q**2 - 732*q - 9624. Let r(d) = 5*d**2 + 148*d + 1925. Let s(y) = 14*r(y) + 3*t(y). Determine n, given that s(n) = 0.
-31
Let k be 6 + (-2121)/(-3) + 7. Factor 42*l + 18*l - 5*l**3 + k + 3*l**2 - 43*l**2 + 0*l.
-5*(l - 4)*(l + 6)**2
Let v(p) = 40*p**2 + 40*p + 64. Let q(i) = -114*i**2 - 120*i - 192. Let o(b) = 6*q(b) + 17*v(b). Find f such that o(f) = 0.
-8, -2
Let w = -68621 - -205864/3. Factor -w*t**2 + 2/3*t + 1.
-(t - 3)*(t + 1)/3
Let p(z) = 5*z**2 + 180*z - 170. Let a(q) = -1. Let h(j) = 15*a(j) + p(j). Factor h(c).
5*(c - 1)*(c + 37)
Let f(d) be the second derivative of 5*d**4/36 - 50*d**3/9 + 70*d**2 - 659*d. Determine m, given that f(m) = 0.
6, 14
Suppose -t = 3*t - l - 10, 2 = -2*t + 4*l. Factor -25*u**2 + 1590*u**3 + 5*u**4 + 0*u**4 - 1610*u**t.
5*u**2*(u - 5)*(u + 1)
Suppose -i - 2 = 0, 214 = 3*j - 4*i - i. Let 2*h**2 - 42*h - 42*h + 4 + j*h - 44 = 0. Calculate h.
-2, 10
Let j(q) be the first derivative of -15*q**5/16 - 235*q**4/8 - 91*q**3/2 - 27*q**2 - 22*q + 43. Let s(n) be the first derivative of j(n). Factor s(v).
-3*(v + 18)*(5*v + 2)**2/4
Let h(l) = -l**2 + 6*l - 9. Let i be h(5). Let y = i + 9. Solve y*k**2 + 3*k - 9 - 6 - 5*k - 8*k = 0.
-1, 3
Let g(f) be the first derivative of 2*f**3/33 - 21*f**2/11 - 200*f/11 - 1035. Factor g(s).
2*(s - 25)*(s + 4)/11
Let b(k) be the first derivative of 31*k**5/5 + 125*k**4/16 - 41*k**3/4 - 125*k**2/8 - k/4 - 666. Find s, given that b(s) = 0.
-1, -1/124, 1
Suppose -10*r - 1893 = 3577. Let u = r + 6025/11. Solve 1/11*s**2 + 0 - u*s = 0.
0, 8
Suppose -29*s**2 + 58*s**2 + 11*s**2 + 193*s - 4*s**3 + 104 - 45*s = 0. Calculate s.
-2, -1, 13
Let h be 6/5 - (-44)/55. Determine t so that 5*t**3 - 16*t + 26*t**4 - 23*t**h - 24*t**4 - 17*t**3 + 47*t**2 = 0.
0, 2
Let d(i) be the second derivative of -2*i**7/21 - 74*i**6/15 + 78*i**5/5 - 2*i**4/3 - 154*i**3/3 + 78*i**2 - 136*i + 12. Factor d(o).
-4*(o - 1)**3*(o + 1)*(o + 39)
What is u in 243*u**2 + 3/2*u**4 + 240*u + 159/2 + 84*u**3 = 0?
-53, -1
Let a = -3255255/2 + 1627637. Solve 277/4*h**2 - 399*h + 1/4*h**4 + a*h**3 + 441 = 0 for h.
-21, 2
Let h(v) be the first derivative of -v**5/30 + 9*v**4/8 + 11*v**3/6 - 143*v**2/12 + 14*v + 1182. Factor h(d).
-(d - 28)*(d - 1)**2*(d + 3)/6
Determine c so that 12*c**2 - 8*c - 232*c**3 + 20*c - 230*c**3 + 459*c**3 - 3*c**4 = 0.
-2, -1, 0, 2
Suppose -47*k - 6 = -46*k + 2*z, -4*z = 3*k + 8. Let f(o) be the second derivative of -1/9*o**k + 0 + 1/30*o**5 + 2/3*o**2 - 1/9*o**3 - 23*o. Factor f(a).
2*(a - 2)*(a - 1)*(a + 1)/3
Let i(k) be the third derivative of k**6/120 + k**5/5 - 2*k**4/3 - k**3 + 10*k**2. Let j be i(-13). Factor j - 4*y**4 + 4*y**2 - 33.
-4*y**2*(y - 1)*(y + 1)
Let -134 - 3*l**4 + 36*l - 36*l**3 + 383 - 133 - 155 + 42*l**2 = 0. What is l?
