
Let s = 3065 + -6129/2. Let d(n) be the second derivative of 0 - s*n**2 - 7/60*n**4 + 11/30*n**3 + 1/100*n**5 - 11*n. Let d(a) = 0. What is a?
1, 5
Factor 9418 + 14*m**2 - 2558 - 4*m**3 - 2156*m + 182*m**2.
-4*(m - 35)*(m - 7)**2
Let j(o) be the third derivative of o**5/60 - 4*o**4/3 + 56*o**3/3 + o**2 + 1317*o. Factor j(r).
(r - 28)*(r - 4)
Let q = 285639 + -285635. Suppose m + 0*m**q + 1/4*m**5 - 5/4*m**3 + 0*m**2 + 0 = 0. Calculate m.
-2, -1, 0, 1, 2
Let r be (-3108)/(-2880) - 14/21. Let q(s) be the third derivative of r*s**5 - 7/160*s**6 + 0 + 0*s - 19*s**2 - s**3 - 9/16*s**4. Factor q(k).
-3*(k - 4)*(k - 1)*(7*k + 2)/4
Let j be (-1)/((1 - (-51)/(-12)) + 3). Suppose j*b + 6 = u, -4*u - 3 + 9 = 2*b. Factor -4*i**5 - 1021*i**4 + 40*i**u - 30*i**3 + 24*i**5 + 996*i**4 - 15 + 10*i.
5*(i - 1)**3*(i + 1)*(4*i + 3)
Let h(d) = 3*d**3 - 129*d**2 - 4091*d - 11161. Let r(m) = 20*m**3 - 776*m**2 - 24548*m - 66965. Let a(v) = 39*h(v) - 6*r(v). Factor a(o).
-3*(o + 3)*(o + 61)**2
Suppose 746 = -11*n - 707 + 1486. Find t such that 3/5*t**4 - 6*t**n + 0*t + 0*t**2 + 0 = 0.
0, 10
Let r(j) = 134*j**2 + 8*j + 16. Let l be r(-4). What is q in -48*q**3 + l*q**4 - 13*q**2 - 2149*q**4 + q**2 = 0?
-2, -2/7, 0
Let y be (-6)/27 - (-4079)/9. Let f = y + -453. Suppose f + 5/9*c**2 - 1/9*c**5 - 1/9*c**4 + 2/9*c + 1/3*c**3 = 0. What is c?
-1, 0, 2
Suppose -5488/3 - 9826/3*a**4 - 14756*a**2 + 34102/3*a**3 + 25480/3*a = 0. What is a?
14/17, 1
Let w(u) = 119*u + 131. Let b be w(-4). Let t = 348 + b. Solve -28/3*r + 4/3*r**t + 40/3 - 16/3*r**2 = 0.
-2, 1, 5
Let k(a) = -a**3 + 13*a**2 - 6*a + 8. Let n be k(12). Let z be (-1*2)/((-10)/n). Determine c so that -32*c**2 + z*c + 5 + 36*c**2 + 1 + 6 = 0.
-3, -1
Let i(o) be the second derivative of o**6/40 - 3*o**5/4 + 19*o**4/16 - 693*o. Suppose i(j) = 0. Calculate j.
0, 1, 19
Find r such that -5/4*r**4 - 33/4*r**2 + 245/4*r - 41/4*r**3 + 25/2 = 0.
-5, -1/5, 2
Let p = -559 + 563. Let m(i) be the first derivative of 45/4*i**p + 0*i + 3*i**5 + 2 - 10/3*i**6 + 10/3*i**3 + 0*i**2. Suppose m(h) = 0. Calculate h.
-1, -1/4, 0, 2
Suppose -5 = -5*n - 0. Suppose 15 = 2*g + n. Factor 2*p**2 + 10*p - g*p - 4 + p - 3*p**2.
-(p - 2)**2
Let y(h) = 18*h**3 + 951*h**2 + 1184*h + 401. Let j(r) = 5*r**2 + 1. Let a(m) = 18*j(m) - 2*y(m). Factor a(i).
-4*(i + 49)*(3*i + 2)**2
Determine s, given that 27*s**3 + 2833733*s**5 - 2833727*s**5 - 353*s**2 + 83*s**2 + 93*s**4 = 0.
-15, -2, 0, 3/2
Find a, given that 0*a - 19/4*a**2 + 1/2*a**3 + 0 = 0.
0, 19/2
Suppose 0 = -140*u + 152*u - 108. Let l be (u/12)/((-69)/(-12) - 4). Suppose l*b**5 + 0*b + 0*b**2 + 12/7*b**4 + 9/7*b**3 + 0 = 0. What is b?
-3, -1, 0
Let n(r) be the first derivative of r**6/16 - 3*r**5/20 - 9*r**4/16 + 5*r**3/2 - 57*r**2/16 + 9*r/4 - 1442. Factor n(y).
