+ 1)
Let a(w) be the third derivative of -768/5*w**5 + 243*w**2 + 0 - 2*w + 0*w**3 + 0*w**4 - 2/105*w**7 - 16/5*w**6. Suppose a(n) = 0. Calculate n.
-48, 0
Let t(s) = -133*s - 2*s**2 + 41*s + 45*s + 48*s + s**2 - 1. Let k(n) = n**3 - n**2 + 4*n + 1. Let a(b) = 4*k(b) + 20*t(b). Factor a(r).
4*(r - 4)*(r - 1)**2
Factor -1436*y + 297*y**2 - 750 + 1055*y - 300*y**2.
-3*(y + 2)*(y + 125)
Find m, given that -2/7*m**3 + 494/7*m + 248/7 + 244/7*m**2 = 0.
-1, 124
Suppose -6*s = -s - 245. Suppose -3*q - s = -61. What is t in 5*t**4 + t**4 + q*t**4 - 11*t**4 = 0?
0
Let m be 3/(-15) + -4 + 1980/25. Factor 18*z + 12*z**4 + 36*z**3 + m*z**2 - 14*z**4 - 19*z**4.
-3*z*(z - 3)*(z + 1)*(7*z + 2)
Let w(m) = m**3 - 2*m**2 - 2*m + 7. Let l be w(3). Let v(x) = -x. Let f be v(-3). Factor 2*d**5 - 11*d**2 + l*d**4 + 24*d**3 + 19*d**2 - 8*d**f.
2*d**2*(d + 1)*(d + 2)**2
Let m(i) = -7*i**2 + 214*i + 98. Let d be m(31). Let l(p) be the first derivative of 19 + 1/18*p**2 - 1/9*p**3 - 1/36*p**4 + 1/45*p**d + 2/9*p. Factor l(z).
(z - 2)*(z - 1)*(z + 1)**2/9
Let m be 548046/(-68058)*(-19)/6. Let 3/2*z**4 + m*z**3 + 135/2*z**2 + 129/2*z + 21 = 0. What is z?
-14, -1
Let k be (-64)/6*(-9)/6. Let b = k - 11. Let g(x) = -x**2 + x. Let f(y) = -8*y**2 - y. Let v(p) = b*g(p) - f(p). Determine l so that v(l) = 0.
-2, 0
Factor 57/7*f + 59/7 - 2/7*f**2.
-(f + 1)*(2*f - 59)/7
Let w(p) = -2*p**2 + 53*p + 642. Let s be w(-9). Let v(k) be the second derivative of -3/2*k**2 - 1/4*k**4 + 0 + k**s - 49*k. Suppose v(r) = 0. What is r?
1
Suppose 103*f - 100*f - 1059 = 0. Let b = 357 - f. What is w in 0*w + 0*w**2 - 1/3*w**5 + 1/3*w**3 + 0 + 0*w**b = 0?
-1, 0, 1
Let o(a) be the second derivative of 4/7*a**4 - 32/7*a**2 + 3 + 3*a - 1/5*a**5 + 2/105*a**6 + 8/21*a**3. Suppose o(g) = 0. Calculate g.
-1, 2, 4
Factor -2/9*h**5 + 142/9*h**2 + 0*h + 94/3*h**3 + 0 + 46/3*h**4.
-2*h**2*(h - 71)*(h + 1)**2/9
Let k(c) be the second derivative of c**4/8 + 345*c**3/2 + 357075*c**2/4 + 402*c. Factor k(u).
3*(u + 345)**2/2
Let v(p) be the first derivative of 16/3*p**6 + 136/3*p**3 - 152/5*p**5 + 17*p**4 - 134 + 16*p - 50*p**2. Suppose v(y) = 0. Calculate y.
-1, 1/4, 1/2, 1, 4
Let d(n) be the first derivative of -n**3/6 + 10*n**2 - 13721. Factor d(u).
-u*(u - 40)/2
Let d(r) be the third derivative of r**5/80 + 43*r**4/32 - 45*r**3/4 - 2825*r**2. Find s, given that d(s) = 0.
-45, 2
Let y(x) be the second derivative of -x**4/4 + 674*x**3 - 681414*x**2 + 10488*x. Let y(k) = 0. What is k?
674
Suppose 93/5*d - 3 - 78/5*d**2 = 0. What is d?
5/26, 1
Let b(y) be the second derivative of -y**5/10 + 2137*y**4/22 + 106*y**3/3 + 31*y + 140. What is z in b(z) = 0?
-2/11, 0, 583
Let f be 6/(-14) + (-205)/(-70) + -1. Let a be ((-5)/(-2))/(135/108). Find r, given that 9/2*r - f*r**a + 6 = 0.
