7*z**3 - w + 4/7*z**2 - 2/7*z = 0.
-2, -1, 1
Factor 307*w**4 - 245*w**5 + 90*w**2 + 99*w**4 + 28*w**5 - 465*w**3 - 28*w**5 + 294*w**4.
-5*w**2*(w - 2)*(7*w - 3)**2
Factor -78/5*o + 1/5*o**3 + 0 + 77/5*o**2.
o*(o - 1)*(o + 78)/5
Suppose -7*p - 13*p + 124 = 11*p. Let z(w) be the first derivative of 8/3*w**3 + w**2 + 0*w + 2*w**p - 22. Factor z(j).
2*j*(2*j + 1)**2
Factor 4*m**5 - 132*m**3 - 5*m**3 + 20*m**4 + 43*m**3 - 50*m**3 - 128*m**2 + 32*m**3.
4*m**2*(m - 4)*(m + 1)*(m + 8)
Let k(f) be the third derivative of f**5/90 + 467*f**4/9 + 872356*f**3/9 - 706*f**2 - f - 2. What is b in k(b) = 0?
-934
Let j = 11 - 3. Factor n**3 + 4*n**2 + 4*n**3 - 8*n**2 - 38*n**2 - j*n**2.
5*n**2*(n - 10)
Let h = 525 - 525. Let b be 6*8/(-32) + (h - -2). Find r such that -b*r**2 - 1/6*r + 0 = 0.
-1/3, 0
Let u(x) be the first derivative of -5*x**4/4 - 20*x**3 - 195*x**2/2 - 140*x + 852. Find t, given that u(t) = 0.
-7, -4, -1
Suppose -669*b = -671*b - 44. Let l(v) = -v**3 - 18*v**2 + 91*v + 66. Let y be l(b). Solve y + 5/4*g + 5/4*g**2 = 0.
-1, 0
Let k(w) = -26*w**2 + 80*w + 432. Let c(h) = -40*h**2 + 78*h + 432. Let r(l) = -2*c(l) + 3*k(l). Let r(p) = 0. What is p?
-36, -6
Let d(c) be the second derivative of c**4/4 - 11*c**3/2 - 414*c**2 - 648*c. Find k, given that d(k) = 0.
-12, 23
Factor 136*h - 85*h**2 + 50*h**2 + 31*h**2.
-4*h*(h - 34)
Let k = -614172 + 1228367/2. Factor 1/4*d**5 - 7/4 + 29/4*d + 17/2*d**3 - 11/4*d**4 - k*d**2.
(d - 7)*(d - 1)**4/4
Let a(y) be the second derivative of 3/50*y**5 - 4/225*y**6 - 1/15*y**4 + 0*y**2 + 1/45*y**3 - 14*y + 4. Factor a(o).
-2*o*(o - 1)**2*(4*o - 1)/15
Let d(s) be the third derivative of -s**6/120 - 13*s**5/4 - 1089*s**4/8 - 4779*s**3/2 + 1787*s**2. Factor d(a).
-(a + 9)**2*(a + 177)
Suppose -3*o + 81*o = 39702. Suppose -o + 521 = 4*c. Factor 0*l - 1/2*l**5 + 3/2*l**2 + 1/2*l**4 + 5/2*l**c + 0.
-l**2*(l - 3)*(l + 1)**2/2
Let m(y) be the first derivative of y**6/6 + 4*y**5/5 - 3*y**4/4 - 10*y**3/3 + 4*y**2 + 992. Factor m(l).
l*(l - 1)**2*(l + 2)*(l + 4)
Suppose 26/5*w**2 - 32/15*w**4 + 16/15*w**3 + 12/5*w + 0 = 0. What is w?
-3/4, 0, 2
Factor 950 + 476*x + 1/2*x**2.
(x + 2)*(x + 950)/2
Let y(n) be the first derivative of 2*n**3/9 + 43*n**2/3 - 2533. Factor y(m).
2*m*(m + 43)/3
Let d(j) = j**2 - 14*j - 42. Let v be d(17). What is k in -24 + 3*k**2 - 41 - v*k - 12 - 7 = 0?
-4, 7
Solve 65/2*c**2 - 5/4*c**3 + 745/4*c + 465/2 = 0 for c.
-3, -2, 31
Let x(b) be the second derivative of -9025*b**2 - 190/3*b**3 - 1/6*b**4 + 2*b - 14. Solve x(y) = 0 for y.
-95
Let u(p) = -2*p**3 - 18*p**2 + 30*p - 501. Let d be u(-12). What is s in s**d + 1/2 - 1/2*s**2 - s = 0?
-1, 1/2, 1
Let x(a) = -8*a**2 + 927*a - 9936. Let i be x(12). Solve 48 - 1/3*n**4 + 4/3*n - 13*n**3 - i*n**2 = 0.