-13, -1, 1
Let p(w) = -172*w - 1018. Let a be p(-6). Let q be (-385)/25*(6 - 86/a). Solve q*s - 6/5 - 3/5*s**2 = 0.
2/3, 3
Suppose -q - 3 = -m, 0 = q - 4*m - 0 - 12. Let j be ((-9)/(-6))/(22/q - -5). Factor -2/3*o**3 + 1/6*o + 1/2*o**5 - o**2 + 1/3 + j*o**4.
(o - 1)*(o + 1)**3*(3*o - 2)/6
Let q(x) be the first derivative of 2/45*x**5 - 54 + 4/9*x**2 + 0*x**4 + 8/3*x - 2/3*x**3. Factor q(u).
2*(u - 2)**2*(u + 1)*(u + 3)/9
Let l(c) = 2*c**3 - 6*c**2 - 9*c + 18. Let g be l(6). Factor 500*q + 5*q**3 - g + 140*q**2 + 312 + 335 + 13.
5*(q + 2)**2*(q + 24)
Let x(b) be the third derivative of -1/8*b**4 + 1/8*b**6 + 2*b - 9*b**2 + 3/2*b**3 - 7/20*b**5 + 0. Determine s so that x(s) = 0.
-3/5, 1
Let i(f) = -78*f**2 + 3360*f - 3373. Let w(o) = 22*o**2 - 1120*o + 1124. Let c(m) = -2*i(m) - 7*w(m). Factor c(z).
2*(z - 1)*(z + 561)
Let y(t) be the first derivative of -t**4/24 - t**3/6 - 49*t + 64. Let h(u) be the first derivative of y(u). Let h(k) = 0. Calculate k.
-2, 0
Let a(d) be the first derivative of -5/18*d**3 - 5/12*d**4 + 7 - 1/6*d**5 + 0*d**2 + 0*d. Solve a(w) = 0 for w.
-1, 0
Let m = 60 + -54. Suppose m*f = 28 - 10. Factor f*y + y**5 + 13*y**3 - 19*y**3 + y**5 + y**5.
3*y*(y - 1)**2*(y + 1)**2
Let q(r) be the second derivative of -3*r**6/10 + 309*r**5/20 - 98*r**4 + 26*r**3 + 360*r**2 + 424*r. Find k such that q(k) = 0.
-2/3, 1, 4, 30
Let j(q) = q**3 - 41*q**2 + 44*q - 168. Let x be j(40). Let o be -7 - -7 - 6*4/x. Solve -2 - 1/3*m + 4/3*m**2 - 1/3*m**o = 0.
-1, 2, 3
Let z(i) be the first derivative of 2*i**5/15 + 4*i**4 - 118*i**3/9 - 62*i**2 - 208*i/3 + 1700. Find m such that z(m) = 0.
-26, -1, 4
Let u(f) be the second derivative of 5*f**7/42 + 2*f**6/3 + f**5/2 - 5*f**4/3 - 5*f**3/2 + 585*f. Factor u(r).
5*r*(r - 1)*(r + 1)**2*(r + 3)
Factor -3/4*h**3 + 75/2*h**2 + 0 + 825/4*h.
-3*h*(h - 55)*(h + 5)/4
Let 4 + 344*q**3 - 4 - 49*q**4 + 196*q**3 - 275*q**4 - 64*q - 152*q**2 = 0. What is q?
-2/9, 0, 8/9, 1
Let d(c) = 979*c - 2933. Let f be d(3). Suppose -2*o + 14 = 2*t, -10 = -2*t - 3*o + 8. Find v such that 6/5*v + 0 - 12/5*v**t - 9/5*v**f + 3*v**2 = 0.
-2, -1/3, 0, 1
Let c = -56 + 80. Suppose -4*n = -4*h - 0*h + 28, c = 2*h - 4*n. Factor -3*x - 2*x + 179 + 20*x**h + 5*x**3 - 199.
5*(x - 1)*(x + 1)*(x + 4)
Let p(i) be the third derivative of -i**8/2016 + i**7/210 - i**6/360 - i**5/10 + 3*i**4/16 + 3*i**3/2 - 2*i**2 - 2074. Factor p(f).
-(f - 3)**3*(f + 1)*(f + 2)/6
Let x = -114651 - -114654. Factor -3456/7*j - 27648/7 - 144/7*j**2 - 2/7*j**x.
-2*(j + 24)**3/7
Let f(v) be the third derivative of v**5/40 - 29*v**4/16 + 45*v**3 - 1184*v**2. Factor f(n).
3*(n - 20)*(n - 9)/2
Let x = -79/6 - -37/2. Let n(s) = s**3 - 4*s**2 + 2. Let r be n(4). Factor -20/3*k + 4/3*k**r + x.
