 y + 2*y**3 - 4. Let b(v) = -13*v**3 + v**2 - v - 5. Let x(t) = -3*b(t) + 5*f(t). Find r such that x(r) = 0.
-2, -1, 0
Let x(w) be the third derivative of -w**6/480 + 19*w**5/240 + 21*w**4/16 - 6*w**3 + 16*w**2 + 4. Find t, given that x(t) = 0.
-6, 1, 24
Suppose 3*d - 111 = 5*n, 12*n + 59 = 9*n - 2*d. Let t(v) = 7*v + 147. Let g be t(n). Find h, given that -8/15 + g*h + 2/15*h**2 = 0.
-2, 2
Let y(p) be the second derivative of p**6/30 - 553*p**5/20 - 1391*p**4/6 - 2230*p**3/3 - 1116*p**2 + 10269*p. Factor y(b).
(b - 558)*(b + 1)*(b + 2)**2
Suppose 21*w = -177 - 12. Let q be (-5 + w/(-2))*(2 + -7). Factor 0 + q*g**3 + 0*g - 1/2*g**2 - 25/8*g**4.
-g**2*(5*g - 2)**2/8
Let d(o) = -11*o**3 + o**2 + 2*o + 2. Let m be d(-1). Solve -8*z**2 - 36*z**5 + 2*z - 6*z + m*z**5 + 8*z**3 + 4 + 4*z**4 + 20*z**5 = 0.
-1, 1
Let h(g) be the third derivative of g**7/168 - 7*g**6/72 - 11*g**3/3 - 48*g**2. Let c(r) be the first derivative of h(r). Factor c(m).
5*m**2*(m - 7)
Let n = 7287 + -7282. Let r(l) be the second derivative of 4*l + 2/15*l**5 + 1/45*l**6 + 0*l**2 + 5/18*l**4 + 2/9*l**3 - n. Find m, given that r(m) = 0.
-2, -1, 0
Let m be (-5409)/(-111780) + 4/(-80). Let n = m + 139/621. Factor -10/9 + 4/3*p - n*p**2.
-2*(p - 5)*(p - 1)/9
Let w be (4/6)/(6/585). Suppose 80 - w = 5*j. Factor -404*o**3 + 5*o**4 - 10*o**2 - 6*o - 3*o**4 + 402*o**j.
2*o*(o - 3)*(o + 1)**2
Let o(q) be the first derivative of -6*q**2 - 4*q**3 - 46 + 9/4*q**4 + 0*q. Let o(b) = 0. Calculate b.
-2/3, 0, 2
Factor -9800/11*p + 394/11*p**2 - 4/11*p**3 + 4802/11.
-2*(p - 49)**2*(2*p - 1)/11
Let m(v) be the second derivative of -5*v**7/42 - 2*v**6/3 - v**5/2 + 5*v**4/3 + 5*v**3/2 - 58*v + 6. Determine o, given that m(o) = 0.
-3, -1, 0, 1
Factor -25*h + 1/2*h**2 + 49/2.
(h - 49)*(h - 1)/2
Let z(c) be the second derivative of -1/66*c**4 - 6*c - 10/33*c**3 + 2 - 16/11*c**2. Let z(t) = 0. Calculate t.
-8, -2
Let x(s) = -11*s**3 - 15*s**2 - 15*s + 4. Let d(q) = 2*q**3 + q**2 - q + 1. Let r(c) = 5*d(c) + x(c). Let z be r(-7). Factor -z*p - 2/5*p**3 - 4/5 - 8/5*p**2.
-2*(p + 1)**2*(p + 2)/5
Let v be -816*(51/12 - 5). Factor 4 + 8974*b**2 - 76*b - v*b + 20610*b**2.
4*(86*b - 1)**2
Let r(t) be the third derivative of t**5/75 + 158*t**4/5 + 149784*t**3/5 + 1739*t**2. Factor r(g).
4*(g + 474)**2/5
Let g be (-25)/20*60/(-25). Let w(t) be the third derivative of 1/2*t**4 + 0 + 1/15*t**5 + 4/3*t**g + 0*t - t**2. Find a such that w(a) = 0.
-2, -1
Suppose -2*o = -6*o + 20. Let k be o/2*23/(4140/24). Factor k*i**4 + 0*i + 2/3*i**2 - i**3 + 0.
i**2*(i - 2)*(i - 1)/3
Let d(y) be the first derivative of -64*y**6/21 + 1088*y**5/35 - 506*y**4/7 + 24*y**3 + 351*y**2/7 + 108*y/7 - 1926. Solve d(g) = 0.
-1/4, 3/2, 6
Factor -225 + 1/4*k**2 - 899/4*k.