-36, -2, 1
Let a(m) = -m - 24. Let j be a(-17). Let q be 2 + (2/j)/((-5)/35). Find u such that -2*u + 4*u**2 - 6*u + q*u = 0.
0, 1
Let w = 106744/266855 - 2/266855. Factor w*q + 0*q**2 - 1/5 + 1/5*q**4 - 2/5*q**3.
(q - 1)**3*(q + 1)/5
Let p = -985 - -9851/10. Let m(v) be the third derivative of -1/6*v**4 + 0*v + 0*v**3 - p*v**6 - 7*v**2 - 1/5*v**5 + 0 - 2/105*v**7. Factor m(c).
-4*c*(c + 1)**3
Suppose 0 = -5*g + 2*n + 12, 3*g + 9*n - 13*n = 10. Determine s so that 3*s**5 + 72*s**3 + 48 + 37*s**2 - 80*s - 14*s**4 - 15*s**4 - 61*s**g = 0.
-1, 2/3, 2, 6
Let b(w) be the second derivative of -16*w + 35/4*w**4 + 3 + 143/4*w**3 - 3/40*w**5 + 54*w**2. Factor b(f).
-3*(f - 72)*(f + 1)**2/2
Let j(r) = 3639*r + 50950. Let u be j(-14). Solve 0 - 14/3*n**3 + 4/3*n**2 + 10/3*n**u + 0*n = 0.
0, 2/5, 1
Let w be ((-2)/(-48))/((-632)/(-49296)). Factor -5*b**2 + 9/4*b**3 + w*b - 1/2.
(b - 1)**2*(9*b - 2)/4
Suppose 976 = 17*u + 942. Let c(z) be the third derivative of 0 + 0*z - 1/25*z**5 + z**u - 3/200*z**6 + 1/5*z**3 + 1/40*z**4. Factor c(b).
-3*(b + 1)**2*(3*b - 2)/5
Let d(v) be the third derivative of -85*v**7/126 + 497*v**6/12 + 387*v**5/5 + 485*v**4/9 + 16*v**3 - 2*v**2 - 12*v - 16. Let d(a) = 0. What is a?
-2/5, -2/17, 36
Let a(q) be the first derivative of 0*q + 2*q**3 - 13 - 1/20*q**5 + 3/8*q**4 + 13/2*q**2. Let v(x) be the second derivative of a(x). Factor v(l).
-3*(l - 4)*(l + 1)
Let c(a) be the first derivative of -3*a**4/4 - 8*a**3 + 159*a**2/2 + 180*a - 1265. Factor c(v).
-3*(v - 5)*(v + 1)*(v + 12)
Let b(i) = 3*i**2 - 42*i + 2. Let f(z) = z**3 - 18*z**2 + 46*z - 1. Let c be f(15). Let j be b(c). Factor 0*u - 1/4*u**j + 0 - 1/4*u**3.
-u**2*(u + 1)/4
Let m(z) be the first derivative of z**5/40 + 5*z**4/16 - z**3/24 - 5*z**2/8 + 712. What is t in m(t) = 0?
-10, -1, 0, 1
Let m = -1 + 5. Let g(t) = -3*t - 75. Let y be g(-26). What is n in 32*n**2 + 4*n**5 - 15*n - 2*n**y - 8*n**m - n - 10*n**3 = 0?
-2, 0, 1, 2
Suppose 20 = -137*f + 142*f. Let 3*q**4 + 3*q**2 + 17*q**f + 4*q**5 + 13*q**2 + 51*q**3 - 19*q**3 = 0. Calculate q.
-2, -1, 0
Let x(i) = 12*i**2 - 2481*i + 34. Let f(w) = -2*w**2 + 417*w - 6. Let m(b) = 34*f(b) + 6*x(b). What is t in m(t) = 0?
0, 177
Let c(f) = f**2 - 4*f + 1. Let v(m) = -40*m**2 + 660*m - 13555. Let t(b) = 35*c(b) + v(b). Factor t(q).
-5*(q - 52)**2
Factor -215 - 25 - 46*a - 21*a**2 + 74*a**2 - 54*a**2.
-(a + 6)*(a + 40)
Let u(n) be the third derivative of -n + 0*n**3 - 25*n**2 + 1/12*n**4 + 0 - 1/24*n**5 + 1/240*n**6. Factor u(i).
i*(i - 4)*(i - 1)/2
Let p(c) = 10*c - 44. Let k(g) = g**3 + 8*g**2 + 14*g + 2. Let a be k(-5). Let j be p(a). Factor 17*v**2 - j - 1 + 18*v - 20*v**2.
