 + 2)
Let t(q) be the first derivative of -q**7/420 - q**6/60 - q**5/30 + 56*q**3/3 - 85. Let p(y) be the third derivative of t(y). Factor p(u).
-2*u*(u + 1)*(u + 2)
Let p be 1 + (-16)/(-3) - (-10)/15. Factor 147 + 5*q**3 + 182*q + 69*q**2 + 4*q**3 - p*q.
(q + 3)*(3*q + 7)**2
Let s(x) be the first derivative of -51 - 2/35*x**5 + 0*x**2 + 0*x - 1/28*x**4 + 1/42*x**6 + 2/21*x**3. Factor s(f).
f**2*(f - 2)*(f - 1)*(f + 1)/7
Let -13/4*b**4 - 8 + 46*b**3 + 375/4*b**2 + 73/2*b = 0. Calculate b.
-1, 2/13, 16
Let i(l) = 13*l**4 + 7*l**3 - 122*l**2 + 128*l - 92. Let q(p) = 12*p**4 + 9*p**3 - 122*p**2 + 129*p - 79. Let j(m) = 3*i(m) - 4*q(m). Factor j(z).
-(z - 2)*(z + 5)*(3*z - 2)**2
Let r(i) = -i**3 + 24*i**2 + 24*i + 64. Let n be r(25). Suppose 30*p - n*p = -18. Solve 0*s + 0 + 1/3*s**p = 0 for s.
0
Let i(a) = -205*a**2 - 30336*a + 594. Let v be i(-148). Find q such that 2/9*q**3 + 0 + 0*q + 26/9*q**v = 0.
-13, 0
Let s be (1 + 0)*(-2 + (-181608)/152). Let j = s + 1197. Factor 2/19*m**4 - 4/19*m**3 - j*m**2 + 2/19 + 2/19*m + 2/19*m**5.
2*(m - 1)**2*(m + 1)**3/19
Let h(t) be the first derivative of -t**5/15 + 35*t**4/6 - 1153*t**3/9 - 420*t**2 - 432*t + 762. Let h(i) = 0. What is i?
-1, 36
Let c be ((-2)/(-5))/(48/(-120))*-11. Solve 2*r + r**2 - c*r + 7 - 28 - 1 = 0.
-2, 11
Let t(x) be the first derivative of 69 - 9/8*x + 1/8*x**3 - 3/8*x**2. Let t(p) = 0. Calculate p.
-1, 3
Let z(a) be the first derivative of -a**3 - 87*a**2 + 744*a - 1357. Factor z(p).
-3*(p - 4)*(p + 62)
Determine t, given that 56 - 842/5*t - 286/5*t**3 + 2/5*t**4 + 846/5*t**2 = 0.
1, 140
Let b be (35 + 5)/8 - 129/27. Let h(j) be the second derivative of -4/27*j**3 - 10*j + 2/45*j**6 + 0 - 1/189*j**7 + b*j**4 - 13/90*j**5 + 0*j**2. Factor h(k).
-2*k*(k - 2)**2*(k - 1)**2/9
Let x(b) be the third derivative of 9*b**8/560 + 11*b**7/280 + b**6/60 + 29*b**3/3 + 14*b**2 - 1. Let n(p) be the first derivative of x(p). Factor n(h).
3*h**2*(h + 1)*(9*h + 2)
Let v(x) be the third derivative of -x**7/1470 + x**6/120 + 17*x**5/420 + 3*x**4/56 - 3*x**2 + 190*x. Factor v(u).
-u*(u - 9)*(u + 1)**2/7
Let j(h) be the second derivative of 0 + 35*h + 4/3*h**2 + 1/18*h**4 - 13/27*h**3. Factor j(b).
2*(b - 3)*(3*b - 4)/9
Suppose -3*j - 6 = 0, 55*j - 50*j = -5*i. Let g = 43 - 171/4. Determine x so that -3/2 - 7/4*x**i - g*x**3 + 13/4*x + 1/4*x**4 = 0.
-3, 1, 2
Let g = 11492 + -11492. Let m(c) be the second derivative of g + 1/5*c**5 - 22*c + 0*c**3 + 0*c**2 - 2/21*c**7 - 1/3*c**4 + 2/15*c**6. Solve m(w) = 0.
-1, 0, 1
Let r(p) be the first derivative of 4*p**5/5 - 88*p**4 + 980*p**3 - 3824*p**2 + 5056*p + 1963. Factor r(x).
4*(x - 79)*(x - 4)**2*(x - 1)
Suppose 14 = m + 4*s, -4 = 2*m - 3*s + 1. Suppose m*w - 105 = -33*w. Factor -2/3*k**2 + 2/3*k**4 - 2/3*k**5 + 0*k + 2/3*k**w + 0.