4*(k - 4)*(k - 1)/3
Let c = -685866 + 685869. Let w = -4 + 4. Solve w + 4/5*i + 24/5*i**c - 2*i**4 - 18/5*i**2 = 0 for i.
0, 2/5, 1
Determine x so that -50*x**3 - 2*x**5 + 23*x**2 - 20*x + 31*x**2 + 181*x**4 - 163*x**4 = 0.
0, 1, 2, 5
Find f, given that -93/4*f + 1/4*f**2 + 0 = 0.
0, 93
Let y = 12896/92445 - 38/6163. Solve 24/5 - 6/5*u**3 - 2/5*u - 46/15*u**2 - y*u**4 = 0 for u.
-4, -3, 1
Let b(q) be the third derivative of -19*q**6/600 - q**5/4 - 3*q**4/5 + 2*q**3/15 - 1065*q**2 + 2. Factor b(x).
-(x + 2)**2*(19*x - 1)/5
Let j(c) be the third derivative of -c**7/1260 + 29*c**6/720 - 23*c**5/40 + 331*c**4/144 - 38*c**3/9 + 17*c**2 - 4*c. Solve j(k) = 0.
1, 8, 19
Let n = -7075/3 + 2359. Let u(c) be the third derivative of -1/90*c**6 + n*c**3 - 17/36*c**4 + 11/90*c**5 - 5*c**2 + 0*c + 0. Find m, given that u(m) = 0.
1/2, 2, 3
Let d = 4100 - 2452. Let w = -8192/5 + d. Determine a so that 24/5*a + w + 3/5*a**2 = 0.
-4
Let h(c) be the third derivative of -c**7/4620 - c**6/1980 - 35*c**3/6 + 49*c**2. Let l(o) be the first derivative of h(o). Let l(v) = 0. Calculate v.
-1, 0
Factor -2676*r - 43633*r**2 + 43638*r**2 + 3365 - 694*r.
5*(r - 673)*(r - 1)
Let o be 14/6 + -1*(-1)/(-3). Suppose 0 = 3*v + 2*z + 5 - 7, -v = 2*z + o. What is i in -54*i + 6 + 231/2*i**v = 0?
2/11, 2/7
Suppose m = p, -81*p - 6 = -80*p - 3*m. Factor 1/2*v**4 - 4*v - 3*v**2 + 0 + 3/2*v**p.
v*(v - 2)*(v + 1)*(v + 4)/2
Factor -11148/5 + 11152/5*d - 4/5*d**2.
-4*(d - 2787)*(d - 1)/5
Let h(p) = -2*p**3 - p**2 + p - 2. Let n(o) = -7*o**3 - 237*o**2 - 18249*o - 474558. Let t(b) = -6*h(b) + 2*n(b). Factor t(f).
-2*(f + 78)**3
Let c(f) be the third derivative of 2*f**2 + 1/40*f**5 + 14*f - 1/48*f**4 + 0 + 1/240*f**6 - 1/420*f**7 - 1/6*f**3. Let c(s) = 0. What is s?
-1, 1, 2
Let s be (-36 + 37)*(1 - -1) - 0. Factor -22/5*a**s + 10*a - 26/5 - 2/5*a**3.
-2*(a - 1)**2*(a + 13)/5
Let y(c) = -7*c + 28. Let i be y(-17). Factor i*u - 285*u + 140*u + 18*u**2.
2*u*(9*u + 1)
Determine t, given that 0*t - 1/2*t**5 + 0*t**4 - 6*t**2 + 0 + 13/2*t**3 = 0.
-4, 0, 1, 3
Let t(p) be the first derivative of p**6/240 - p**5/4 + 25*p**4/4 - 43*p**3/3 - 8. Let i(x) be the third derivative of t(x). Determine s, given that i(s) = 0.
10
Let o(p) = 30*p + 5. Let b be o(1). Suppose -4*v - v - 5*j + b = 0, v = -4*j + 22. Find q, given that -q**4 - 12 - 12 - 2*q + 24 + 3*q**v = 0.
-2, 0, 1
Let s(f) be the first derivative of -4*f**5/5 - 4*f**4 + 76*f**3/3 - 28*f**2 - 61. Factor s(u).
-4*u*(u - 2)*(u - 1)*(u + 7)
Let m(q) = -4*q**2 - 741*q + 1399. Let p(z) = 13*z**2 + 2239*z - 4200. Let a(c) = -10*m(c) - 3*p(c). Factor a(n).
(n - 2)*(n + 695)
Let b = -1356/31 - -5455/124. Factor 3/4*j**3 + 0 + b*j**4 + 1/2*j**2 + 0*j.
j**2*(j + 1)*(j + 2)/4
Suppose 10*y = 147 - 457. Let d = 