-1, 4
Let i = 28 + -26. Suppose 3*h + i = 11. Factor 6*t**3 - 22*t**h + 3*t**2 + 10*t - 15*t**2 - 6*t.
-4*t*(t + 1)*(4*t - 1)
Let g(j) be the second derivative of -j**4/12 + 11*j**3/3 - 48*j**2 + 2364*j. Solve g(k) = 0 for k.
6, 16
Let v(x) = -3*x**2 + 28*x - 101. Let w(l) be the first derivative of 10*l**3/3 - 55*l**2 + 405*l + 38. Let d(j) = 15*v(j) + 4*w(j). Factor d(m).
-5*(m - 3)*(m + 7)
Factor 141 + 79 + 435*z + 1197*z**5 - 1192*z**5 - 210*z**4 - 10*z**2 - 551*z**3 + 111*z**3.
5*(z - 44)*(z - 1)*(z + 1)**3
Let l(f) be the third derivative of 2/63*f**7 - 9*f**2 + 0*f**3 - 1/504*f**8 - 3/4*f**4 - 1/5*f**6 + 0 + 3/5*f**5 + 0*f. Suppose l(a) = 0. Calculate a.
0, 1, 3
Let r(q) be the third derivative of -q**7/140 - 77*q**6/80 - 151*q**5/40 - 75*q**4/16 + 1912*q**2. Determine j, given that r(j) = 0.
-75, -1, 0
Suppose 2*r - 5*g - 12 = 8, -4*g - 16 = -3*r. Let u(z) = 8*z**2 - 286*z - 69. Let a be u(36). Find c, given that 1/8*c**a + 0 + 0*c + 1/8*c**4 + r*c**2 = 0.
-1, 0
Let f(t) be the first derivative of t**6/3 - 4*t**5 + 18*t**4 - 116*t**3/3 + 43*t**2 - 24*t - 3341. Let f(m) = 0. Calculate m.
1, 3, 4
Let m(o) be the first derivative of 20*o**4 - 64*o + 80*o**2 + 1/3*o**6 - 61 - 4*o**5 - 160/3*o**3. Solve m(b) = 0.
2
Let o(w) be the second derivative of w**5/15 + 80*w**4/9 - 18*w**3 + 3*w - 250. Determine i, given that o(i) = 0.
-81, 0, 1
Solve 8/19*c**3 - 36/19*c + 6/19*c**2 - 2/19*c**4 + 0 = 0.
-2, 0, 3
Suppose 313/2*y**2 - 1/4*y**5 - 211/4*y - 52*y**4 + 53*y**3 - 209/2 = 0. What is y?
-209, -1, 1, 2
Let z be ((-8)/(-190))/((-4214)/56945). Let l = 2/817 - z. What is p in -l - 2/7*p + 2/7*p**2 = 0?
-1, 2
Let m(o) be the second derivative of -42/5*o**6 + 132/5*o**5 + 20/3*o**3 - 10 - 3*o + 0*o**2 - 67/3*o**4. Factor m(x).
-4*x*(3*x - 1)**2*(7*x - 10)
Let v be ((-16 + 16)/(-7))/(-2). Let g(s) be the first derivative of -2/3*s**3 - 16 + 0*s**2 + v*s - 1/8*s**4. Factor g(b).
-b**2*(b + 4)/2
Let n(i) be the first derivative of 3*i**4/4 - 11*i**3 - 63*i**2 + 4052. Solve n(l) = 0.
-3, 0, 14
Suppose -155042 + 47879 = -441*z. Find h, given that 9*h**2 + z*h + 1/9*h**3 + 2187 = 0.
-27
Factor 2809*b**2 + 0*b + 0 + 1/4*b**4 + 53*b**3.
b**2*(b + 106)**2/4
Let h be (-30)/135*4 - (-107)/90. Let o be (-14)/(-105)*3/4. Find g such that -o*g - h*g**2 + 3/10 + 1/10*g**3 = 0.
-1, 1, 3
Let j(h) = 53*h**3 - 39*h + 44. Let g(s) = -132*s**3 - s**2 + 77*s - 89. Let n(x) = -2*g(x) - 5*j(x). Solve n(v) = 0.
-6, 1, 7
Suppose -564 = -23*r + 517. Suppose -37 = -28*x + r. Factor -9/7*l**x - 3/7*l**4 + 0 - 3/7*l - 9/7*l**2.
-3*l*(l + 1)**3/7
Let p(d) be the second derivative of d**5/40 + 2*d**4/3 - d**3/12 - 4*d**2 - 974*d. Solve p(v) = 0.
