20/9*k**2 - 4/9*k**a + 2/9*k**5 - 10/9*k**4 + 2/9*k = 0.
-1, 1, 5
Suppose -30 = 51*t + 64*t - 130*t. Factor 4/3*o**4 + 0 - 4/3*o**3 + 0*o**t + 0*o.
4*o**3*(o - 1)/3
Let z(n) be the third derivative of 1/600*n**6 + 1/2*n**3 - 1/100*n**5 - 3/40*n**4 + 0 - 8*n**2 + 0*n. Let l(s) be the first derivative of z(s). Factor l(x).
3*(x - 3)*(x + 1)/5
Let s(n) = 9*n**3 - 5*n**2 + 4*n + 4. Let q(o) = 48*o**3 - 24*o**2 + 21*o + 21. Let g(l) = -4*q(l) + 21*s(l). Factor g(c).
-3*c**2*(c + 3)
Factor 2/11*w**2 + 80/11 + 28/11*w.
2*(w + 4)*(w + 10)/11
Let z(d) be the first derivative of d**6/13 + 34*d**5/65 - 101*d**4/26 - 178*d**3/39 + 98*d**2/13 + 144*d/13 + 630. Determine g, given that z(g) = 0.
-9, -1, -2/3, 1, 4
Let a(z) be the third derivative of -z**6/360 + 5*z**5/36 - 13*z**4/9 + 40*z**3/9 + z**2 - 50*z. Find y such that a(y) = 0.
1, 4, 20
Suppose 10*a - 6*a + 4*q = 0, 5*q + 9 = 4*a. Let s be (a*2)/(-21 + 12 + 10). Factor -25/6*p + 5/3 + 5/6*p**3 + 5/2*p**s - 5/6*p**4.
-5*(p - 1)**3*(p + 2)/6
Let b be (-1132)/1144 - (-4 - -3). Let n = b + 2267/2002. Factor 4/7*p - 4/7*p**2 + n.
-4*(p - 2)*(p + 1)/7
Suppose 5*k - 28 = -q + 4, -2*q = 3*k - 29. Suppose -q*l + 43*l = 108. Factor 2*s + 2/5 + 14/5*s**2 + 6/5*s**l.
2*(s + 1)**2*(3*s + 1)/5
Let b(z) = -5*z**3 + 13*z**2 + 34*z + 4. Let l(y) = -15 + 235*y + 20*y**3 - 31*y**2 - 30*y**2 + 11*y**2 - 370*y. Let o(p) = 15*b(p) + 4*l(p). Factor o(u).
5*u*(u - 3)*(u + 2)
Let h(m) = -30*m**3 - 230*m**2 - 632*m - 400. Let w(r) = -41*r**3 - 307*r**2 - 843*r - 533. Let a(k) = 11*h(k) - 8*w(k). Factor a(n).
-2*(n + 1)*(n + 2)*(n + 34)
Let q be (-452)/(-16)*(-3)/(-11) + (-7659)/3404. Factor 6/11*n**4 + 18*n**2 - q*n**3 - 240/11*n + 96/11.
6*(n - 4)**2*(n - 1)**2/11
Let x = -405505/3 + 2027543/15. What is r in 1/5*r + 1/5*r**5 + 0 - 4/5*r**4 - 4/5*r**2 + x*r**3 = 0?
0, 1
Let b be 126/28 + 10/(-12) + -3 + (-52)/312. Let u = 5 + -3. Factor -1/2*w**5 - 2*w**u + 0 - 2*w**4 - 3*w**3 - b*w.
-w*(w + 1)**4/2
Let p = -74 - -133. Let l = 62 - p. Factor -4*r**2 - 10*r**2 + r**l - 31 + 5*r**2 + 27*r + 4.
(r - 3)**3
Let v be (-933)/135 + 42/(-189). Let t = v - -142/15. Factor -1/3 - 2*a**2 + t*a**4 + 2/3*a**3 - 5/3*a + a**5.
(a - 1)*(a + 1)**3*(3*a + 1)/3
Let t be (-1452)/(-462)*(28/158)/2. Let h = t + -53/474. Factor -5/6 - y - h*y**2.
-(y + 1)*(y + 5)/6
Let 56/9*i - 2/9*i**5 + 8/3 - 2/3*i**3 + 34/9*i**2 - 10/9*i**4 = 0. Calculate i.
-3, -2, -1, 2
Suppose 4*f - 3*w = 11, 0 = -5*f - 31*w + 30*w + 9. Let s(p) be the first derivative of 49*p + 1/3*p**3 + 18 - 7*p**f. Suppose s(v) = 0. Calculate v.
7
Suppose -1/5*h**3 - 19/5*h - 6 + 2*h**2 = 0. What is h?
-1, 5, 6
Let r(w) be the second derivative of -w**6/120 + w**5/10 - w**4/2 + 4*w**3/3 - 2*w**2 - 503*w. Factor r(f).
