 - 1296/7 - 1/7*t**2.
-(t - 36)**2/7
Let u be 98/32 - (79 - 36)/688. Let r(s) be the first derivative of 18*s**2 - 18/5*s**5 + 0*s + 29/2*s**4 - 26 - 26*s**u + 1/3*s**6. Solve r(n) = 0.
0, 1, 2, 3
Let j(w) be the third derivative of 0 - 7*w - 2*w**2 + 1/100*w**5 + 1/100*w**6 + 0*w**3 - 1/350*w**7 - 1/20*w**4. Factor j(g).
-3*g*(g - 2)*(g - 1)*(g + 1)/5
Let c be 152/19836*-29*-2*(-9)/(-2). Let r(y) be the third derivative of 1/570*y**5 - 1/114*y**4 - 22*y**c + 0*y + 1/57*y**3 + 0. Suppose r(g) = 0. Calculate g.
1
Let u(x) = x**3 + x. Let l(r) = 2*r**3 - 204*r**2 + 2598*r - 2400. Let z(h) = l(h) + 2*u(h). Factor z(g).
4*(g - 30)*(g - 20)*(g - 1)
Determine x, given that -1821/5*x - 6/5*x**3 + 57*x**2 + 168 = 0.
1/2, 7, 40
Solve -948/5*g**4 - 2/5*g**5 - 5728/5*g**2 + 3822/5*g - 956/5 + 3812/5*g**3 = 0.
-478, 1
Let g(k) be the second derivative of -3*k**5/80 + 12*k**4 + 387*k**3/8 + 291*k**2/4 - 1684*k + 3. Find q, given that g(q) = 0.
-1, 194
Suppose -3*l + 5*l - 8 = 0, -5*l = -3*y + 3526. What is c in -1177*c**5 - 7 + 5*c - 10*c**3 + 50*c**2 - 18 - 25*c**4 + y*c**5 = 0?
-1, 1, 5
Let m be (-930)/28*(361380/45075 + -8). Let v = -2/601 - m. Let 6/7*u - 2/7*u**5 - 4/7*u**3 + v*u**2 - 6/7*u**4 + 2/7 = 0. What is u?
-1, 1
Let r(f) be the first derivative of 41 + 5/14*f**4 + 2/35*f**5 - 12/7*f + 10/21*f**3 - 5/7*f**2. Determine o, given that r(o) = 0.
-3, -2, -1, 1
Let u = 761881 + -2285597/3. Factor -u*r - 529/3*r**2 - 1/3.
-(23*r + 1)**2/3
Let b be 17/5 - 18/45. Let a = -198 + 198. Factor -6 + 2*n**4 + 2*n**5 + 0*n**4 + 3*n**3 + a*n**4 + 10*n + 4*n**2 - 15*n**b.
2*(n - 1)**3*(n + 1)*(n + 3)
Suppose 5*x = -l + 11, 0 = 4*x - 2*x + 2*l - 6. Suppose -2*g + 32 = 5*k + x*g, 2*g = -5*k + 26. Factor 75*n**4 + 60*n**3 - 36*n**k - 45*n**2 - 59*n**4.
-5*n**2*(2*n - 3)**2
Suppose 33*y = 15*y + 90. Factor -35*m + y - m**3 + 11 + 24*m**2 + 71*m + 5*m**3.
4*(m + 1)**2*(m + 4)
Let j = -36722 - -36734. Factor 3/2*q**3 + 21/2*q + 0 + j*q**2.
3*q*(q + 1)*(q + 7)/2
What is w in -195*w**2 + 185*w + 3*w**3 - 5*w**4 + 72*w**3 - 5 - 79 + 24 = 0?
1, 12
Let d(n) be the second derivative of 5*n**4/24 - 55*n**3/6 + 140*n**2 - 8*n + 14. Factor d(i).
5*(i - 14)*(i - 8)/2
Let v = -59647/36 - -1657. Let l = v - -1/12. Factor 0*j + 2/9 - l*j**2.
-2*(j - 1)*(j + 1)/9
Let w(d) be the second derivative of 7/4*d**4 + d**3 + 0 + 0*d**2 - 5/14*d**7 + 66*d - 7/10*d**6 + 9/20*d**5. Let w(z) = 0. Calculate z.
-1, -2/5, 0, 1
Let v(g) be the second derivative of g**5/110 + 35*g**4/66 - 73*g**3/33 + 37*g**2/11 - 7776*g. Factor v(j).
2*(j - 1)**2*(j + 37)/11
Let u be (16/(5984/(-119)))/((-21)/12) - -10. Suppose 32/11*n**2 - 4/11*n**4 - 14/11*n**5 - 224/11*n + u*n**3 - 64/11 = 0. What is n?
