factor 0*v - g*v**s + 1/3.
-(v - 1)*(v + 1)/3
Let o(t) = 7*t**3 + t**2 - 2*t + 1. Let r be o(1). Factor 6*l**3 + 4*l**2 + r*l**2 - 7*l**2 - 2*l.
2*l*(l + 1)*(3*l - 1)
Let r(z) = -8*z**2 + 16*z + 17. Let k(n) = 4*n**2 - 8*n - 9. Let a(q) = 7*k(q) + 3*r(q). Find i such that a(i) = 0.
-1, 3
Let y = 1655/3 + -551. Determine r, given that y + 5/3*r**3 - 5/3*r - 2/3*r**2 = 0.
-1, 2/5, 1
Let n(p) be the second derivative of p**7/10080 - p**5/480 - p**4/3 + 4*p. Let u(w) be the third derivative of n(w). Factor u(k).
(k - 1)*(k + 1)/4
Let x(m) = m**3 - 13*m**2 - 13*m - 11. Suppose 4*a - 4*v - 48 = 0, 2*v = -3*a - 13 + 59. Let g be x(a). Suppose -w**g + 1/4 + w - 1/4*w**2 = 0. What is w?
-1, -1/4, 1
Let s be -1 + 30/4 + 4. Factor 37/2*c**2 + 2*c**4 - 12*c + 2 - s*c**3.
(c - 2)**2*(c - 1)*(4*c - 1)/2
Let l(c) be the third derivative of c**8/1280 - c**7/210 + 11*c**6/960 - c**5/80 - c**4/12 - 3*c**2. Let k(t) be the second derivative of l(t). Factor k(m).
3*(m - 1)**2*(7*m - 2)/4
Let c(u) be the third derivative of -5*u**8/952 - 16*u**7/1785 + 11*u**6/1020 + 8*u**5/255 + u**4/51 - 9*u**2. Suppose c(z) = 0. What is z?
-1, -2/3, -2/5, 0, 1
Let x = 34 + -32. Solve 5/2*l**x - 5/2*l**4 - l + 0 - 1/2*l**3 + 3/2*l**5 = 0 for l.
-1, 0, 2/3, 1
Let a be (-7)/((-28)/(-8))*3. Let g = 8 + a. Factor 0*m**g - 2/9*m + 0*m**4 + 0 - 2/9*m**5 + 4/9*m**3.
-2*m*(m - 1)**2*(m + 1)**2/9
Let u(o) = -o**2 + 8*o - 7. Let p be u(7). Solve -v**4 + 4*v + p*v**5 - v**5 - v**3 - 2*v**4 - 2*v + 3*v**2 = 0 for v.
-2, -1, 0, 1
Let p be 9/(-15) + 28/5. Suppose 10*m - 40 = p*m. Let 0 - 14/3*a**3 - m*a**2 + 8/3*a = 0. Calculate a.
-2, 0, 2/7
Let f be 4/300*(-27)/(-21). Let i(c) be the third derivative of 0*c + 0 - 14/75*c**5 + c**2 - f*c**7 - 1/10*c**6 - 2/15*c**4 + 0*c**3. Factor i(t).
-2*t*(t + 2)*(3*t + 2)**2/5
Let w(d) be the first derivative of 5*d**4/16 - 5*d**3/3 + 15*d**2/8 + 16. Suppose w(y) = 0. What is y?
0, 1, 3
Factor 15*x - 3*x**2 + 6*x**3 - x**3 + 23*x**2.
5*x*(x + 1)*(x + 3)
Let z(k) = 5*k**4 + 5*k**3 + 4*k**2 - 4*k. Let q(u) = 4*u**4 + 4*u**3 + 3*u**2 - 3*u. Let x = 11 - 8. Let o = x - 0. Let w(i) = o*z(i) - 4*q(i). Factor w(y).
-y**3*(y + 1)
Let b(z) be the second derivative of 7*z**6/16 - 177*z**5/160 - 21*z**4/16 + 11*z**3/4 - 3*z**2/2 + z + 7. Find s, given that b(s) = 0.
-1, 2/7, 2/5, 2
Let a(b) be the first derivative of 0*b**2 - 1/9*b**6 - 1/2*b**4 - 2/5*b**5 - 1 + 0*b - 2/9*b**3. Let a(o) = 0. What is o?
-1, 0
Let z = -1306/5 + 263. Factor 6/5*o**2 + 21/5*o + z.
3*(o + 3)*(2*o + 1)/5
Let i(c) be the third derivative of c**7/70 + c**6/20 - c**5/20 - c**4/4 + 4*c**2. Factor i(f).
3*f*(f - 1)*(f + 1)*(f + 2)
Factor 32/5*r + 6/5*r**2 + 2.
2*(r + 5)*(3*r + 1)/5
Let d be (-2)/12 - 309/(-18). Suppose -5 = 3*v - d. Let 8*u**4 + 2*u**2 + 2*u**5 + 2*u**3 - 10*u**v - 4*u**3 = 0. What is u?
-1, 0, 1
Let b(a) be the first derivative of -a**5/120 - a**4/12 - a**3/3 + a**2/2 + 3. Let t(w) be the second derivative of b(w). Factor t(u).