-(f - 2)**4/4
Let c = -492 + 797. Suppose -d = -q + 61, 5*q - 4*d = -6*d + c. Factor 2*n**2 + 61 - q.
2*n**2
Let v be 96/18*-7*(-26)/1365. Let c(h) be the second derivative of -8/25*h**5 + 0*h**2 + 0 - 1/315*h**7 + 4/75*h**6 + v*h**4 + 0*h**3 + 22*h. Factor c(n).
-2*n**2*(n - 4)**3/15
Let w = 1136 - 1028. Let c be (2/(-6))/((-18)/w). Factor -1/4*i**3 + 1/4*i + 1/4*i**c - 1/4*i**4 + 0.
-i*(i - 1)*(i + 1)**2/4
Suppose 184*h + 10 = 189*h. Let g(k) = 8*k**3 + 24*k**2 + 12*k - 6. Let p(v) = 8*v**3 + 25*v**2 + 13*v - 7. Let n(t) = h*p(t) - 3*g(t). Factor n(y).
-2*(y + 1)*(y + 2)*(4*y - 1)
Let c be 1424/(-120) + 0 - (-4)/(-30). Let h be 2*(-155)/(-200) + 9/c. Factor -34/5*l - h - 6*l**2.
-2*(l + 1)*(15*l + 2)/5
Let v(m) be the first derivative of -4*m**3/3 + 286*m**2 + 2352*m + 565. Factor v(r).
-4*(r - 147)*(r + 4)
Let b(n) be the third derivative of n**6/120 + 191*n**5/60 - 8*n**4 - 115*n**2. Find p such that b(p) = 0.
-192, 0, 1
Suppose -z = -c + 73, 3*z + 7 - 60 = -c. Factor -c + 68*m - 33 - 4*m**2 + 37.
-4*(m - 16)*(m - 1)
Suppose -b - 2*a + 84 = 0, -2*b + 2*a = -2*a - 208. Let k be b/8 - 296/37. What is i in 0*i + 0 + 15/4*i**4 + 5/4*i**2 + k*i**3 + 5/4*i**5 = 0?
-1, 0
Suppose 3*b - 791 + 273 = -d, -2*b + 2*d = -356. Let o = b + -174. Solve 3/5*k**4 + 12/5*k**3 + o*k + 12/5*k**2 + 0 = 0 for k.
-2, 0
Let i = 14949/332 - 3260/83. Solve -7/4 - b**3 - i*b**2 + 17/2*b = 0 for b.
-7, 1/4, 1
Let a(z) be the first derivative of -6/19*z**4 + 28/57*z**3 - 24/19*z + 1/57*z**6 + 49 + 11/19*z**2 - 4/95*z**5. Solve a(s) = 0 for s.
-3, -1, 1, 4
Let z be (-10 - (-150)/14) + (-63)/(-49). Let t(r) be the first derivative of 1/2*r + 20 - 1/12*r**3 + 1/8*r**z. Factor t(n).
-(n - 2)*(n + 1)/4
Suppose -s + 5*h + 1 + 28 = 0, 2*s + 2*h + 2 = 0. Factor -13*o**4 + 4*o**4 - 2*o**5 + 5*o**4 + 4*o**2 - 2*o + s*o**5.
2*o*(o - 1)**3*(o + 1)
Let g(j) be the third derivative of j**6/120 - 22*j**5/15 + 242*j**4/3 + 2*j**2 - 132. Factor g(q).
q*(q - 44)**2
Let f(o) = -33*o**2 + 2935*o + 178. Let g be f(89). Let g - 11/7*m**3 - 6/7*m**2 - 1/7*m**5 - 6/7*m**4 + 0*m = 0. Calculate m.
-3, -2, -1, 0
Let o = 6378/5 + -19114/15. Suppose -1/3*g**4 + g**2 - 2/3*g**3 - 4/3 + o*g = 0. What is g?
-2, 1
Suppose -53*d = -24*d - 145. What is u in d - 5 + 2375*u**2 - 2376*u**2 + 13*u = 0?
0, 13
Let b(y) be the second derivative of y**4/96 - 187*y**3/48 - 2966*y. Factor b(g).
g*(g - 187)/8
Let h be (-5)/(75/(-7)) - (-10)/50. Let o(d) be the first derivative of -15 + 8*d - h*d**3 + 0*d**2. Determine s, given that o(s) = 0.
-2, 2
Let k = 95475 - 95473. Factor -12/7*o + 2*o**k + 0 - 2/7*o**3.
-2*o*(o - 6)*(o - 1)/7
Let j = 4/2337 + 48757/186960. Let h(f) be the second derivative of 0 + 5*f + 0*f**2 + 0*f**3 - j*f**5 - 1/10*f**6 + 1/8*f**4. Factor h(y).
