 - 160*k**2 + 810*k - 50. Let j(l) = -4*l**3 + 240*l**2 - 1216*l + 80. Let o(q) = -5*j(q) - 8*n(q). Determine x so that o(x) = 0.
0, 10
Let x(i) = -i**2 + 45*i + 46. Let m be x(46). Let u(s) be the second derivative of m - 14*s + 0*s**4 + 0*s**2 + 0*s**3 - 1/40*s**5. Suppose u(y) = 0. What is y?
0
Let v(t) = -3*t**3 - 42*t**2 + 12*t + 170. Let p be v(-14). Suppose -4/5*o**2 + 0 + p*o**4 + 0*o + 6/5*o**3 = 0. What is o?
-1, 0, 2/5
Let p(w) be the first derivative of 2*w**6/15 - 228*w**5/25 - 2*w**4/5 + 152*w**3/5 + 2*w**2/5 - 228*w/5 - 316. Find b, given that p(b) = 0.
-1, 1, 57
Factor 143995537952 + 3219888*x**2 + 2*x**4 - 1708*x**3 - 2436*x**3 + 48767685*x - 310699867*x - 850002474*x.
2*(x - 518)**4
Let z = 281547 - 1407732/5. Let z*l + 4/5 - 1/5*l**2 = 0. What is l?
-1, 4
Let a(x) = 7*x - x**3 - 44 + 17*x**2 - 27*x + 40. Let q(l) = 18*l**2 - 21*l - 3. Let i(t) = -3*a(t) + 4*q(t). Factor i(g).
3*g*(g - 1)*(g + 8)
Let 30/11*u - 2/11*u**2 - 72/11 = 0. Calculate u.
3, 12
Solve 4*j**3 - 10729*j**2 - 10748*j**2 + 416*j - 10718*j**2 - 704 + 32119*j**2 = 0 for j.
4, 11
Solve 705/2*b**3 + 2145/2*b**2 + 360 - 5/2*b**4 + 2155/2*b = 0.
-1, 144
Let q(h) be the third derivative of -h**7/105 + 17*h**6/60 + 17*h**5/6 - 17*h**4/12 - 28*h**3 - 635*h**2. Solve q(k) = 0.
-4, -1, 1, 21
Suppose -b = -5*w + 12, -4*w + 3*b + 8 = 5. Solve w*p**3 + p**3 - 393*p + 397*p - 9*p**3 + p**5 = 0 for p.
-2, -1, 0, 1, 2
Suppose 16*v - 270 = 6*v. Let g = 36 - v. Factor 5*d**3 + g*d**3 - 5*d**3 - 3*d**2 + 3*d**5 - 9*d**4.
3*d**2*(d - 1)**3
Let k(d) = -5*d**2 + 2*d**3 + 4*d**4 - 7*d**4 + 9 - 150*d - 6*d**4 + 158*d. Let n(j) = -8*j**4 - 4*j**2 + 8*j + 8. Let o(w) = -4*k(w) + 5*n(w). Factor o(y).
-4*(y - 1)*(y + 1)**3
Let b = -193970 - -1357791/7. Factor -1521/7 + 78/7*d - b*d**2.
-(d - 39)**2/7
Let o be 15 - (-1 + 16)/5*1. Factor o*v - 19*v**2 + 15*v**2 + 20*v.
-4*v*(v - 8)
Let x(s) = s**2 - 417*s - 842. Let b(d) = -8*d**2 + 2496*d + 5050. Let t(p) = -2*b(p) - 13*x(p). Factor t(w).
3*(w + 2)*(w + 141)
Let q(d) = -5*d**2 + 21*d - 186. Let m(t) = 11*t**2 - 45*t + 373. Let c(l) = 6*m(l) + 13*q(l). Factor c(b).
(b - 12)*(b + 15)
Solve -2/3*q**2 + 676/3 - 334/3*q = 0 for q.
-169, 2
Let c be (-39)/2 - (-79245)/990. Let 834/11*z**3 - 360/11*z**4 + 216/11*z - c*z**2 - 24/11 = 0. Calculate z.
1/4, 2/5, 2/3, 1
Let x be (-28)/24717*-159*6/(-4). Let m = 10/107 - x. Factor -2/11*u**2 + 6/11*u - m.
-2*(u - 2)*(u - 1)/11
Suppose -424*l = -4*q - 425*l + 15, 2*q = -4*l + 32. Solve -9/2 + 1/4*r**q - 7/4*r = 0 for r.
-2, 9
Let j(f) be the first derivative of 1/36*f**4 + 11 - 4/9*f**3 - 42*f + 8/3*f**2. Let y(s) be the first derivative of j(s). Let y(m) = 0. What is m?
4
Factor 56*s**2 + 256 - 38*s**2 + 536 - 123*s - 15*s**2.
