 445*w + 5*z + 17. Determine c, given that -36/5 + 3/5*c + 3/5*c**w = 0.
-4, 3
Let x(v) be the first derivative of -6852*v**3 - 3744*v**2 + 3537/5*v**5 - 2514*v**4 - 768*v + 252 - 81/2*v**6. Let x(j) = 0. Calculate j.
-1, -2/9, 8
Let y(a) = a**4 - a**3 + a. Let j = 56 + 43. Let f = j - 104. Let w(o) = -o**4 + 12*o**2 + 9*o. Let g(r) = f*y(r) + w(r). Factor g(p).
-p*(p - 2)*(2*p + 1)*(3*p + 2)
Suppose -69*i = -120*i. Let f(r) be the first derivative of -1/8*r**4 + r + i*r**3 + 3/4*r**2 - 17. Determine w, given that f(w) = 0.
-1, 2
Suppose -5*o + 44*y = 46*y - 101, -10*o + 98 = -4*y. Find b such that 3/2*b**3 - 12 - o*b**2 + 51/2*b = 0.
1, 8
Suppose 0 = -10*k - 507482 + 507502. Determine d, given that k*d - 5/4*d**2 + 1 = 0.
-2/5, 2
Suppose 607 + 219 = 14*r. Solve -102*n - 4*n**2 - 23 + r*n + 3*n**2 + 67*n = 0.
1, 23
Let h(s) be the first derivative of 4/3*s**3 + 38*s + 0*s**2 - 33 + 1/12*s**4. Let d(w) be the first derivative of h(w). Suppose d(b) = 0. What is b?
-8, 0
Let j = 189256/9 - 21028. Let l(s) be the first derivative of 2/3*s**2 - 3 + 8/3*s - j*s**3. Factor l(x).
-4*(x - 2)*(x + 1)/3
Suppose -a + 2 = -3*g - 3, g + 25 = 5*a. Let x(l) be the third derivative of -1/12*l**a + 34*l**2 + 0*l**3 + 5/24*l**4 + 0 + 0*l. Factor x(h).
-5*h*(h - 1)
Let w be ((111 + -23)/22)/(-3 + 185/61). What is a in -w*a**3 - 25/2*a**5 - 265/4*a**4 - 32*a - 94*a**2 - 4 = 0?
-2, -1/2, -2/5
Suppose 711 = 13*b - 10*b. Let y = 240 - b. Factor 0 + 4/5*q**y + 2/5*q**4 - 2/5*q**2 - 4/5*q.
2*q*(q - 1)*(q + 1)*(q + 2)/5
Let h(u) be the third derivative of -u**6/660 + u**5/110 + 9*u**4/11 + u**2 - 19*u - 32. Factor h(p).
-2*p*(p - 12)*(p + 9)/11
Let j = 2954/33 + -20348/231. What is y in 2/7*y**3 + 8/7*y + 0 - j*y**2 = 0?
0, 1, 4
Let w(o) be the first derivative of -o**4/10 - 20*o**3/3 - 97*o**2/5 - 96*o/5 + 322. Determine x, given that w(x) = 0.
-48, -1
Let a(t) be the first derivative of -t**5/45 - 41*t**4/36 - 152*t**3/27 - 74*t**2/9 + 1440. Let a(q) = 0. What is q?
-37, -2, 0
Find f, given that 132425 - 2788*f + 4*f**2 + 488519 - 209*f - 155*f = 0.
394
Factor 345*d + 15*d**2 + 20*d - 1704 - 12*d**2 + 481*d.
3*(d - 2)*(d + 284)
Let c(p) = -2*p**3 + 8*p**2 - 10*p + 16. Let q be c(4). Let b(y) = -y**3 - 24*y**2 + 2*y + 50. Let i be b(q). Factor 450/19*g**i + 8/19 + 120/19*g.
2*(15*g + 2)**2/19
Let r(i) be the third derivative of -i**7/70 + 3*i**6/8 - 21*i**5/10 - 23*i**4/2 + 60*i**3 - 2*i**2 + i - 294. Find n, given that r(n) = 0.
-2, 1, 6, 10
Let q(y) be the third derivative of -1/330*y**5 + 0*y - 17/66*y**4 + 0 - 289/33*y**3 - 25*y**2. Suppose q(h) = 0. What is h?
-17
Determine j, given that -1938637*j - 1 + 1938781*j - 282*j**2 - 2*j**5 + 129*j**3 + 1 + 12*j**4 - j**5 = 0.
-6, 0, 1, 8
Let r(i) = -7*i + 77. Let f be r(-9). Suppose 146*j - 12 = f*j. Let 0 + 4/9*p**3 - 2/9*p**4 - 16/9*p + 8/9*p**j = 0. What is p?