-16, -1, 1
Suppose 0 = -106*t + 110*t - 16. Suppose 0 = -d + r + 3, -28 = t*d - 2*r - 40. Solve -d*c**3 + 0 + 0*c - 18/5*c**2 - 3/5*c**5 + 16/5*c**4 = 0 for c.
-2/3, 0, 3
Let t(w) be the first derivative of 490*w**6 - 2611*w**5 - 25855*w**4/12 + 5960*w**3/9 - 50*w**2 + 456. What is f in t(f) = 0?
-3/4, 0, 2/21, 5
Let q = 126874 + -126869. Let r be (2/(-4))/((-6)/9). Factor 3*y - 1/2*y**3 + r*y**2 - q.
-(y - 2)**2*(2*y + 5)/4
Suppose 2*t - 3*m = 67, 4*t - 2*m - 2*m = 140. Suppose 35*x + 15 = t*x. Factor 6/11*z - 4/11*z**3 - 6/11*z**4 + 4/11*z**2 - 2/11*z**x + 2/11.
-2*(z - 1)*(z + 1)**4/11
Let c(w) be the first derivative of w**8/84 - 4*w**7/105 - w**6/30 + 2*w**5/15 - 88*w**2 - 94. Let p(y) be the second derivative of c(y). Factor p(b).
4*b**2*(b - 2)*(b - 1)*(b + 1)
Let b(u) be the third derivative of u**6/960 + 37*u**5/240 + 73*u**4/192 - 1522*u**2. Suppose b(g) = 0. What is g?
-73, -1, 0
Let n be (0 - -5)*2/5. Let y = -821211/4 - -205303. Suppose 0*v - y*v**3 + 1/4*v**n + 0 = 0. Calculate v.
0, 1
Suppose 0 = 3*w - 5*q + 67 - 53, 3*q = -3*w + 66. Factor 15*h**2 - 9/2*h**3 - 22*h + 1/2*h**4 + w.
(h - 3)*(h - 2)**3/2
Let d(o) be the second derivative of o**5/80 + 43*o**4/48 + 65*o**3/3 + 150*o**2 - 406*o. What is l in d(l) = 0?
-20, -3
Let u(z) = 7*z**2 - 2292*z + 435483. Let q(v) = 2*v**2 - 3*v. Let t(b) = -2*q(b) + u(b). Find o such that t(o) = 0.
381
Let a = -2763 + 16583/6. Let b(s) be the second derivative of 1/4*s**5 + 20*s + 0*s**2 + a*s**4 + 5/6*s**3 + 0. Suppose b(t) = 0. What is t?
-1, 0
Let m be ((-2)/12 + 87/(-18))/(-1). Suppose 0 = -m*f - o + 11, 8*f - 5*o = 13*f - 15. Solve -1/6*y**f - 25/6 - 5/3*y = 0.
-5
Let v be (-2046)/(-440) + 3*1 - 4. Let s = -17/5 + v. Suppose 0*d**2 + 0*d + s*d**3 + 0 = 0. Calculate d.
0
Factor -138*z - 223*z - 121*z - 2*z**2 + 64*z.
-2*z*(z + 209)
Let p be 6*-2*1298/1089. Let y = -139/11 - p. Determine r, given that -1/3*r**2 - y*r - 2 = 0.
-3, -2
Let v(n) = 295*n - 146*n - 148*n + 1 + n**3. Let s(y) = -7*y - 4*y**2 - 4 - y**3 + 2*y**3 - 3*y**3 + 5*y. Let t(c) = -s(c) - 4*v(c). Factor t(k).
-2*k*(k - 1)**2
Let y = 1892127/7 + -270297. Factor -6/7*d**2 + 124/7*d - y - 10/7*d**3.
-2*(d - 3)*(d + 4)*(5*d - 2)/7
Let g(a) = -3*a**2 - 9*a - 10. Let t be g(-5). Let q = t - -44. Factor -2*w**5 + 6*w - 4*w**4 - 4*w + 3*w**q + 5*w**4 - 4*w**2.
-2*w*(w - 1)**3*(w + 1)
Suppose v + 4*h = -66 + 87, 4*v + 4*h = 36. Find c such that 0 - 19/5*c**4 + 3/10*c**v + 66/5*c**3 - 36/5*c**2 + 0*c = 0.
0, 2/3, 6
Let b(l) be the second derivative of -6*l**5/5 - 173*l**4 + 695*l**3/4 - 261*l**2/4 - 238*l + 2. Factor b(n).
-3*(n + 87)*(4*n - 1)**2/2
Let g be (1 - (-18)/(-81))*(-27)/(-126). Let j(m) be the first derivative of g*m**4 - 5/3*m**2 - 8/9*m**3 + 0*m + 5. Let j(t) = 0. What is t?
-1, 0, 5
Suppose -6*b - 9/2*