3*(y - 2)*(y - 1)**3*(y + 3)/8
Suppose 0 = 3*x - 5*j - 40, -5*x + 814*j = 811*j - 24. Let s(t) be the first derivative of x*t - 6*t**2 - 4/3*t**3 - 39. Factor s(b).
-4*b*(b + 3)
Suppose 122*n + 4 = 124*n. Factor y**2 + 87 + 28 + 6*y**n - 223 - 3*y**2 - 104*y.
4*(y - 27)*(y + 1)
Let m(l) = -56*l**4 - 83*l**3 + 1241*l**2 - 493*l + 54. Let z(x) = -2*x**4 - x**3 + x**2 - 3*x + 2. Let f(q) = -2*m(q) + 6*z(q). Let f(w) = 0. What is w?
-6, 1/5, 4
Let k(v) be the first derivative of 2*v**5/35 + 379*v**4/14 + 754*v**3/21 - 379*v**2/7 - 108*v + 3095. Suppose k(w) = 0. What is w?
-378, -1, 1
Let p(f) be the third derivative of -1/8*f**4 + 0 - f**3 + 1/20*f**5 + 0*f + 79*f**2. Solve p(a) = 0.
-1, 2
Suppose 86*m + 18 = 84*m. Let x(n) = -n**4 - 6*n**3 + 3*n**2. Let j(q) = 5*q**4 + 25*q**3 - 12*q**2. Let r(u) = m*x(u) - 2*j(u). Solve r(l) = 0 for l.
0, 1, 3
Let w(i) be the third derivative of -i**6/240 - 7*i**5/16 - 151*i**4/96 + 17*i**3/4 - 950*i**2. Factor w(h).
-(h + 2)*(h + 51)*(2*h - 1)/4
Let y be (-13560)/(-1980) - ((-3)/((-81)/6) + (-80)/1980). Determine p so that -74/3*p**3 - 32/3 - 104/3*p - y*p**4 - 128/3*p**2 - 2/3*p**5 = 0.
-4, -2, -1
Factor 43/5*u - 1/5*u**2 - 352/5.
-(u - 32)*(u - 11)/5
Suppose 0 = 5*v + 2*b + 1323, 11*v - 2*b = 13*v + 534. Let c = v - -267. Factor -8/7*u**2 + 0 + 8/7*u**3 - 2/7*u**c + 0*u.
-2*u**2*(u - 2)**2/7
Let f = 509 - 507. Solve 587*h**2 - 8*h**4 + 20*h - 285*h**f - 278*h**2 - 36*h**3 = 0.
-5, -1/2, 0, 1
Let a(o) = -22*o + 77. Let j be a(4). Let r be 35*(-2 - -1)*j/77. Solve 4/11*d**4 + 0 - 2/11*d**3 + 2/11*d**r - 4/11*d**2 + 0*d = 0.
-2, -1, 0, 1
Let y be 6/252*12 - (-299)/7. Factor -16*p**2 - 2*p**3 + 5*p**3 + 18*p + y*p**2 - 6*p**2.
3*p*(p + 1)*(p + 6)
Let f = 658930 + -1317831/2. Let 1/2*g**5 - 11/2*g**3 - 4 - f*g**2 - 13*g + 1/2*g**4 = 0. Calculate g.
-2, -1, 4
Let k(l) = -9*l**3 - 12*l**2 - 21*l - 18. Let v be (-1)/(1/((-5)/1)). Let q(m) = -8*m**3 - 13*m**2 - 22*m - 17. Let o(y) = v*k(y) - 6*q(y). Factor o(t).
3*(t + 1)**2*(t + 4)
Factor -383217*k - 4*k**2 + 191183*k - 1728 + 191162*k.
-4*(k + 2)*(k + 216)
Let h be ((-4)/38)/(710/(-26980)). Find r, given that 24*r + 26/3*r**3 + 0 - 2/3*r**h - 32*r**2 = 0.
0, 1, 6
Let a(k) be the second derivative of -k**4/4 - 135*k**3/2 + 204*k**2 + 1282*k + 1. Factor a(b).
-3*(b - 1)*(b + 136)
Let r(m) be the third derivative of m**5/4 - 2825*m**4/12 - 1885*m**3/6 - 1178*m**2. Factor r(g).
5*(g - 377)*(3*g + 1)
Let l(z) be the second derivative of 7*z**4 + 4*z - 2 + 6*z**2 + 4/5*z**6 + 17/2*z**3 + 1/14*z**7 + 33/10*z**5. What is i in l(i) = 0?
-4, -1
Let x(u) = 48*u + 242. Let n be x(-5). Factor -11*s**3 - 5*s**3 - 8 + 4*s**3 - 55*s + 31*s - 2*s**4 - 26*s**n.