-2, -2/7, 2
Solve 2*v**5 + 40/9*v**3 + 8*v**4 - 64/9*v**2 + 0*v + 0 = 0.
-8/3, -2, 0, 2/3
Let y(r) be the third derivative of r**7/5040 - r**6/720 - r**5/16 + 23*r**4/24 + r**3/6 - 5*r**2 + 1. Let p(s) be the second derivative of y(s). Factor p(k).
(k - 5)*(k + 3)/2
Let a(w) be the first derivative of -2/65*w**5 - 7/26*w**4 - 9/13*w**2 + 0*w - 18 - 10/13*w**3. Factor a(m).
-2*m*(m + 1)*(m + 3)**2/13
Let j(l) be the third derivative of l**8/3360 - l**6/720 + 191*l**3/6 + 177*l**2. Let a(m) be the first derivative of j(m). Factor a(i).
i**2*(i - 1)*(i + 1)/2
Let r be (-2)/(-4) - -2*(-81)/(-36). Factor -74*v**2 + 60*v**3 + 974*v - 1106*v + 25*v**4 + 126 - r.
(v - 1)**2*(5*v + 11)**2
Suppose 114 + 32 = 73*m. Let l(n) be the second derivative of 3/5*n**5 + 13*n + 0*n**4 + 0 + 0*n**m - 2/3*n**3 - 4/15*n**6. Find t such that l(t) = 0.
-1/2, 0, 1
Suppose -11681 = l + 3*l - 5*d, -3*d - 2916 = l. Let q = l - -37995/13. Factor -4/13 - 22/13*p**3 - 30/13*p - q*p**2.
-2*(p + 1)**2*(11*p + 2)/13
Let q be ((-2057)/(-176) + -12)*(17 - 33). Determine s, given that 0 - 4/7*s - 4/7*s**q - 25/7*s**4 - 25/7*s**2 - 6*s**3 = 0.
-4, -1, -1/4, 0
Let w(j) = -19*j**3 + 3584*j**2 - 134100*j - 33775. Let s(c) = -48*c**3 + 8961*c**2 - 335250*c - 84435. Let x(r) = 5*s(r) - 12*w(r). Factor x(b).
-3*(b - 75)**2*(4*b + 1)
Let t(n) be the second derivative of n**2 + 1/24*n**4 + 0 + 1/3*n**3 - 27*n. Solve t(s) = 0 for s.
-2
Let m(r) = r**3 + 4*r**2 - 3*r - 6. Let w(d) = -d**3 - 5*d**2 + 3*d + 7. Let u be (-33)/(-88) - 37/(-8). Let l(z) = u*m(z) + 4*w(z). Factor l(j).
(j - 2)*(j + 1)**2
Suppose -10*n = -24 - 76. Find v such that 9*v**3 + 85 - 85 - 3*v + 4*v**4 - n*v**2 = 0.
-3, -1/4, 0, 1
Let f be (-10)/2*(-26)/65. Factor -11*l**2 - 3*l**2 + 9*l + 3*l**3 + 30*l**2 - l**2 - 3*l**f.
3*l*(l + 1)*(l + 3)
Let r be -4 + 25/(500/120). Let y(o) be the third derivative of -1/18*o**4 - 1/9*o**3 - 1/90*o**5 + 0*o + 0 - 9*o**r. Find m such that y(m) = 0.
-1
Suppose 99*l - 101*l - 2*n - 24 = 0, -3*l + 100 = -5*n. Factor 14/5*o + 44/5*o**2 + 0 + 2/5*o**l + 4*o**4 + 48/5*o**3.
2*o*(o + 1)**3*(o + 7)/5
Find s, given that 35*s + 22*s + 7*s - 4*s**2 + 506 + 138 = 0.
-7, 23
Let b(g) be the first derivative of -g**4/30 + 32*g**3/15 - 256*g**2/5 - 124*g + 30. Let l(i) be the first derivative of b(i). Factor l(w).
-2*(w - 16)**2/5
Let p(a) be the second derivative of 9*a - 9/2*a**2 + 1/12*a**5 + 0 + 0*a**4 - 5/6*a**3. Let n(l) be the first derivative of p(l). Factor n(q).
5*(q - 1)*(q + 1)
Let m(n) be the third derivative of 22/15*n**5 + 0*n + 1/168*n**8 + 11/20*n**6 + 2/21*n**7 + 0*n**3 + 5/3*n**4 + 31*n**2 + 4. Factor m(w).
2*w*(w + 1)*(w + 2)**2*(w + 5)
What is w in -1031*w - 4*w**2 + 4842 - 573358 - 1985*w = 0?
