ose 4*i - 2*j - 6 = 0, 6*i - 7*i - 21 = -5*j. Let m(v) be the second derivative of -3/2*v**i - 6/5*v**5 + 0 - 2/3*v**3 + v + 0*v**2 - 1/3*v**6. Factor m(d).
-2*d*(d + 1)**2*(5*d + 2)
Let y be (18/36)/(1/4) - 2. Let t(a) be the first derivative of -1/9*a**3 + y*a + 13 + 1/3*a**2. Let t(u) = 0. Calculate u.
0, 2
Let b(m) be the third derivative of 0 + 1/60*m**4 + 0*m - 24*m**2 + 1/100*m**6 + 0*m**3 + 1/525*m**7 + 1/50*m**5. Find p such that b(p) = 0.
-1, 0
Let b be (-26)/12 + (-4)/168*-7. Let u be 4/(-4 - b) - (10 - 16). Factor 0 - 1/3*t**5 + 0*t**2 + 0*t - t**u + 0*t**3.
-t**4*(t + 3)/3
Let r = 85 + -82. What is j in -r*j**2 + 24*j - 20 - j**2 + 0*j**2 = 0?
1, 5
Let g(b) = -12*b**2 + 0*b + 21*b**2 + 6 - 9*b + 9*b**3 + 1. Let q(m) = m**3 + m**2 - m + 1. Let a(t) = 3*g(t) - 24*q(t). Factor a(w).
3*(w - 1)*(w + 1)**2
Let l be (-12)/4*(-17)/204. Let t(q) be the first derivative of -5 - 1/12*q**3 - l*q + 1/4*q**2. Factor t(u).
-(u - 1)**2/4
Suppose 6*u + 1/2*u**3 + 4*u**2 + 0 = 0. What is u?
-6, -2, 0
Let o(i) be the third derivative of i**6/280 - i**5/28 - 13*i**4/56 - i**3/2 - 46*i**2. Suppose o(k) = 0. Calculate k.
-1, 7
Let b = 487 + -485. Let d(u) be the first derivative of 1/4*u**4 - 3/2*u**2 + b*u - 2 + 0*u**3. What is p in d(p) = 0?
-2, 1
Suppose -20 = -t + f + 2, 4*f = -t + 42. Let t + 28*h**3 + 5*h**4 - 24*h - 3*h**5 - h**3 - 2*h**4 - 39*h**2 + 10 = 0. Calculate h.
-3, -1, 1, 2
Let o(d) = d**3 - 16*d**2 + 16*d - 2. Let v be o(15). Let y = 13 - v. Let 0 + 1/4*h**2 + y*h = 0. What is h?
0
Let y(d) be the second derivative of 2 + 1/50*d**5 + 0*d**2 - 2/15*d**3 - 31*d + 1/30*d**4. Factor y(s).
2*s*(s - 1)*(s + 2)/5
Solve -32/9 - 8/9*o**2 + 4/9*o**4 - 2/9*o**5 + 22/9*o**3 - 56/9*o = 0 for o.
-2, -1, 2, 4
Let j be (2 + -48 + 1)*(5 + -4). Let z = 48 + j. Factor -4/3*y - 2/3*y**4 + 4/3*y**z + 2/3*y**2 + 0.
-2*y*(y - 2)*(y - 1)*(y + 1)/3
Suppose u = 5, -2*y - 5*u + 3*u - 6 = 0. Let f be y/(-12) - ((-14)/(-6) - 2). Factor 0 + 0*p + 1/3*p**3 - f*p**4 - 1/3*p**5 + 1/3*p**2.
-p**2*(p - 1)*(p + 1)**2/3
Let j(u) = -310*u + 932. Let d be j(3). Determine q so that 0*q - 3/5*q**d + 12/5*q**4 + 9/5*q**3 + 0 = 0.
-1, 0, 1/4
Let u(b) be the first derivative of 4*b - 12 + 3/2*b**2 - 1/3*b**3. Factor u(q).
-(q - 4)*(q + 1)
Let r be 12/(-7)*(-42)/12. Let f(y) be the third derivative of -4*y**2 + 1/48*y**4 + 0*y**3 + 0 + 1/840*y**7 - 1/80*y**5 + 0*y + 0*y**r. Factor f(k).
k*(k - 1)**2*(k + 2)/4
Let c(s) be the third derivative of s**11/66528 - s**9/12096 + 5*s**5/12 - 13*s**2. Let u(q) be the third derivative of c(q). What is v in u(v) = 0?
-1, 0, 1
Factor 561*u**3 - 298*u**3 + 780*u**2 + 12 - 245*u - 443*u**3 + 8.
-5*(u - 4)*(6*u - 1)**2
Let c(i) be the second derivative of 5*i**5/4 - 10*i**4/3 + 5*i**3/6 + 5*i**2 + 2*i + 38. Let c(g) = 0. What is g?