3*(s - 33)*(s - 8)
Let z(s) be the first derivative of 3/13*s**2 + 0*s - 77 + 20/39*s**3 + 1/39*s**6 + 12/65*s**5 + 6/13*s**4. Let z(t) = 0. Calculate t.
-3, -1, 0
Let b(m) = 23 + 5*m**2 - 15 - 6*m - 4*m**2. Let a be b(6). Factor a*d**3 - d**4 + 2*d**5 + 3*d**3 - 12*d**3.
d**3*(d - 1)*(2*d + 1)
Let g be ((-3)/((-63)/(-6)))/((-5)/35). Factor -26*q**g - 20*q**2 + 2 + 10*q**2 + 3*q - 81*q**3.
-(3*q + 1)**2*(9*q - 2)
Let o be 6/(-10) + 13 + (-1092)/130. Let b(x) be the first derivative of -17/5*x**3 - 33/5*x**2 - 36 - 9/20*x**o - 24/5*x. Find y such that b(y) = 0.
-4, -1, -2/3
Let a(d) be the first derivative of -5*d**3/3 - 75*d**2/2 - 212. Find f such that a(f) = 0.
-15, 0
Suppose 1858*q + 270*q = -2469*q - 1264*q. Factor q*z**2 - 5*z**4 + 25/2*z**5 + 0*z + 0 + 0*z**3.
5*z**4*(5*z - 2)/2
Suppose -v + 56 = 25*f, 699*v = -3*f + 694*v + 36. Factor 1/2*r**f + 30*r + 450.
(r + 30)**2/2
Let z = 3628 + -3628. Let u(p) be the third derivative of -1/8*p**3 + 0*p + z - 16*p**2 - 1/48*p**4 + 1/240*p**5. Determine w, given that u(w) = 0.
-1, 3
Let r(z) be the third derivative of -z**5/240 + 79*z**4/96 - z**2 - 95*z. Find l such that r(l) = 0.
0, 79
Let n(a) = 7*a**2 + 44*a + 33. Let o be n(-6). Suppose -6*u + o*u = 0. Factor -q**3 - 2*q**2 + 1/2*q**4 + 0*q + u + 1/4*q**5.
q**2*(q - 2)*(q + 2)**2/4
Suppose 5*q - 385 = -3*b + 391, -10 = 2*q. Suppose 2*f - 5*r = -0*r + b, -3*r = 2*f - 259. Factor 29*c + 3*c**2 + 61 + f - 77*c.
3*(c - 8)**2
Let k(y) be the second derivative of y**6/120 - 73*y**5/80 - 805*y**4/48 - 2075*y**3/24 - 4*y + 34. Determine m, given that k(m) = 0.
-5, 0, 83
Suppose 0 = 5*c + 3*j - 8, c + 0*c + 8 = -3*j. Let h(q) = 21*q - 80. Let b be h(c). Let 0 + 6/5*x**3 - 12/5*x**2 - 8/5*x + 3/5*x**5 + 11/5*x**b = 0. What is x?
-2, -2/3, 0, 1
Solve 1910/7*p**2 - 2/7*p**5 - 78/7*p**4 - 2076/7*p - 474/7*p**3 + 720/7 = 0.
-30, -12, 1
Let r(g) be the third derivative of g**6/24 - 203*g**5/2 - 5*g**4/24 + 1015*g**3 - 9384*g**2. Factor r(m).
5*(m - 1218)*(m - 1)*(m + 1)
Let b(g) be the second derivative of -g**4/48 - 47*g**3/24 - 69*g**2 - 239*g. Solve b(m) = 0.
-24, -23
Let p = 7425 - 7425. Let k(l) be the third derivative of 1/68*l**4 + p + 0*l**5 - 6*l**2 - 1/1020*l**6 - 2/51*l**3 + 0*l. Factor k(s).
-2*(s - 1)**2*(s + 2)/17
Let l(t) be the second derivative of -t**4/3 + 8*t**3/3 + 280*t**2 + 2875*t. Factor l(y).
-4*(y - 14)*(y + 10)
Let t be (-10)/35 + -766*(-5)/(-70). Let i = 58 + t. Solve 15/7*b**2 + 12/7 - 3/7*b**i - 24/7*b = 0.
1, 2
Suppose -4*w + 3*w - 43 = 0. Let j = -41 - w. Factor -15*v + 12*v**4 + 0*v**5 - 6*v**2 + 12*v**3 + 3*v**5 + 0*v**j - 6.
3*(v - 1)*(v + 1)**3*(v + 2)
Factor -29*d**2 - 120*d + 256*d**3 + 579*d**2 - 721*d**3 - 682593*d**4 + 682628*d**4.