-377
Let i = -151471/6 - -75736/3. Solve -i*v**2 + 23/3*v - 529/6 = 0 for v.
23
Let f(h) be the third derivative of 17*h**5/20 - 1549*h**4/8 + 91*h**3 - 1635*h**2 + h. Factor f(y).
3*(y - 91)*(17*y - 2)
Let r(x) = 12*x**3 + 126*x**2 + 203*x + 67. Let a(g) = 130*g - 2*g**3 - 1 + 150*g - 281*g. Let n(f) = 22*a(f) + 2*r(f). Suppose n(i) = 0. Calculate i.
-1, -2/5, 14
Let u(m) be the second derivative of -3*m**5/10 + 35*m**4/24 + 89*m**3/12 + 21*m**2/2 + 4*m - 99. Solve u(g) = 0 for g.
-1, -3/4, 14/3
Let y = -3015862/13 + 231990. Find d such that 0 + 16/13*d**3 + 0*d - y*d**2 + 2/13*d**5 - 10/13*d**4 = 0.
0, 1, 2
Let q be -1 + 3 + 5 + 0 + -2. Suppose -3*h - 6 = 0, 6 = -2*d + q*h + 26. Factor -d*y**3 - 4*y + 2*y**3 - 5*y + 6*y**2 + 6*y**3.
3*y*(y - 1)*(y + 3)
Let l(t) be the third derivative of -1/20*t**5 - 1 + 7/8*t**4 + 4*t**3 + 51*t**2 + 0*t. Factor l(y).
-3*(y - 8)*(y + 1)
Let v(t) be the second derivative of 0 - 1/15*t**4 + 1/50*t**5 - 1/15*t**3 + 2/5*t**2 + 130*t. Factor v(b).
2*(b - 2)*(b - 1)*(b + 1)/5
Factor 9/2*f - 185/3 + 1/6*f**2.
(f - 10)*(f + 37)/6
Let p(i) be the third derivative of i**8/1176 + i**7/735 - i**6/420 - i**5/210 - 14*i**2 + 53*i + 1. Factor p(u).
2*u**2*(u - 1)*(u + 1)**2/7
Suppose 4584 = -77*z + 81*z. Let p = -1146 + z. Factor -1/4*m**2 + p + 1/8*m**3 - 3/8*m.
m*(m - 3)*(m + 1)/8
Let v(q) be the first derivative of -q**4/90 - 7*q**3/45 - 10*q - 43. Let r(y) be the first derivative of v(y). Factor r(b).
-2*b*(b + 7)/15
Let l(c) be the first derivative of 9*c**5 - 1095*c**4 - 2935*c**3/3 - 245*c**2 + 1208. Suppose l(r) = 0. Calculate r.
-1/3, 0, 98
Let t(c) be the third derivative of c**8/100800 - c**7/210 + c**6 - c**5/15 - 7*c**3/2 + 103*c**2. Let b(d) be the third derivative of t(d). Factor b(z).
(z - 60)**2/5
Determine y so that -513 + 53 - 170*y - 136*y - 156*y + 2*y**2 - 4 = 0.
-1, 232
Factor -4*k + 2/7*k**2 + 48/7.
2*(k - 12)*(k - 2)/7
Let b = -19935 + 19937. Let y(p) be the second derivative of 1/6*p**5 + 0*p**3 + 0 + 1/20*p**6 + 0*p**b + 1/18*p**4 + 10*p. Solve y(g) = 0.
-2, -2/9, 0
Let p be (-48)/(-18)*(4 + -7). Let j be p/36 + 1930/180. Suppose j - 3/2*d**2 - 9*d = 0. What is d?
-7, 1
Let b(t) = 50*t - 79. Let l(h) = -52*h + 76. Let q(y) = 4*b(y) + 3*l(y). Let p be q(2). Solve 1/11*o**2 + 0 + p*o = 0.
0
Let t(u) be the first derivative of -u**4/12 + 280*u**3/9 - 551*u**2/2 + 822*u - 3034. Suppose t(i) = 0. What is i?
3, 274
Let r(s) be the second derivative of 1/50*s**5 - 3 + 0*s**2 + 0*s**3 - 26*s - 34/15*s**4. Factor r(w).
2*w**2*(w - 68)/5
Let u(s) be the third derivative of 0 - 2*s**2 + 0*s**3 + 1/12*s**4 + 59*s + 1/60*s**5. Factor u(g).
g*(g + 2)
Let w = 9161/3876 - -1/204. Let i = 237/76 - w. Factor -9/2*r**3 + 27/4*r**2 + 0*r + i*r**4 + 0.
3*r**2*(r - 3)**2/4
Let m(a) be the first derivative of -1/70*a**5 + 3*a + 