 = 8*u**2 + 140*u - 3180. Let j(t) = -2*g(t) - 20*r(t). Factor j(w).
4*(w - 40)**2
Let u(n) be the third derivative of -n**5/240 - 19*n**4/16 + 115*n**3/24 - 1546*n**2. Factor u(w).
-(w - 1)*(w + 115)/4
Suppose 168 = 31238*x - 31224*x. Determine f so that -39*f + x + 39/2*f**2 + 15/2*f**3 = 0.
-4, 2/5, 1
Find p such that -4*p**3 - 170*p + 68*p**2 - 82*p + 0*p**3 - 324 = 0.
-1, 9
Let w(m) = m**3 - 46*m**2 - 52*m + 237. Let g be w(47). Suppose q - 2*j - 9 + 0 = 0, 4*j = 5*q - 33. Factor -381*h**3 + 380*h**3 - g - 5*h + h**2 - q*h**2.
-(h + 1)**2*(h + 2)
Let l(c) be the first derivative of -c**4/4 - 2*c**3 - 6*c**2 + 19*c + 105. Let x(p) be the first derivative of l(p). Factor x(m).
-3*(m + 2)**2
Let w(k) be the first derivative of 6/65*k**5 + 1/26*k**4 - 2/13*k**2 - 2/13*k**3 - 274 + 0*k + 1/39*k**6. Solve w(u) = 0 for u.
-2, -1, 0, 1
Let g(c) be the second derivative of -1/4*c**4 + 0 + 0*c**2 - 10*c**3 + 84*c. Factor g(i).
-3*i*(i + 20)
Let z(u) be the third derivative of 1/20*u**5 - 3 + 128*u**3 + 11*u**2 + 0*u + 4*u**4. What is c in z(c) = 0?
-16
Let g be (-11)/(-2) - 9/6. Let w be 8 - (5 + 4 + -1). Factor 1/3*s**2 - 1/6*s**5 + 1/6*s + w - 1/3*s**g + 0*s**3.
-s*(s - 1)*(s + 1)**3/6
Let n(i) be the second derivative of -5*i**4/12 + 5*i**3/6 + 15*i**2 + 1900*i. Factor n(p).
-5*(p - 3)*(p + 2)
Let n = -1657 - -1647. Let y be (-4)/42 - (n/105 - 3). Find o, given that 0 + 3/4*o**y + 3/4*o**2 - 3/2*o = 0.
-2, 0, 1
Let f = 44651/14 - 6377/2. Factor -768/7 - 432/7*s**2 - f*s**4 + 12*s**3 + 960/7*s.
-6*(s - 4)**3*(s - 2)/7
Let z(s) be the first derivative of s**4/6 + 5*s**3/3 + 4*s**2 + 13*s + 5. Let u(p) be the first derivative of z(p). Suppose u(h) = 0. What is h?
-4, -1
Factor -151*s**2 + 24*s**4 + 515*s**2 - 158*s**2 + 60*s**3 - 174*s**2 - 4*s**5.
-4*s**2*(s - 8)*(s + 1)**2
Let o(c) = -c**3 - 54*c**2 - 680*c + 2. Let p be o(-20). Let p*h - 20 + 2/5*h**3 + 16/5*h**2 = 0. Calculate h.
-5, 2
Let b(n) = -n**5 - n**3 - 1. Let p(g) = 4*g**5 - 20*g**4 + 20*g**3 + 68*g**2 + 40*g + 8. Suppose 22 = 16*l + 150. Let v(i) = l*b(i) - p(i). Factor v(d).
4*d*(d - 2)*(d + 1)**2*(d + 5)
Let v(z) be the third derivative of z**7/28 + 209*z**6/96 + 367*z**5/48 + 655*z**4/96 - 55*z**3/8 + 2*z**2 - 3*z + 7. Suppose v(c) = 0. Calculate c.
-33, -1, 1/6
Let t(d) = -2*d**3 - 6*d**2 + 13 + d**3 - 2*d**3. Let w = 33 - 28. Let p(q) = 4*q**3 + 6*q**2 - 14. Let k(b) = w*p(b) + 6*t(b). What is g in k(g) = 0?
-1, 2
Suppose -373*u - 20*u + 109 + 515 = -185*u. Factor 0*q + 3/5*q**4 - 12/5*q**u + 0 - 3*q**2.
3*q**2*(q - 5)*(q + 1)/5
Let o(v) be the first derivative of -5/3*v**3 + 0*v - 10*v**2 + 88. Find l such that o(l) = 0.
-4, 0
Suppose -140*w = -36*w. Let x(g) be the third derivative of 1/4*g**4 - 1/20*g**5 - 1/40*g**6 + 0 + 0*g**3 - 6*g**2 + w*g. Solve x(p) = 0 for p.