-2/5, 1
Let v(m) be the first derivative of 16/9*m**3 - 13 + 0*m - 2/15*m**5 - 4*m**2 + 1/6*m**4. Suppose v(o) = 0. Calculate o.
-3, 0, 2
Suppose -j + 54 = 17*j. Let q(g) be the third derivative of -5*g**2 + 1/6*g**j + 27/160*g**6 + 3/16*g**5 + 0 + 0*g - 1/3*g**4. Factor q(h).
(h + 1)*(9*h - 2)**2/4
Let b(k) be the first derivative of 1/3*k**6 - 1/2*k**4 + 0*k**5 + 11 + 0*k**3 + 0*k + 0*k**2. Suppose b(n) = 0. Calculate n.
-1, 0, 1
Factor 72 + 69 + 68 - 217 + l**2 - 7*l.
(l - 8)*(l + 1)
Let b be (-42)/(-36)*-2 + 1 + 2. Factor -2/9*t**2 - 4/9*t + b.
-2*(t - 1)*(t + 3)/9
Let h = -1205 + 1207. Solve -6/11*a**3 + 0 + 2/11*a**4 + 0*a + 4/11*a**h = 0.
0, 1, 2
Let x = 39979 + -159903/4. Factor x*z**2 - 1/2*z + 0 - 5*z**3 + 9/4*z**4.
z*(z - 1)**2*(9*z - 2)/4
Let f(i) be the second derivative of i**6/60 - 3*i**5/40 + i**4/24 + i**3/4 - i**2/2 - 63*i. Factor f(z).
(z - 2)*(z - 1)**2*(z + 1)/2
Let p(k) be the second derivative of -k**10/36288 - k**9/9072 - k**8/8064 - k**4/6 - 7*k. Let q(a) be the third derivative of p(a). Factor q(d).
-5*d**3*(d + 1)**2/6
Solve -2/17*s**3 - 12/17 + 12/17*s**2 + 2/17*s = 0.
-1, 1, 6
Let r(h) be the third derivative of -h**7/3780 - 11*h**6/1620 - 2*h**5/45 + h**4/3 + 19*h**3/3 + 8*h**2. Let i(a) be the first derivative of r(a). Factor i(n).
-2*(n - 1)*(n + 6)**2/9
Suppose -x = -1 - 1. Let d be (10/(-4) - -1)*-2. Factor -4*f + 2*f**2 - d*f + 3*f + x*f**3.
2*f*(f - 1)*(f + 2)
Factor -20*i - 62 + i**4 + 25*i**2 - 9*i**3 - 2*i - 5*i + 72.
(i - 5)*(i - 2)*(i - 1)**2
Factor -14/11 + 8/11*t**3 + 2/11*t**4 + 40/11*t - 36/11*t**2.
2*(t - 1)**3*(t + 7)/11
Let q(g) be the third derivative of g**6/30 + 14*g**5/15 - 5*g**4/2 + 128*g**2. Solve q(m) = 0.
-15, 0, 1
Let g(m) be the third derivative of m**7/630 + 17*m**6/360 - 29*m**5/90 + 5*m**4/9 + 205*m**2. Let g(l) = 0. Calculate l.
-20, 0, 1, 2
Let g be ((-2)/(-6))/((-1)/(-6)). Let u(n) = n**3 + 2*n**2 - 12*n - 13. Let j be u(-4). What is w in 12*w + 0*w**j + 54 + 18*w**2 + g*w**3 + 42*w = 0?
-3
Suppose 3*g = 3*i - 24, 0*g = -3*i + g + 16. Factor -6 - 530*h**2 - 1624*h**i + 301*h - 405*h - 2 - 784*h**5 - 1324*h**3.
-2*(2*h + 1)**3*(7*h + 2)**2
Let w(r) = -r**3 + 3*r**2 - r. Let h be w(2). Factor 6*i - 4*i**4 - 3*i - i + 5*i**4 - 3*i**h.
i*(i - 1)**2*(i + 2)
Factor 681/5*f**2 + 5776/5 - 3496/5*f + 1/5*f**4 - 46/5*f**3.
(f - 19)**2*(f - 4)**2/5
Let l(d) be the second derivative of -d**6/15 - 4*d**5/5 - d**4 + 8*d**3/3 + 7*d**2 - 4*d - 5. Factor l(r).
-2*(r - 1)*(r + 1)**2*(r + 7)
Let b(o) = 5*o**5 + 4*o**4 - o**3 - 2*o**2 + 2. Let x(n) = -36*n**5 - 27*n**4 + 9*n**3 + 15*n**2 - 15. Let w(v) = -15*b(v) - 2*x(v). Factor w(s).
