
Suppose -x = -2*s - 2*x - 9, s - 4*x = 0. Let b be (-7 - -1)/(s/94). Let 147*o**4 - b*o**4 + 108*o**2 + 50*o**3 - 57 - 5 - 2 = 0. What is o?
-4, -1, 2/3
Let d(o) = -o - 1. Let w(c) = 5*c**4 + 5*c**3 - 25*c**2 + 13*c - 2. Suppose -12 = -7*f - 19. Let z(i) = f*w(i) + 2*d(i). Determine a so that z(a) = 0.
-3, 0, 1
Let i(f) be the second derivative of 131*f**4/14 - 112*f**3/3 - 4*f**2/7 - 9*f - 192. Solve i(o) = 0.
-2/393, 2
Let j(l) = 15*l**4 - 670*l**3 - 820*l**2 + 3430*l - 1995. Let k(s) = -2*s**4 + 96*s**3 + 117*s**2 - 490*s + 285. Let o(c) = -3*j(c) - 20*k(c). Factor o(i).
-5*(i - 19)*(i - 1)**2*(i + 3)
Factor 236/3*i + 43/3*i**2 - 1/3*i**3 + 64.
-(i - 48)*(i + 1)*(i + 4)/3
Suppose -32/5 - 47/5*t**3 + 128/5*t - 42/5*t**2 - 7/5*t**4 = 0. Calculate t.
-4, 2/7, 1
Let t(a) be the second derivative of a**7/210 + 3*a**6/50 - 11*a**5/50 + a**4/30 + 7*a**3/10 - 11*a**2/10 - 404*a + 3. Factor t(v).
(v - 1)**3*(v + 1)*(v + 11)/5
Solve -4*u - 1/6*u**2 + 25/6 = 0 for u.
-25, 1
Let t be 366/(-1708) + (-5)/(-7). Let h(b) be the first derivative of -3 + 3*b**2 - t*b**3 - 9/2*b. Let h(v) = 0. Calculate v.
1, 3
Factor 352*k**2 - 16*k + 138*k**3 + 80*k**3 - 38*k**3.
4*k*(k + 2)*(45*k - 2)
Factor 1521 + 31/2*k**2 + 1651/2*k - 19/2*k**3 - 1/2*k**4.
-(k - 9)*(k + 2)*(k + 13)**2/2
Let f(q) be the second derivative of -24*q**2 - 83*q - 4*q**3 + 0 - 1/4*q**4. Factor f(o).
-3*(o + 4)**2
Let u(p) be the second derivative of 1369/4*p**2 + 37/2*p**3 - 56*p - 1 + 3/8*p**4. Determine i, given that u(i) = 0.
-37/3
Let -1487*g**3 - 60 - 85 + 170*g - 18*g**2 + 1485*g**3 - 5 = 0. What is g?
-15, 1, 5
Let x(i) be the first derivative of -i**5/10 + 3*i**4/8 + 17*i**3 + 22*i**2 - 96*i + 1866. Let x(k) = 0. What is k?
-8, -2, 1, 12
Factor 1/8*w**4 - 31/8*w**2 + 3/4*w**3 + 45/2 - 39/2*w.
(w - 5)*(w - 1)*(w + 6)**2/8
Factor -192/5 - 68/5*r**2 - 3/5*r**3 - 332/5*r.
-(r + 6)*(r + 16)*(3*r + 2)/5
Let q be 3/(-2) - (-270)/36. Let b(w) be the second derivative of w**5 + 0*w**3 - 1/6*w**q - 30*w + 0 - 5/4*w**4 + 0*w**2. Factor b(j).
-5*j**2*(j - 3)*(j - 1)
Let w(m) be the first derivative of 4*m**5/5 + 1001*m**4/2 + 1000*m**3/3 + 3111. Let w(g) = 0. What is g?