-2*k**2*(k - 1)**2*(k + 1)/3
Let b(s) be the first derivative of -5*s**4/4 - 50*s**3/3 + 115*s**2/2 - 60*s + 11736. Factor b(y).
-5*(y - 1)**2*(y + 12)
Let p = 150/1031 + 473772/17527. Solve p*d + 98/17 - 138/17*d**2 + 10/17*d**3 = 0.
-1/5, 7
Let o be 9/35 - (44/(-28))/11. Let f(c) = 5*c - 2. Let v be f(1). Let 0*s + 2/5*s**2 - 2/5*s**4 - 2/5*s**v + 0 + o*s**5 = 0. What is s?
-1, 0, 1
Suppose 4*o = -4*j + 28, -1608*o - j + 15 = -1603*o. Factor -2/11*w**o - 4/11*w + 0.
-2*w*(w + 2)/11
Suppose 3*b - 48465 = -48429. Let d(k) be the first derivative of 12*k - 25 - b*k**2 + 3*k**3 + 3/2*k**4 - 3/5*k**5. Determine f so that d(f) = 0.
-2, 1, 2
Solve 64*q + 0 - 148/3*q**2 - 74/3*q**3 + 28/3*q**4 + 2/3*q**5 = 0.
-16, -2, 0, 1, 3
Let w(x) be the first derivative of x**6/420 + x**5/140 - 11*x**4/168 - x**3/7 - 26*x**2 + 80. Let u(q) be the second derivative of w(q). Factor u(r).
(r - 2)*(r + 3)*(2*r + 1)/7
Let b = 21 - 19. Suppose 4*g + 14 = -0*f + f, -f - b*g = 4. Factor -f*i**4 + i**2 + 2*i**3 + 7*i**4 + 4*i**5 - 12*i**4 + 0*i**3.
i**2*(i - 1)**2*(4*i + 1)
Let z(y) = 19*y - 663. Let t be z(32). Let m be (((-15)/6)/(t/572))/10. Suppose -21/5*u**3 + 1/5*u - 9/5*u**4 - m*u**2 + 2/5 = 0. What is u?
-1, -2/3, 1/3
Let o(d) be the second derivative of 38*d**7/189 + 7*d**6/5 + 49*d**5/30 - 2*d**4/27 + 6*d + 715. Find j, given that o(j) = 0.
-4, -1, 0, 1/38
Let k = 9063 - 1305065/144. Let m(j) be the third derivative of 1/180*j**5 + 1/9*j**3 - 20*j**2 - 1/720*j**6 + 0 + 0*j + k*j**4. Factor m(d).
-(d - 4)*(d + 1)**2/6
Suppose -3*z**2 - 1179/5*z + 1194/5 = 0. Calculate z.
-398/5, 1
Let v = -36291/2 - -18148. Let h(z) be the second derivative of -v*z**3 + 6*z + 0 - 5/12*z**4 + 0*z**2. Factor h(p).
-5*p*(p + 3)
Let v = 2767 + -2763. Let g(r) be the first derivative of 20 + 4/9*r**3 + 0*r + 5/6*r**2 - 1/12*r**v. Factor g(l).
-l*(l - 5)*(l + 1)/3
Let p = 383 - 380. Determine l, given that 7*l**2 + 2*l**3 + 6*l**3 - 29*l**2 - 3*l**3 - 4*l**p = 0.
0, 22
Let b(s) be the first derivative of -5*s**3/3 - 10705*s**2 - 22919405*s - 4989. Let b(d) = 0. Calculate d.
-2141
Let t(s) = 4*s + 12. Let c(x) = -2*x - 6. Let r(g) = 7*c(g) + 3*t(g). Let i be r(-4). Solve -7*h**3 - 6*h**5 + 485*h**2 - 487*h**2 + i*h**4 + 13*h**5 = 0 for h.
-1, -2/7, 0, 1
Let t(v) be the first derivative of -v**4/4 + 55*v**3/3 + 89*v**2 - 232*v + 2302. Factor t(o).
-(o - 58)*(o - 1)*(o + 4)
Let b(w) be the second derivative of w**6/15 + 37*w**5/10 + 71*w**4/6 + 35*w**3/3 - 1791*w. Let b(f) = 0. Calculate f.
-35, -1, 0
Let x(f) be the third derivative of -19*f**8/2352 - 61*f**7/1470 - 5*f**6/84 - 2*f**5/105 + 2*f**2 + 336*f. Suppose x(a) = 0. What is a?