-2, 0, 2
Factor -92*n**2 + 240 + 17*n**2 + 18*n**2 - 92*n + 23*n**2 + 38*n**2.
4*(n - 20)*(n - 3)
Let s(m) be the third derivative of -m**2 + 13/6*m**4 - 1 + 1/30*m**5 + 0*m + 169/3*m**3. Factor s(k).
2*(k + 13)**2
Let v = -350113/2 + 175062. Factor 0 - 9*d**3 - 2*d**4 - v*d**2 - d + 4*d**5.
d*(d - 2)*(2*d + 1)**3/2
Let o(v) be the first derivative of -v**4/3 + 44*v**3 - 2178*v**2 - 34*v - 111. Let b(h) be the first derivative of o(h). Let b(l) = 0. Calculate l.
33
Let i(d) = 19*d + 19. Let n be i(-5). Let a = n + 151. Factor -36*l - 8*l + 20 + a*l**2 + 124*l.
5*(3*l + 2)*(5*l + 2)
Find s such that -608/11 + 2/11*s**4 + 196/11*s + 354/11*s**2 + 56/11*s**3 = 0.
-19, -8, -2, 1
Suppose 4*k - 5*y + 32 = 0, -309 + 355 = 7*k + 4*y. Factor 450/7 + 60/7*j + 2/7*j**k.
2*(j + 15)**2/7
Let v(n) be the first derivative of -n**4/20 - 13*n**3/15 - 31*n**2/10 + 9*n + 893. Find q, given that v(q) = 0.
-9, -5, 1
Suppose 2/3*j**2 + 120 + 56/3*j = 0. Calculate j.
-18, -10
Determine k, given that -55*k - 3025/2 - 1/2*k**2 = 0.
-55
Let i(u) = -3*u**3 + u**2 - 2*u. Let b(q) = -2*q**4 - 12*q**3 - 2*q**2 - 52*q. Let d(l) = -b(l) + 10*i(l). Factor d(w).
2*w*(w - 8)*(w - 2)*(w + 1)
Suppose -770 = -3*t - 758. Let v(l) be the second derivative of 1/24*l**6 + 1/8*l**3 - 3/80*l**5 - 7/48*l**t + 1/4*l**2 + 3 + 3*l. Factor v(s).
(s - 1)**2*(s + 1)*(5*s + 2)/4
Suppose 40 = -14*m + 19*m. Factor -m - u**2 - 4*u**3 - 3*u**2 + 8.
-4*u**2*(u + 1)
Factor 0 + 27/7*k - 3/7*k**4 + 3/7*k**2 - 27/7*k**3.
-3*k*(k - 1)*(k + 1)*(k + 9)/7
Let p(d) be the second derivative of 11*d**4/30 + 139*d**3/3 + 126*d**2/5 + 10*d + 89. Solve p(w) = 0.
-63, -2/11
Let v(g) be the second derivative of 31*g - 1/8*g**4 - 21/2*g**2 + 1/120*g**6 + 0*g**5 - 1/3*g**3 + 0. Let h(c) be the first derivative of v(c). Factor h(i).
(i - 2)*(i + 1)**2
Let y = -46504 + 325531/7. Factor -y*l**2 - 18/7 + 15/7*l.
-3*(l - 3)*(l - 2)/7
Factor -8341*t**2 + 0*t**3 + 2*t**3 - 1171 - t**3 + 8030 + 8398*t**2 + 1083*t.
(t + 19)**3
Suppose 20*f - 128 + 18 = -2*f. Let r(k) be the second derivative of 55/6*k**3 + f*k**2 + 13*k - 65/12*k**4 + 0. Suppose r(u) = 0. Calculate u.
-2/13, 1
Suppose -20*s + 9 + 11 = 0. Let y be s/7 - (4 - (-162)/(-42)). Suppose 0 + 2/11*z**5 + y*z - 4/11*z**2 - 6/11*z**3 + 0*z**4 = 0. Calculate z.
-1, 0, 2
Let d = -50 - -75. Suppose -5*v = -5*a - d, -3*v + 0*a + 4*a + 17 = 0. Determine o, given that -6*o**3 - 2*o**4 - 3*o**5 + 18*o**3 - 15*o**v - 4*o**4 = 0.
-1, 0
Let x(p) be the second derivative of 22387280000*p**6/3 - 97336000*p**5 + 529000*p**4 - 4600*p**3/3 + 5*p**2/2 + 3*p - 2267. Solve x(k) = 0.
1/460
Factor -358*c + 268/5*c**2 + 1524/5 - 2/5*c**3.