-3*(v - 3)**2
Let c(g) be the third derivative of 2*g**2 + 0 + 35*g**3 + 3*g - 1/8*g**6 - 31/6*g**5 + 115/24*g**4. Factor c(j).
-5*(j - 1)*(j + 21)*(3*j + 2)
Suppose -803 = 123*c - 3755. Determine w, given that 75/2*w**5 + 168*w - 420*w**2 + 456*w**3 - 435/2*w**4 - c = 0.
2/5, 1, 2
Let v = 11665018/1215105 - 2/243021. Factor 256/5 - 64/5*l - v*l**2 + 4*l**3 - 2/5*l**4.
-2*(l - 4)**3*(l + 2)/5
Let x(q) be the first derivative of q**5/210 + q**4/42 - 5*q**3/7 - q**2/2 - 4*q - 50. Let l(d) be the second derivative of x(d). Factor l(z).
2*(z - 3)*(z + 5)/7
Let z = -178 - -182. Factor -b**4 + 0*b**z - b**4 + 14*b**3 - 26*b**2 - 32*b + 46*b**2.
-2*b*(b - 8)*(b - 1)*(b + 2)
Let c = -405237 - -405240. What is u in 14*u - 6 - 19/2*u**2 + u**c + 1/2*u**4 = 0?
-6, 1, 2
Let n(j) be the first derivative of -1/6*j**6 + 0*j**2 - 4/5*j**5 - j**4 + 7 + 0*j**3 + 0*j. Suppose n(g) = 0. What is g?
-2, 0
Let l(p) be the third derivative of 0*p + 68*p**2 - 7/24*p**6 + 0*p**3 - 1/2*p**5 + 0*p**4 + 0 + 0*p**7 + 5/336*p**8. Find s, given that l(s) = 0.
-2, -1, 0, 3
Let k(x) be the third derivative of -x**5/15 - 49*x**4/6 + 68*x**3 + 829*x**2. Factor k(l).
-4*(l - 2)*(l + 51)
Let b(n) = 3*n**2 + 2148*n + 359148. Let l(t) = 6*t**2 + 4308*t + 718296. Let y(c) = 13*b(c) - 6*l(c). Find v, given that y(v) = 0.
-346
Solve 1272*l - 1441/2*l**2 - 126 + 19/2*l**4 + 75*l**3 = 0.
-14, 2/19, 3
Let x be 638/8*(-13 + 11). Let s = -158 - x. Let 3/2 + s*k**2 + 3*k = 0. What is k?
-1
Suppose -14*s + 426 = 57*s. Solve 0 + 10/3*i + 2*i**3 + 2/3*i**4 - s*i**2 = 0 for i.
-5, 0, 1
Let s(x) be the first derivative of -1/3*x**4 - 14/9*x**3 + 0*x - 4/3*x**2 - 16 + 2/15*x**5. Factor s(k).
2*k*(k - 4)*(k + 1)**2/3
Let h(a) be the second derivative of -a**6/120 + a**5/10 + 65*a**4/48 - 2487*a. Factor h(l).
-l**2*(l - 13)*(l + 5)/4
Let i = 38 + -34. Suppose -o = 4*d - i, 4*d - 3*o + 9 = 29. Factor 5 + 3 + 4*r**3 - 4*r - 4*r**2 - 2*r**d - 2*r**2.
4*(r - 2)*(r - 1)*(r + 1)
Let v(x) be the first derivative of 651249*x**5/5 + 648021*x**4/4 - 3224*x**3/3 + 2*x**2 - 5001. Suppose v(z) = 0. What is z?
-1, 0, 2/807
Let l(f) be the first derivative of 1/3*f**3 + 124 - f**2 - 8/3*f + 1/12*f**4. Factor l(p).
(p - 2)*(p + 1)*(p + 4)/3
Let o(u) be the second derivative of -5/36*u**4 + 13*u - 5/36*u**3 + 5/252*u**7 + 1 + 1/18*u**6 + 0*u**2 + 0*u**5. Determine p so that o(p) = 0.
-1, 0, 1
Let h(s) be the second derivative of -s**4/15 + 2416*s**3/15 - 2395*s. Factor h(w).
-4*w*(w - 1208)/5
Let 288/11*p - 2/11*p**3 + 640/11 + 24/11*p**2 = 0. What is p?
-4, 20
Factor 1015/6*c + 5/6*c**2 - 1025/3.
5*(c - 2)*(c + 205)/6
Let j = -266 - -269. Suppose -5*a + 5*r = 10, -a - r = 3*r - 23. Factor t**3 + 5*t**3 - a*t**2 + t**4 - 4*t**4 + 0*t**j.
-3*t**2*(t - 1)**2
Let t(d) be the first derivative of -9*d**2 + 0*d + 1/210*d**5 + 1/21*d**3 - 13 + 1