-3*s**3*(s + 1)**2
Let x(n) be the first derivative of 3*n**3/7 - 3*n**2/2 - 30*n/7 - 172. Factor x(g).
3*(g + 1)*(3*g - 10)/7
Factor -2/13*u**2 + 44/13 + 18/13*u.
-2*(u - 11)*(u + 2)/13
Let n(o) be the third derivative of 5*o**8/112 - 9*o**7/35 + 17*o**6/40 - o**4/2 + 51*o**2. What is y in n(y) = 0?
-2/5, 0, 1, 2
Let b(c) = -c + 4. Let z be b(0). Let w = 27 + -25. Let -2*d - 4*d**3 - d**z - 3*d**3 + 3*d**3 - 5*d**w = 0. Calculate d.
-2, -1, 0
Determine x, given that 7/3*x - 8/3 + 1/3*x**2 = 0.
-8, 1
Let m(c) be the second derivative of c**6/60 + 67*c**5/20 + 253*c**4 + 24200*c**3/3 + 42592*c**2 + 15*c - 9. Find r such that m(r) = 0.
-44, -2
Let a(o) be the second derivative of -o**4/60 + 326*o**3/15 - 53138*o**2/5 + 170*o - 3. Factor a(k).
-(k - 326)**2/5
Let x(z) be the third derivative of -1/600*z**6 + z**2 - 1/15*z**3 + 0*z + 16 + 1/120*z**4 + 1/100*z**5 - 1/1050*z**7. Solve x(c) = 0 for c.
-2, -1, 1
Let n(u) = -11*u**4 + 13*u**3 - 12*u**2 - 17*u. Let p(a) = -3*a**4 + 4*a**3 - 4*a**2 - 6*a. Let t(i) = 2*n(i) - 7*p(i). Find z such that t(z) = 0.
-2, 0, 2
Let d(s) be the third derivative of -s**7/42 + 5*s**6/12 - 7*s**5/3 + 5*s**4 - 593*s**2 + s. Factor d(o).
-5*o*(o - 6)*(o - 2)**2
Let j = -27 - -35. Suppose 3*d - 7*d + j = 0. Factor 8/9*w**3 - 2/9 - 2/9*w**4 + 8/9*w - 4/3*w**d.
-2*(w - 1)**4/9
What is u in 13 + 76*u**2 - 12 + 49*u + 11 + 115*u**5 + 16*u**4 + 54*u**3 - 114*u**5 = 0?
-12, -1
Suppose -7*w - 28 = -2*h - 2*w, 0 = -h - 5*w - 16. Factor -d**3 + 11*d**3 - 2*d**5 + h*d**2 - 4*d**3.
-2*d**2*(d - 2)*(d + 1)**2
Let g be (-20)/(-9) + -2 + (-56)/252. Let p(b) be the third derivative of 0*b**3 + 1/240*b**5 - 1/480*b**6 - b**2 + 0*b + 1/48*b**4 + g. Factor p(m).
-m*(m - 2)*(m + 1)/4
Suppose 8*j - 2*x = 4*j + 6, 2*x + 6 = 3*j. Determine t, given that -2/5*t**2 - 4/15*t + j - 2/15*t**3 = 0.
-2, -1, 0
Suppose -32*i + 41 = -183. Let z(n) be the third derivative of -2*n**2 + 0*n**5 + 0*n**3 + 0 - 1/1155*n**i + 0*n + 1/660*n**6 + 0*n**4. Factor z(x).
-2*x**3*(x - 1)/11
Let w(m) be the first derivative of m**5 + 35*m**4/4 - 5*m**3 - 115*m**2/2 - 70*m + 374. Factor w(g).
5*(g - 2)*(g + 1)**2*(g + 7)
What is h in -512*h**2 - 8*h**3 + 8*h**4 - h**5 + 10*h**5 + 32*h**4 - 392 + 868*h - 5*h**5 = 0?
-7, 1, 2
Let z(s) be the second derivative of s**4/6 - 5*s**3 + 26*s**2 + 110*s - 2. Factor z(h).
2*(h - 13)*(h - 2)
Let h(r) be the third derivative of r**5/20 + 25*r**4/4 + 625*r**3/2 + 3*r**2 + 18*r. Factor h(s).
3*(s + 25)**2
Let g = -33895 - -576235/17. Factor -44/17*a**2 + 10/17*a**3 + g - 2*a.
2*(a - 5)*(a + 1)*(5*a - 2)/17
Suppose -32*h + 16 = -28*h. Let -7*v**3 + 5*v**3 - 3*v**2 - 5*v**2 - 2*v - h*v = 0. Calculate v.
-3, -1, 0
Let g = 1825 - 54749/30. Let w(u) be the third derivative of 0*u + 0 + 0*u**3 + 1/75*u**5 - u**2 - g*u**4. Factor w(