-2*(c - 127)*(c - 6)*(c - 1)/5
Solve -585/7*s**3 + 3/7*s**5 - 75*s**2 + 1122/7*s - 15/7*s**4 + 0 = 0.
-11, -2, 0, 1, 17
Let f be (0 - -1)*15*3/81. Let m(a) be the second derivative of 0 + 13*a - f*a**3 + 5/36*a**4 + 0*a**2. Factor m(k).
5*k*(k - 2)/3
Suppose -8*j**2 - 689*j - 261*j - 195 - 475*j + 455*j - 47 = 0. What is j?
-121, -1/4
Let u(x) = 2*x**2 + 35*x + 51. Let j(z) = 3*z**2 + 54*z + 77. Let q(m) = 5*j(m) - 8*u(m). Let v be q(-5). Factor -14/19*l - 6/19 - 10/19*l**v - 2/19*l**3.
-2*(l + 1)**2*(l + 3)/19
Let x(p) = 3*p + 41. Let h be x(-13). Find y such that -170*y - 174*y + h*y**2 + 322*y = 0.
0, 11
Let s(z) be the second derivative of -z**5/5 - 2*z**4 + 2*z**3/3 + 12*z**2 + 10*z - 4. Factor s(i).
-4*(i - 1)*(i + 1)*(i + 6)
Let f be (-126)/189 + (-424)/(-6). Solve 314 + 5*x**3 + 159 + 333 - f*x**2 - 166 + 160*x = 0 for x.
-2, 8
Suppose 29536*z**2 - 29571*z**2 - 930 + 9*z**3 + 615*z - 195 - 24*z**3 = 0. Calculate z.
-25/3, 3
Let a = 34386/7 + -4912. Let i(w) be the third derivative of 8*w**2 + 1/12*w**4 - 3/35*w**5 + 0*w + a*w**3 + 1/84*w**6 + 0. Factor i(q).
2*(q - 3)*(q - 1)*(5*q + 2)/7
Solve -12722/5*s**2 + 42/5*s**4 + 210*s**3 - 208416/5*s - 194688/5 - 2/5*s**5 = 0 for s.
-13, -1, 24
Let c(f) be the first derivative of 9*f**5/10 + 23*f**4/2 - 79*f**3/6 - 11*f**2/2 - 594. Determine q, given that c(q) = 0.
-11, -2/9, 0, 1
Let y(x) be the second derivative of -2*x**6/135 - 89*x**5/45 - 175*x**4/27 - 58*x**3/9 - 2215*x. Factor y(r).
-4*r*(r + 1)**2*(r + 87)/9
Let o = -79837 + 1037893/13. Factor 2/13*x**4 + 0 + 0*x + o*x**2 + 10/13*x**3.
2*x**2*(x + 2)*(x + 3)/13
Let d(f) be the second derivative of 5*f**4/12 - 155*f**3/3 + 305*f**2/2 + 819*f. Solve d(h) = 0 for h.
1, 61
Suppose -2*q + 5*r + 302 - 265 = 0, -2*r = -2*q + 22. Let l(s) be the second derivative of -s + 0 + 2/3*s**3 + q*s**2 + 1/36*s**4. Let l(x) = 0. What is x?
-6
Let b(x) be the first derivative of x**4/4 + 2*x**3 - 15*x**2/2 + 38*x - 78. Let z(l) be the first derivative of b(l). Factor z(g).
3*(g - 1)*(g + 5)
Let z(q) = q**3 + q**2 - 6*q - 2. Let a(s) = -8*s**3 + 30*s**2 - 20*s - 266. Let c(u) = 3*a(u) + 21*z(u). Suppose c(g) = 0. What is g?
-2, 4, 35
Let f(i) be the first derivative of i**4/14 + 316*i**3/21 + 313*i**2/7 + 312*i/7 + 514. Determine k, given that f(k) = 0.
-156, -1
Let u = 68 - 30. Factor u + 33*s - 38 - 9*s**3 + 36*s**2 + 12*s**3.
3*s*(s + 1)*(s + 11)
Let z be (-3 - 15/(-3)) + 2. Suppose -z*j = -t - 149, -4*t - 7 = 13. Let f**3 - 30*f**2 - 28*f**3 + j*f**2 = 0. Calculate f.
0, 2/9
Let c(q) = 5*q**3 - 160*q**2 + 2365*q + 11. Let w(f) = -2*f**3 + 62*f**2 - 788*f - 4. Let m(x) = -4*c(x) - 11*w(x). Solve m(d) = 0 for d.
-12, 0, 33
Let q(h) = h**2 + h - 15. Let w be q(-5). Let p(b) = 514