-3*y**2*(y + 2)*(4*y - 1)/4
Let g = 40 - 20. Let a = g + -17. Factor 75*m - 25*m + 3*m**2 - 26*m - 30*m + a.
3*(m - 1)**2
Let w(q) be the second derivative of 3/8*q**2 - 1/8*q**3 - 1 - 1/8*q**4 + 1/40*q**6 - 3*q + 3/40*q**5 - 1/56*q**7. Factor w(a).
-3*(a - 1)**3*(a + 1)**2/4
Let j(t) = t**2 + 9*t - 62. Let z be j(16). Factor 674*w**2 - 348*w**2 - z*w**2 + 18*w + 2*w**3.
2*w*(w - 3)**2
Let z be 11060/(-126) - 4/18. Let g = 90 + z. What is q in 2*q**4 - q**4 + 9*q**2 - 13*q**g - 2*q**3 + 5*q**2 = 0?
0, 1
Let q = 1490 + -5957/4. Let k be (8/(-7))/(2/(-7)). Factor 0 + 3/4*h**k - q*h**2 + 1/4*h**3 - 1/2*h + 1/4*h**5.
h*(h - 1)*(h + 1)**2*(h + 2)/4
Let u(c) be the third derivative of -c**5/300 - 1133*c**4/60 - 1283689*c**3/30 - 96*c**2 - 7*c. Solve u(q) = 0.
-1133
Let w(o) = -663 + 2*o**3 + 1329 - 667 + o + o**4. Let b(t) = 4*t**4 - 2*t**3 - 36*t**2 - 34*t - 22. Let j(p) = -b(p) + 6*w(p). Solve j(y) = 0.
-2, -1
Let o = -265 + -85. Let h = 353 + o. Factor 64/3*w**2 + 44/3*w**4 + 0 + 256/3*w - 48*w**h - 4/3*w**5.
-4*w*(w - 4)**3*(w + 1)/3
Let s = 5261 - 105219/20. Let d(m) be the third derivative of 0*m + 0*m**3 + 0*m**4 - s*m**5 + 1/48*m**6 + 0 - 1/420*m**7 - 44*m**2. Factor d(w).
-w**2*(w - 3)*(w - 2)/2
Suppose 2*r + 2 = -4*i - 0*i, -5*r - i = 23. Let m be r + (-4)/((-16)/52) - 3. Solve -2*a**m + 0 + 5*a**2 + 3/4*a + 5/2*a**4 + 35/4*a**3 = 0.
-1, -1/2, -1/4, 0, 3
Let m(w) = -960*w - 17259 - 51*w**2 - 928*w + 448*w. Let s(r) = -5*r**2 - 144*r - 1726. Let v(n) = -2*m(n) + 21*s(n). Determine t, given that v(t) = 0.
-24
Let l(x) be the third derivative of -13/56*x**7 + 5/2*x**4 + 33/32*x**6 - 35/16*x**5 + 0 + 53*x**2 + 1/64*x**8 - 3/2*x**3 + 0*x. Solve l(p) = 0 for p.
2/7, 1, 6
Let s(f) be the third derivative of f**8/1680 + 24*f**7/175 + 283*f**6/300 + 211*f**5/75 + 187*f**4/40 + 14*f**3/3 - 252*f**2 + 6. Suppose s(d) = 0. What is d?
-140, -1
Let s(v) be the third derivative of v**6/280 - 193*v**5/140 + 187*v**4/7 - 1480*v**3/7 + 1696*v**2 - 1. Suppose s(o) = 0. What is o?
4, 185
Determine v, given that 88*v**2 - 494*v**3 + 96*v**5 + 64 - 8*v**4 - 1387*v - 1528*v**2 + 1563*v - 662*v**3 = 0.
-2, -1/6, 1/4, 4
Suppose -29*c - 24 = -41*c. Let n(u) = -u**3 + 5*u**2 - 3*u - 2. Let l be n(c). Find m such that -144/7 - 52/7*m**2 - 40/7*m**3 + 240/7*m - 4/7*m**l = 0.
-6, 1
Let m be ((-10)/6)/(17/(-51)). Suppose 3*k + m*t = -8, -1 = k - t - 9. Factor 4*j**3 - 48*j**2 + 32*j + 9*j**4 + 3*j**k - 12*j**3.
4*j*(j - 2)*(j + 2)*(3*j - 2)
Find o such that -280 + 292*o + o**4 - 220721*o**3 - 73*o**2 - 5*o**2 + 441440*o**3 - 220720*o**3 = 0.
-10, 2, 7
Let o(l) be the third derivative of -l**8/672 - l**7/140 + l**6/48 + l**5/40 - l**4/12 - 102*l**2 - 3. Find b such that o(b) = 0.
-4, -1, 0, 1
Suppose l + n