-2*(s + 1)**2*(s + 2)**2
Suppose 74226*i = 74106*i + 360. Solve 3 + 25/4*a + 1/4*a**i + 7/2*a**2 = 0.
-12, -1
Let i(m) = -m**3 - 3*m + 111. Let g be i(0). Let a = g - 92. Suppose -97*x**3 - x**2 - 9*x**4 - 7*x**4 - a*x**2 + 13*x**3 = 0. Calculate x.
-5, -1/4, 0
Let s(a) = 3*a - 47. Let l be s(17). Find z, given that -4*z - 5*z**5 - 10263*z**3 - 10*z**4 + 10258*z**3 + l*z = 0.
-1, 0
Let m(k) be the first derivative of -4*k**3/3 + 13076*k**2 - 42745444*k - 9872. Find c such that m(c) = 0.
3269
Let c be (22/30 + 82/(-246))/(15 + -13). Let 0 + c*j**4 + 1/5*j**3 + 8/5*j - 2*j**2 = 0. Calculate j.
-4, 0, 1, 2
Let c(w) be the second derivative of -1/36*w**4 - 1/6*w**2 - 1/9*w**3 - 3*w - 20. Find l such that c(l) = 0.
-1
Suppose -56 = -5*g + 4. Factor 4*j**4 - 8*j + g*j + 3*j**4 - 8*j**2 + j**4 - 4*j**5.
-4*j*(j - 1)**3*(j + 1)
Let l(x) be the first derivative of 7/8*x**2 - 3/4*x**3 + 11 - 1/2*x - 1/20*x**5 + 5/16*x**4. Factor l(m).
-(m - 2)*(m - 1)**3/4
Let k(j) = -j**3 - 16*j**2 + 33*j - 51. Let l be k(-18). Let w(a) be the first derivative of -10*a - 10 + 5/3*a**l + 5/2*a**2. What is h in w(h) = 0?
-2, 1
Let g(k) = -k**3 + k. Suppose 4*u = -20, -3*c + 6*c - 1 = -u. Let d(z) = 0*z - 3*z + 4*z - c*z. Let t(p) = 5*d(p) + 5*g(p). Factor t(w).
-5*w**3
Let u(k) be the first derivative of -k**3/6 - 145*k**2/4 - 282*k + 325. Let u(x) = 0. What is x?
-141, -4
Determine v, given that 27*v**4 + 9*v**3 - 105 + 9*v**5 + 26*v**4 - 936 - 255 - 6*v**5 + 4536*v - 1953*v**2 = 0.
-12, 1/3, 3
Suppose 0 = 3*p + 15, 5*o - 4*p + 25 = 2*o. Let v be 5 + o*7/42. Factor 10*h - 1/4*h**4 - 4 + v*h**3 - 33/4*h**2.
-(h - 4)**2*(h - 1)**2/4
Factor 27*o**3 + 4160224*o**2 - 4160326*o**2 + 5*o**4 - 2*o**4 + 72*o.
3*o*(o - 2)*(o - 1)*(o + 12)
Let j(d) = 20*d**2 + 200*d + 185. Let a(p) = -9*p**2 - 99*p - 92. Suppose 0 = -6*w + 7*w + 3*b - 4, b + 12 = -3*w. Let v(r) = w*a(r) - 2*j(r). Factor v(y).
5*(y + 1)*(y + 18)
Let h = 3809 + -3809. Let x(q) be the third derivative of 0*q**4 + 1/84*q**8 - 2*q**2 + h + 1/15*q**6 + 0*q**3 - 2/35*q**7 + 0*q**5 + 0*q. Factor x(g).
4*g**3*(g - 2)*(g - 1)
Solve -21/2*i**4 + i**5 + 32*i**3 + 0 + 9*i - 63/2*i**2 = 0.
0, 1/2, 1, 3, 6
Let p = -1377 + 1381. Let u(n) be the second derivative of 1/2*n**p - 1/10*n**6 + 1/2*n**3 + 0 + 1/14*n**7 + n - 3/2*n**2 - 3/10*n**5. Factor u(q).
3*(q - 1)**3*(q + 1)**2
Let k(b) = -3*b + 7. Let l(g) = 2*g**2 + 177*g + 225. Let j(m) = -5*k(m) + l(m). Factor j(c).
2*(c + 1)*(c + 95)
Let t = 53531/8453 - -14/25359. Factor 1/3*x**3 + 2/3*x**2 - 20/3 - t*x.
(x - 4)*(x + 1)*(x + 5)/3
Let r be (12/10)/(58/145). Factor -2*o**2 - 25*o**2 + 18*o + r*o**2 - 39*o - 3*o**3.
-3*o*(o + 1)*(o + 7)
Let n(j) = -j**2 - 18*j - 70. Let q be 1 + ((-3)/15 - (-272)/(-40)). Let i be n(q). Factor -2/5*r**i + 0 - 4/5*r.