-(u + 2)**2/2
Let b be ((-28)/(-6))/((-22)/1). Let v = 6/11 + b. Factor v*c**5 + c**2 + 0 - c**4 + 1/3*c**3 - 2/3*c.
c*(c - 2)*(c - 1)**2*(c + 1)/3
Let r(v) be the third derivative of v**9/1080 + v**8/2240 - v**7/1260 - v**4/8 + 2*v**2. Let t(z) be the second derivative of r(z). Solve t(j) = 0.
-1/2, 0, 2/7
Factor 2*p - 8/3*p**2 + 2/3*p**3 + 0.
2*p*(p - 3)*(p - 1)/3
Let d(j) be the first derivative of j**4/3 + 4*j**3/3 + 2*j**2 - 7*j - 4. Let t(y) be the first derivative of d(y). Solve t(p) = 0 for p.
-1
Let f(r) = -r**3 - 3*r**2 + 2*r - 5. Let v be f(-4). Factor -2 + 4 - 2*l + 6*l**v - 2*l**2 - 4*l**3.
2*(l - 1)**2*(l + 1)
Let v be 33/6 + (-3)/(-6). Let p(i) = i**2 - 5*i - 2. Let o be p(v). Factor -32/3*t + 8/3 - 38/3*t**3 - 2/3*t**5 + 50/3*t**2 + 14/3*t**o.
-2*(t - 2)**2*(t - 1)**3/3
Let r(q) be the third derivative of -q**9/20160 + q**8/3360 - q**7/1680 + 3*q**5/20 - 10*q**2. Let o(k) be the third derivative of r(k). Solve o(u) = 0 for u.
0, 1
Factor 4/9 - 14/9*f**2 - 10/9*f.
-2*(f + 1)*(7*f - 2)/9
Let f(b) = -3*b**2 + 7*b + 1. Let w(g) = g**2 - g - 1. Let h = 11 + -8. Let y(s) = h*w(s) - f(s). Find a such that y(a) = 0.
-1/3, 2
Let m(t) = -2*t. Let h(d) = d**2 + 6*d. Let g(k) = 2*h(k) + 4*m(k). Factor g(v).
2*v*(v + 2)
Let k(u) = -9*u**3 - 21*u**2 + 9*u - 5. Let i(b) = 2*b**3 + 5*b**2 - 2*b + 1. Let m(h) = 26*i(h) + 6*k(h). Determine d, given that m(d) = 0.
-1, 1, 2
Let f(l) be the first derivative of -10*l**6/3 - 5*l**5 + 15*l**4/4 + 25*l**3/3 + 5*l**2/2 - 7. Suppose f(x) = 0. What is x?
-1, -1/4, 0, 1
Let n(w) = w**2 + w. Let i(p) = -25*p**4 - 85*p**3 - 115*p**2 - 65*p - 10. Let g(s) = -i(s) - 10*n(s). What is r in g(r) = 0?
-1, -2/5
Let j(z) be the first derivative of z**4/4 + z**3/3 - 4. Determine o, given that j(o) = 0.
-1, 0
Let c(n) be the first derivative of n**4/14 - 2*n**3/21 - 2*n**2/7 - 3. Factor c(j).
2*j*(j - 2)*(j + 1)/7
Let d(g) be the third derivative of 0*g + g**2 + 0 - 1/6*g**3 + 1/300*g**5 + 0*g**4 - 1/900*g**6. Let z(l) be the first derivative of d(l). Factor z(a).
-2*a*(a - 1)/5
Let z(b) be the first derivative of -b**4/12 - b**3/3 + 4*b/3 - 8. Determine i so that z(i) = 0.
-2, 1
Let c(b) = -b - b + 2 + 3*b. Let i be c(5). Let -x**3 + 3*x**3 - 9*x - 12*x**2 - 2 - i*x**3 = 0. What is x?
-1, -2/5
Let m = -121 - -121. What is l in 4/3*l**2 + m*l + 2/3*l**3 + 0 - 2/3*l**4 = 0?
-1, 0, 2
Let w(u) be the third derivative of -u**8/336 - u**7/105 - u**6/120 - 8*u**2. Factor w(j).
-j**3*(j + 1)**2
Let s(d) be the third derivative of d**8/16800 - d**7/6300 - d**6/900 - d**4/12 + d**2. Let y(x) be the second derivative of s(x). Solve y(k) = 0.
-1, 0, 2
Let i(o) be the first derivative of -o**5/80 + 3*o**4/16 - 9*o**3/8 + 3*o**2/2 + 9. Let g(d) be the second derivative of i(d). Factor g(k).
-3*(k - 3)**2/4
Let h(f) be the second derivative of -1/25*f**6 + 1/6*f**5 + 2/15*f**2 - 6*f + 0 - 7/30*f**4 + 1/15*f**3. Determine n so that h(n) = 0.
-2/9, 1
Let b(o) = 4*o**3 - 8*o**2 - 16*o + 2. Let r(j) = 3*j**3 - 8*j**2 - 15*j + 1