(k - 900)*(k + 1)/4
Suppose 2*t = -3*t + 1225. Suppose -d = 6*d - t. Solve -45*z**3 + 20 + 15*z**2 - 29*z + 69*z - 5*z**4 + d*z**3 = 0 for z.
-2, -1, 2
Let o(q) be the third derivative of q**7/70 - q**6 - 43*q**5/20 + 41*q**4/4 + 1207*q**2 + 3*q. Suppose o(p) = 0. Calculate p.
-2, 0, 1, 41
Suppose 11*n = 32*n + 84. Let k be 278/77 + n/22. Factor 0 + 4/7*f + 36/7*f**3 + 16/7*f**4 + k*f**2.
4*f*(f + 1)**2*(4*f + 1)/7
Let i(h) = 3*h**3 + 14*h**2 - 315*h - 1289. Let x be i(-4). Determine d so that -1/7*d**x - 57*d + 41/7*d**2 - 63 = 0.
-1, 21
Factor 2/3*a**2 + 128/3*a - 130/3.
2*(a - 1)*(a + 65)/3
Factor -84*j + j**2 + 4*j**2 - 7*j**2 - 2*j**2 + j**2 - 588.
-3*(j + 14)**2
Let r be -5 - 1*(-1 - 7). Factor -6*y**3 + 8*y**r - 43*y**2 + 47*y**2.
2*y**2*(y + 2)
Let y = 212 + -209. Factor -3*t - 256 + 256 - 3*t**4 + 23*t**y - 44*t**2 + 23*t.
-t*(t - 5)*(t - 2)*(3*t - 2)
Suppose -5*p + 3*p = -5*h + 4, -3*h = -3*p + 3. Let a be ((-6)/(-9))/(h/(-12)*-2). Find t, given that 15*t**2 - 2*t - 8*t - 20*t**a = 0.
-2, 0
Factor -20800*s - 86528 - 1/2*s**3 + 206*s**2.
-(s - 208)**2*(s + 4)/2
Let s = -455 + 457. Suppose -12 = -5*i + s*i. Determine w, given that -1/2*w**i + 1/2*w**2 + 0*w + 0 + 0*w**3 = 0.
-1, 0, 1
Let i(m) = -283 + 1553*m**3 + 187*m - 5*m**2 - 1552*m**3 - 26*m**2. Let u(l) = l**2 + l - 1. Let p(j) = -2*i(j) - 10*u(j). Factor p(x).
-2*(x - 12)**2*(x - 2)
Factor 4303*h + 4*h**2 + 9834496 + 3926*h - 997*h + 6433*h - 1121*h.
4*(h + 1568)**2
Let d be 6744/(-9273) + (2 + -3)*-1. Factor -1/11*r**4 - d*r - 1/11*r**2 + 2/11 + 3/11*r**3.
-(r - 2)*(r - 1)**2*(r + 1)/11
Let j be (-10)/(-60) + ((-805)/(-345) - (-4)/(-2)). Factor 9 - 7/2*y - j*y**2.
-(y - 2)*(y + 9)/2
Let m(q) be the second derivative of q**6/165 - 9*q**5/110 + 4*q**4/33 - 539*q. Determine w so that m(w) = 0.
0, 1, 8
Let p be 2 + 13 + (-13)/(-715)*-815. Let u(w) = -w**3 + 4*w**2 - w - 3. Let a be u(3). Factor 0*f + 0 + p*f**2 + 1/11*f**a.
f**2*(f + 2)/11
Factor 611 + 852 - 4*h**3 + 360*h**2 - 708*h - 1111.
-4*(h - 88)*(h - 1)**2
Let q(x) be the second derivative of x**6/360 + x**5/15 + 2*x**4/3 - 4*x**3 - 9*x + 1. Let s(o) be the second derivative of q(o). Suppose s(z) = 0. Calculate z.
-4
Let f(v) be the third derivative of -v**6/200 + 3*v**5/25 - 11*v**4/10 + 24*v**3/5 + 2510*v**2. Factor f(i).
-3*(i - 6)*(i - 4)*(i - 2)/5
Let q be (-1)/(-15) + (-59 - (-14240)/240). Let 0*v + 12/5*v**3 + q*v**4 + 0 + 0*v**2 = 0. Calculate v.
-6, 0
Let n = -8778/17 - -219467/425. Let w(l) be the third derivative of 3/40*l**4 + 45*l**2 + n*l**5 + 0*l**3 + 1/200*l**6 + 0 + 0*l. Factor w(f).
3*f*(f + 1)*(f + 3)/5
Let h = -99 - -104. Factor -7*i + 61*i + 7*i - i**2 - h*i**2 + 2*i + 33.