-2, 0, 1
Let s(f) be the second derivative of 0*f**2 - 160*f + 1/50*f**5 - 1/75*f**6 + 2/15*f**4 - 4/15*f**3 + 0. Factor s(w).
-2*w*(w - 2)*(w - 1)*(w + 2)/5
Find y such that 3*y**5 + 295*y + 600*y**3 + 1280*y**2 + 80*y**4 + 302*y - 8*y**5 + 262*y + 21*y = 0.
-2, 0, 22
Let g(h) be the first derivative of -1/3*h**3 - 69 - 3/8*h**2 + 1/4*h. Factor g(r).
-(r + 1)*(4*r - 1)/4
Let c = 868/5 + -133. Let j = c - 39. Determine f, given that -6/5*f**3 + j*f**2 - 4/5 + 2/5*f = 0.
-2/3, 1
Suppose -8/5*o**3 - 144/5 + 132/5*o + 2/5*o**4 - 22/5*o**2 = 0. What is o?
-4, 2, 3
Let h(c) be the third derivative of c**8/336 - 8*c**7/35 - 27*c**6/10 + 3*c**2 - 3*c - 24. Let h(q) = 0. What is q?
-6, 0, 54
Let f(p) = -25*p - 235. Let u be f(-10). Factor -6*v**4 + 3*v**4 + v**3 - u + 0*v**2 + 2*v**2 + 15.
-v**2*(v - 1)*(3*v + 2)
Let m(w) be the third derivative of -w**6/160 - 17*w**5/40 - 151*w**4/32 - 87*w**3/4 - 479*w**2 + 4*w. Let m(x) = 0. Calculate x.
-29, -3, -2
Let w(s) = 4*s**3 + 26*s**2 + 190*s - 672. Let n(p) = p**3 + 8*p**2 + 65*p - 224. Let u(v) = 10*n(v) - 3*w(v). Factor u(f).
-2*(f - 4)**2*(f + 7)
Let t(u) be the second derivative of -5*u**4/12 + 935*u**3/6 - 65*u - 11. Factor t(s).
-5*s*(s - 187)
Let j(z) = z**2 + 76*z - 1523. Let v(r) = r**2 - r - 1. Suppose -30*u - 12 = -24*u. Let a(d) = u*v(d) + j(d). Factor a(w).
-(w - 39)**2
Suppose 248*s - 398 = 346. Let v(c) be the second derivative of -1/18*c**s + 1/90*c**6 + 27*c + 0*c**2 - 1/20*c**5 + 0 + 1/12*c**4. Factor v(i).
i*(i - 1)**3/3
Let f = -2/1857 + 5579/7428. Let x(l) be the third derivative of 7/2*l**3 - f*l**4 - 1/20*l**5 + 0*l + 0 + 21*l**2. What is o in x(o) = 0?
-7, 1
Solve 943/2*g**3 + 1/2*g**5 - 5372*g + 2890 - 65/2*g**4 + 4085/2*g**2 = 0.
-5, 1, 34
Let g(a) = -12*a**2 + 1194*a + 2418. Let b(w) = 3*w**2 + 3*w. Let u(t) = 3*b(t) + g(t). Factor u(n).
-3*(n - 403)*(n + 2)
Let f(x) = x + 2. Let a(b) = 8*b + 21. Let d(w) = a(w) - 2*f(w). Let n be d(-2). Let 4/5*r**n + 0 + 4/5*r**2 - 4/5*r**3 - 4/5*r**4 + 0*r = 0. What is r?
-1, 0, 1
Let f(c) be the first derivative of c**5 - 55*c**4/4 + 45*c**3 + 55*c**2/2 - 140*c - 1246. What is g in f(g) = 0?
-1, 1, 4, 7
Let j be (-3)/3 + (-12)/(-3). Solve 15 + 10 + 2*x + 14*x**j + 38*x - 12*x**3 - 19*x**2 = 0.
-1/2, 5
Suppose 16*r = 25*r - 81. Determine a so that 31*a - r*a - 8*a**2 - 136*a - 28 = 0.
-14, -1/4
Let x be ((-5616)/(-18564))/(48/56). Factor 16/17 - 4/17*u + x*u**3 - 14/17*u**2.
2*(u - 2)*(u + 1)*(3*u - 4)/17
Find v, given that -220/9 + 2/9*v**3 - 38/3*v + 12*v**2 = 0.
-55, -1, 2
Solve -747/2*g**4 - 3945/2*g**2 - 392 + 1428*g + 81/2*g**5 + 2539/2*g**3 = 0 for g.
1, 28/9
Let 31/8*k**3 + 19/4*k**2 - 3/4 - 7/4*k**4 - 13/8*k = 0. Calculate k.