-500, -1/2, 0
Let n(b) be the first derivative of 32/3*b**3 + 238 + 0*b - 64/9*b**2 - 9/2*b**4. Suppose n(y) = 0. What is y?
0, 8/9
Factor -306 + 168*k + 10 - k**2 - 98 - 97 + 324*k.
-(k - 491)*(k - 1)
Let s(g) be the second derivative of -g**4/72 - 27*g**3 - 19683*g**2 + 2787*g. Factor s(u).
-(u + 486)**2/6
Determine y so that 40010 + 225624*y + 6097*y**2 + 34882 + 9*y**3 - 3250*y**2 = 0.
-158, -1/3
Let v(m) be the third derivative of -m**7/735 - 307*m**6/60 + 2151*m**5/70 - 6455*m**4/84 + 2152*m**3/21 + 7*m**2 - m + 1. Factor v(c).
-2*(c - 1)**3*(c + 2152)/7
Let w be (-2)/8 - (-6462)/(-3600)*10. Let c = w + 737/35. Find v such that 10/7*v**4 - 20/7*v**3 - 10/7*v - 2/7*v**5 + 2/7 + c*v**2 = 0.
1
Let y(b) be the third derivative of 121*b**7/1995 - 1067*b**6/570 + 4657*b**5/570 + 159*b**4/19 + 60*b**3/19 + 21*b**2 + 5*b. Determine s, given that y(s) = 0.
-2/11, 3, 15
Let x(s) be the third derivative of 0*s + 0 - 2/15*s**3 - 153*s**2 + 3/20*s**4 - 2/25*s**5 + 1/60*s**6. Find w, given that x(w) = 0.
2/5, 1
Determine x, given that -94/3*x + 20 + 2*x**2 = 0.
2/3, 15
Factor -6387 + 5*w**2 + 105*w + 12133 - 6396.
5*(w - 5)*(w + 26)
Let c = -13925/29 + 266953/551. Solve c*p + 2/19*p**2 - 84/19 = 0.
-42, 1
Let j = 2/781 - -703/30459. Let u(k) be the third derivative of 1/390*k**5 - j*k**3 + 0 + 1/156*k**4 - 12*k**2 + 0*k - 1/780*k**6. Factor u(y).
-2*(y - 1)**2*(y + 1)/13
Suppose -126 + 6 = -5*c. Suppose u + c = 7*u. Factor u*i**3 - 1797*i + 4*i**2 + 1797*i.
4*i**2*(i + 1)
Factor 70 + 31/6*g**2 - 1/6*g**3 - 134/3*g.
-(g - 15)*(g - 14)*(g - 2)/6
Let l be -24*(-3)/(-12) + 11. Let k(q) be the third derivative of 1/210*q**6 + 0*q + 3/14*q**4 + 8/21*q**3 - 28*q**2 + 2/35*q**l + 0. Solve k(g) = 0 for g.
-4, -1
Let a = 30/29023 - -57896/145115. Factor 4/5*j**2 + 14/5*j + 8/5 - a*j**3.
-2*(j - 4)*(j + 1)**2/5
Let u = -168424 + 168433. Factor -2*d + 9/2*d**3 + 12 - 1/2*d**4 - u*d**2.
-(d - 6)*(d - 2)**2*(d + 1)/2
Let k(q) be the second derivative of 2*q**7/21 + 6*q**6/5 - 43*q**5/5 - 569*q**4/3 - 868*q**3 - 1568*q**2 - 848*q + 2. Suppose k(x) = 0. What is x?
-7, -2, -1, 8
Let k(r) be the third derivative of -45*r**2 + r + 0 + 0*r**3 - 1/30*r**6 + 0*r**4 + 2/5*r**5. Factor k(p).
-4*p**2*(p - 6)
Factor 10878*s**3 - 4*s**4 + 20*s**2 + 28*s**2 - 10894*s**3.