5*d*(d - 12)*(d - 1)*(7*d - 2)
Let u(h) be the third derivative of 0*h - 1/84*h**7 + 0 + 1/48*h**5 + 0*h**4 - 1/96*h**6 - 170*h**2 + 0*h**3. Factor u(o).
-5*o**2*(o + 1)*(2*o - 1)/4
Let q = -158 - -160. Factor -5*y**3 - y**2 - y**2 + 6*y + q*y**3 - y**2.
-3*y*(y - 1)*(y + 2)
Let q be (2/5*(-8 + 559/86))/((-6)/4). Factor 0 + 0*w**2 + 0*w - 2/15*w**4 - q*w**3.
-2*w**3*(w + 3)/15
Let h(n) be the second derivative of n**7/13860 + n**6/792 + n**5/110 + 11*n**4/6 - 91*n. Let b(s) be the third derivative of h(s). Suppose b(w) = 0. What is w?
-3, -2
Suppose 120/7*v**3 + 272/7*v**2 + 0 + 12/7*v**4 + 192/7*v - 2/7*v**5 = 0. Calculate v.
-2, 0, 12
Let g(m) be the first derivative of -196*m**5/5 - 1043*m**4 - 5060*m**3 - 7650*m**2 - 1618. Determine c so that g(c) = 0.
-17, -15/7, 0
Let z(f) be the second derivative of f**4/6 + 2866*f**3/3 + 2053489*f**2 + 35*f. Let z(t) = 0. What is t?
-1433
Factor 2*a**2 + 1700 + 81*a + 140*a + a**2 - 8*a**2 + 184*a.
-5*(a - 85)*(a + 4)
Let i(p) = -41*p**3 - 5960*p**2 - 1776104*p + 12. Let j(k) = -24*k**3 - 3576*k**2 - 1065662*k + 7. Let b(n) = -7*i(n) + 12*j(n). What is a in b(a) = 0?
-596, 0
Let v(a) = 23*a**2 - 104*a - 735. Let x(g) = -17*g**2 + 78*g + 551. Let h(y) = -11*v(y) - 15*x(y). Factor h(w).
2*(w - 18)*(w + 5)
Let r(d) be the third derivative of 1/240*d**6 - 7/40*d**5 + 0*d**3 + 0 + 0*d**4 + 52*d - 2*d**2. Solve r(g) = 0.
0, 21
Let v(k) = 3*k**3 - 7*k**2 + 38*k. Let m(p) = -p**3 + p**2 - 17*p. Let y(t) = -2*m(t) - v(t). Determine d, given that y(d) = 0.
0, 1, 4
Let j(q) be the second derivative of -q**4/60 - 1957*q**3/15 - 3829849*q**2/10 + 144*q. Determine n so that j(n) = 0.
-1957
Let o(k) be the third derivative of 0*k - 1/6*k**3 + 0 - 25*k**2 - 1/12*k**4 - 1/60*k**5. Factor o(r).
-(r + 1)**2
Factor 15/7*d**2 + 4/7*d**3 + 0 - 4/7*d.
d*(d + 4)*(4*d - 1)/7
Suppose m - 3*p = -1, 198*p - 203*p + 7 = m. Let d(l) be the first derivative of -68/3*l**3 + 3 - 4/5*l**5 - 34*l**m - 24*l - 7*l**4. Factor d(h).
-4*(h + 1)**2*(h + 2)*(h + 3)
Factor 3/4*n**3 + 12*n - 69/4*n**2 + 99.
3*(n - 22)*(n - 3)*(n + 2)/4
Let u = -859 + 861. Let a(v) be the second derivative of -1/9*v**u - 1/9*v**3 + 0 - 1/18*v**4 - 1/90*v**5 + 17*v. What is q in a(q) = 0?
-1
Suppose 0 = 18*o + 19*o - 888. Suppose -9*v + 12 + o = 0. Let 3/5*u**2 - 2/5 - 1/5*u**v + 1/5*u - 1/5*u**3 = 0. Calculate u.
-2, -1, 1
Suppose -3*d - 9 = -5*w, 0 = -3*w + 12*d - 15*d + 15. Factor -7*c**2 + 4*c**2 - 32*c**4 + 9*c**3 + w*c**5 + 23*c**4.
3*c**2*(c - 1)**3
Suppose 4 - 8 = 2*l, -5*b + 182 = -l. Suppose -125*i = -107*i - b. Find g, given that 3/5*g**i + 3/5*g**3 + 0 + 0*g = 0.
-1, 0
Let g(k) be the third derivative of -1/4*k**4 + 13/240*k**5 + 15 + 0*k**3 + 3*k**2 + 1/840*k**7 + 0*k + 1/48*k**6. Let g(n) = 0. Calculate n.
-8, -3, 0, 1
Suppose