-2, -1, -4/19, 0
Suppose -2181*r = -2193*r + 15048. Let i be 6/(-57) + (2 - 1464/r). Determine l so that 0 + 0*l - 20/11*l**3 + i*l**5 + 6/11*l**2 - 18/11*l**4 = 0.
-1, 0, 1/4, 3
Suppose -4*x - 84 = -2*l, -5*l + 2*x + 74 = -3*l. Suppose -l*s = -25*s. Find m such that 3/4*m**2 + s - m + 1/4*m**3 = 0.
-4, 0, 1
Let k be 19 + (-7373)/438 - (-3)/(-2). Factor -10/3*f + 2/3*f**3 + k*f**2 + 2.
2*(f - 1)**2*(f + 3)/3
Let h(g) be the third derivative of g**7/840 + g**6/120 - g**5/120 - g**4/8 + 23*g**3/3 + 15*g**2. Let d(j) be the first derivative of h(j). Solve d(y) = 0.
-3, -1, 1
Let v(u) be the first derivative of -u**6/2520 + u**5/280 + u**4/42 + u**3/3 - 7*u**2 + 42. Let a(n) be the third derivative of v(n). What is h in a(h) = 0?
-1, 4
Let k be 14 - ((-6)/(-24))/(((-3)/(-84))/(-1)). Let b(r) be the first derivative of 0*r - 1/6*r**2 - r**3 + 5/3*r**5 - 5/4*r**4 - k. Factor b(s).
s*(s - 1)*(5*s + 1)**2/3
Suppose 301*u**4 + 308*u**4 - 924*u**3 - 613*u**4 = 0. Calculate u.
-231, 0
Factor 18*r - 68*r**2 - 113*r**2 + 2*r**2 - 22*r**4 + 26*r**2 + 157*r**3.
-r*(r - 6)*(r - 1)*(22*r - 3)
Let j(g) be the second derivative of -g**5/10 + 13*g**3 + 70*g**2 + 8*g + 2. Solve j(s) = 0.
-5, -2, 7
Let l = -100 + 75. Let q(v) = -2*v**2 - 50*v. Let r be q(l). Factor 5/2*j**3 + 1/2*j**5 + r*j + 0 + j**2 + 2*j**4.
j**2*(j + 1)**2*(j + 2)/2
Let s(q) = -3*q + 19. Let j be s(7). Let u be (-9)/(-6) - j/(-4) - -11. Solve 2 - w**2 - 16 - 22 - u*w + 0*w = 0.
-6
Let i = -3844979/192 - -20026. Let f(z) be the third derivative of 7/960*z**6 + 1/12*z**3 - 28*z**2 + 0*z + 1/1680*z**7 + i*z**4 + 0 + 1/32*z**5. Factor f(h).
(h + 1)**3*(h + 4)/8
Let t(q) = 128*q**2 + 32*q. Let y(j) be the second derivative of 21*j + 0 + 1/2*j**2. Let p(h) = t(h) + 2*y(h). Solve p(m) = 0 for m.
-1/8
Factor 2*f**3 + 1824*f - 231*f - 262*f**2 - f**3 - 509*f**2 - 54*f - 769.
(f - 769)*(f - 1)**2
Let l(d) be the second derivative of d**7/10080 - d**6/320 + d**5/60 - 29*d**4/6 - 20*d - 2. Let x(h) be the third derivative of l(h). Factor x(w).
(w - 8)*(w - 1)/4
Let a(r) be the third derivative of r**8/420 - 12*r**7/175 + 2*r**6/5 - 56*r**5/75 + 398*r**2. Find l, given that a(l) = 0.
0, 2, 14
Solve 721*r + 2338*r - 3*r**2 + 3063*r + 574*r - 3736368 = 0 for r.
1116
Let o(p) = -17*p**3 + 292*p**2 - 81*p + 513. Let d be o(17). Factor -2106/11*i**2 - 4/11*i**4 - 4394/11 + 9802/11*i + 158/11*i**d.
-2*(i - 13)**3*(2*i - 1)/11
Let a be 327/(-2)*((-62)/6 + 11). Let p = -107 - a. Factor 0 - 8/11*g + 50/11*g**4 - 10/11*g**3 - 32/11*g**p.
2*g*(g - 1)*(5*g + 2)**2/11
Find s, given that 4*s**3 + 292 + 705*s - 117*s - 450858*s**2 + 451158*s**2 = 0.
-73, -1
Let h(q) be the first derivative of q**5/5 - 2*q**3 + 4*q**2 - 3*q + 1470. Factor h(r).
(r - 1)**3*(r + 3)
Let j(c) = -40*c**2 + 108*c. Let y(r) = -r**3 - 42*r*