-1, -2/7, 1/2, 3
Suppose 5*c = -17*u + 13*u - 3444, 3*u - c + 2602 = 0. Let t = -866 - u. Determine a so that 6/13*a**2 - 2/13*a**3 - 4/13*a + t = 0.
0, 1, 2
Find u, given that -17/2*u**2 - 49/2*u - 2/3*u**3 + 20/3 = 0.
-8, -5, 1/4
Let i = 38590/7 - 424194/77. Let h = i - 36/11. Factor 0*z**2 + 0*z + 0 - 2/7*z**4 - h*z**3 + 2/7*z**5.
2*z**3*(z - 2)*(z + 1)/7
Let y(f) be the second derivative of -f**6/6 - 7*f**5/4 - 5*f**4/4 + 155*f**3/6 - 50*f**2 - 4*f - 46. Factor y(g).
-5*(g - 1)**2*(g + 4)*(g + 5)
Let r be 2/(-4 - -10) - 12/9. Let f be (20/1050*7)/(r/(-16)). Factor -2/15*h**2 - f + 16/15*h.
-2*(h - 4)**2/15
Let v(g) be the first derivative of g**6/6 - 21*g**5/5 + 99*g**4/4 - 45*g**3 - 181. Factor v(q).
q**2*(q - 15)*(q - 3)**2
Let n(b) be the third derivative of -b**8/336 - b**7/10 + 3*b**6/20 + 207*b**5/10 - 1755*b**4/8 + 2025*b**3/2 - 2*b**2 - 262. Factor n(l).
-(l - 3)**3*(l + 15)**2
Suppose -24013 = -215*h + 204*h. Let w = h + -2180. Factor -32/15*p**w + 28/15*p**2 + 0 - 2/5*p.
-2*p*(2*p - 1)*(8*p - 3)/15
Let -24*m - 4386*m**3 - 21*m**2 + 8773*m**3 + 6*m - 4390*m**3 = 0. Calculate m.
-6, -1, 0
Let v = -226114 - -678346/3. Solve v*k**2 + 8/3*k**3 - 2/3*k**4 - 6 - 8*k = 0 for k.
-1, 3
Suppose -8*w + 6724 = -4*w + 4*o, -3*w = -3*o - 5055. Let r = 1687 - w. Let 184/3*m**r - 56/3*m**5 - 38/3*m + 4/3 - 230/3*m**3 + 136/3*m**2 = 0. What is m?
2/7, 1/2, 1
What is l in -346/5*l**2 + 7/5*l**4 + 52/5*l**3 - 164*l - 429/5 = 0?
-11, -1, 39/7
Factor 3/8*q**2 - 1017/8*q - 1023/4.
3*(q - 341)*(q + 2)/8
Let d(n) be the third derivative of -n**5/12 + 425*n**4/4 - 2545*n**3/6 - 98*n**2 + 2*n. Solve d(s) = 0 for s.
1, 509
Let a(p) be the third derivative of 1/10*p**5 - p**3 - 1/60*p**6 - 4*p**2 + 0 + 1/12*p**4 + 0*p. Determine z so that a(z) = 0.
-1, 1, 3
Let x(q) = -225*q**3 - 225*q**3 + 10*q - 12*q**2 + 446*q**3 - 6. Let u(f) = -5*f**3 - 13*f**2 + 11*f - 7. Let g(m) = -6*u(m) + 7*x(m). Factor g(b).
2*b*(b - 2)*(b - 1)
Solve -2/15*f**5 + 64/5 - 44/5*f**2 + 2/3*f**3 + 64/15*f + 4/5*f**4 = 0.
-3, -1, 2, 4
Let j(r) = -202*r - 5559 - 219 + 7*r**2 - 133*r - 6011 + 2724. Let w(i) = 5*i**2 - 334*i - 9067. Let v(m) = 4*j(m) - 5*w(m). Factor v(n).
3*(n + 55)**2
Solve -4/3*j**3 - 4*j + 50/9*j**2 + 0 - 2/9*j**4 = 0.
-9, 0, 1, 2
Let l = -153287/4 + 38322. Factor 0*z**2 - 1/4*z**4 + 0*z + 0 - l*z**3.
-z**3*(z + 1)/4
Let k(j) = 107*j - 425. Let c be k(4). Let m(v) be the first derivative of 14 + 1/3*v**c + 0*v + 1/20*v**4 + 0*v**2. Let m(f) = 0. Calculate f.
-5, 0
Factor 750/7*z + 2/7*z**2 + 0.
2*z*(z + 375)/7
Suppose 6*p - 4 = 2*p. Let o = p - -1. Factor -3*w**3 + 3*w + 54 - 38*w + 24*w**o - 17*w - 11*w.
-3*(w - 3)**2*(w - 2)
Let k(d) be the first derivative of -2*d**5/5 + 3*d**4 - 2*d**3 - 10*d**2 + 11