-3*(i - 11)*(2*i + 1)
Let u(l) = 25 + 2*l - 2*l - 89 + 4*l**2. Let c(q) be the first derivative of q**3/3 - 13*q - 7. Let o(k) = 16*c(k) - 3*u(k). Suppose o(d) = 0. What is d?
-2, 2
Suppose -857313 - 4*g**3 + 166*g**2 + 451*g**2 - 196500*g + 937*g**2 + g**3 - 378279 = 0. What is g?
-6, 262
Let w(m) = 21*m**3 + 27764*m**2 + 9147600*m + 44. Let k(o) = -3*o**3 - 3966*o**2 - 1306800*o - 6. Let a(i) = 22*k(i) + 3*w(i). Factor a(l).
-3*l*(l + 660)**2
Suppose -2*q = 5*b + 2*q - 54, -4*b - 2*q + 42 = 0. Factor -15*a**4 - b*a**3 - 6*a**2 - 10*a + 10*a + 19*a**4.
2*a**2*(a - 3)*(2*a + 1)
Let i(j) be the second derivative of j - j**3 - 4*j**2 + 1/6*j**4 + 1. Factor i(d).
2*(d - 4)*(d + 1)
Let p be (-11 - 624/(-32))*(-66)/(-935). Let 0 - p*v**4 + 0*v + 9/5*v**3 + 0*v**2 = 0. Calculate v.
0, 3
Let p(y) be the first derivative of y**6/3 - 14*y**5/5 - 15*y**4 + 168*y**3 - 216*y**2 - 10647. Suppose p(q) = 0. What is q?
-6, 0, 1, 6
Solve -13558 - d**3 + 6751 + 50*d + 6759 - d**2 = 0 for d.
-8, 1, 6
Suppose -315*x + 264*x = -204. Let v(s) be the second derivative of -13*s + 2/13*s**3 + 9/13*s**2 + 1/78*s**x + 0. Factor v(g).
2*(g + 3)**2/13
Suppose 5103 + 15329 = -16*c. Let r = c + 1280. Factor 4/3*i**4 + 0*i + 0 + 16/3*i**2 - 16/3*i**r.
4*i**2*(i - 2)**2/3
Suppose 0 = 12*s - 98 + 170. Let z(j) = -j**3 - 7*j**2 + 4*j + 63. Let a be z(s). Factor 1/4*d**2 - d - 1 + 1/4*d**a.
(d - 2)*(d + 1)*(d + 2)/4
Let h be (-4*9/(-234) - (-9)/26)/(14/144). Suppose -3/7*q**5 + 24/7 - 6/7*q**2 - 18/7*q**4 + h*q - 33/7*q**3 = 0. Calculate q.
-2, -1, 1
Let q = 56651/2 + -28325. Factor -q*m**2 - 4*m - 8.
-(m + 4)**2/2
Factor -5400/23 + 2/23*i**3 - 270/23*i + 36/23*i**2.
2*(i - 12)*(i + 15)**2/23
Let d(q) be the second derivative of -3/2*q**4 - 1/2*q**3 + 0 - 65*q + 3/20*q**5 + 9*q**2. Let d(k) = 0. Calculate k.
-1, 1, 6
Let i(u) be the third derivative of u**5/60 - 2*u**4/3 - 17*u**3/6 + u**2 + 24. Let p be i(17). Factor 0 + p*y + 0*y**2 + 5/3*y**5 + 0*y**3 + 5/3*y**4.
5*y**4*(y + 1)/3
Let u be (-10)/((-1)/4*(31 - 21)). Let j be 3 - (u/(-14) - (-1104)/(-252)). Factor 10/3 + 7/3*y**4 - 17/3*y - 19*y**2 - j*y**3.
(y - 5)*(y + 1)**2*(7*y - 2)/3
Let o be (-1)/3 + 1410/(-90). Let d be o/6 + (3 - 0/4). Find v, given that -1/3*v**3 + d*v - 1/3*v**2 + 1/3 = 0.
-1, 1
Let d(q) = -q**3 - q. Let p(x) be the second derivative of -x**5 - 25*x**4 + 908*x**3 + 2888*x**2 + 63*x. Let h(f) = -24*d(f) + p(f). Factor h(j).
4*(j - 38)**2*(j + 1)
Suppose -262*j + 235*j = 57024. Let i be j/256*(-4)/6. Let -i*f - 1/4*f**2 - 121/4 = 0. Calculate f.
-11
Let i(u) be the first derivative of -9*u**5/10 + 219*u**4/4 - 633*u**3/2 + 1131*u**2/2 - 396*u + 105. Suppose i(n) = 0. Calculate n.
2/3, 1, 3, 44
Let z(o) be the second derivative of 0*o**2 - 1/360*o**6 + 13*o + 1/8*o**4 - 1/60*o**5 + 0 - 4/3*o**3. Let t(n) be the second d