-4*s**2*(s - 2)*(s + 6)
Let b(l) be the third derivative of l**7/17640 + l**6/5040 - l**5/70 + 25*l**4/24 - 3*l**2 + 18*l. Let k(n) be the second derivative of b(n). Solve k(a) = 0.
-4, 3
Let d(n) be the first derivative of n**5/16 + 35*n**4/24 + 95*n**3/8 + 45*n**2 - 106*n + 147. Let h(s) be the first derivative of d(s). Let h(z) = 0. What is z?
-8, -3
Let n(x) be the first derivative of x**6/30 - 3*x**5/20 - x**4/12 + x**3/2 + 105*x - 24. Let a(r) be the first derivative of n(r). Factor a(v).
v*(v - 3)*(v - 1)*(v + 1)
Determine u, given that -39/5 + 42/5*u - 3/5*u**2 = 0.
1, 13
Suppose -35*p = -38*p + 27*p - 144. Let n(r) be the second derivative of 3/8*r**4 + 1/60*r**p + 0 + 1/8*r**5 + 7/12*r**3 + 1/2*r**2 + 23*r. Factor n(i).
(i + 1)**3*(i + 2)/2
Let k(q) = 29*q**4 + 4*q**3 - 13*q**2 - 6*q + 30. Let z(p) = -p**4 - p**3 + 2*p**2 - p + 5. Let o(l) = -k(l) + 6*z(l). Factor o(w).
-5*w**2*(w + 1)*(7*w - 5)
Let m = -44/20789 + 124954/103945. Find a such that 6/5*a**3 - 12/5 + 2/5*a**4 - 22/5*a - m*a**2 = 0.
-3, -1, 2
Suppose -393 = -5*h + 2*c, c + 2*c + 243 = 3*h. Find f, given that -83*f**3 + 54*f - 36*f**2 + 2*f**4 + h*f**3 + 81 + f**4 = 0.
-3, -1, 3
Let d(x) be the first derivative of -2*x**7/105 + x**6/30 - 77*x**2/2 - 79. Let c(f) be the second derivative of d(f). Suppose c(g) = 0. What is g?
0, 1
Let k = -2/1394849 - -18133041/2789698. Factor -1/4*t**2 + k*t + 0.
-t*(t - 26)/4
Let g be (120/28)/((-10026)/(-15596)). Find a such that -1/3*a**2 + g - 1/3*a = 0.
-5, 4
Let i(g) be the second derivative of -g**5/8 + 13*g**4/72 + g**3/12 - g**2/12 - g + 622. Solve i(t) = 0 for t.
-1/3, 1/5, 1
Let q(k) = 2*k**3 + 3*k**2 - 5*k - 24. Let h be q(5). Let x = h - 5240/19. Let -2/19*y**5 + x*y**2 + 0*y**4 + 0*y + 6/19*y**3 + 0 = 0. What is y?
-1, 0, 2
Let o(l) be the third derivative of l**5/20 - 119*l**4/2 + 28322*l**3 - 1836*l**2. Factor o(b).
3*(b - 238)**2
Let f(y) be the first derivative of y**4/2 - 7*y**3/3 + 2*y**2 + 4*y - 101. Factor f(w).
(w - 2)**2*(2*w + 1)
Let a(x) be the third derivative of -x**7/1470 + 5*x**6/56 + 51*x**5/140 + 11*x**4/24 - 2*x**2 - x + 73. Factor a(c).
-c*(c - 77)*(c + 1)**2/7
Suppose 2558 + 3610 = 8*v. Factor v + 787 - 4*h**2 + 40*h - 1462.
-4*(h - 12)*(h + 2)
Factor -3*z**4 - 2010 + 2010 + 55875*z - 1188*z**3 + 181731*z - 116415*z**2.
-3*z*(z - 2)*(z + 199)**2
Let t(s) = 125*s**2 + 700*s + 125. Let v(d) = -9*d**2 - 50*d - 9. Let c(p) = -p - 4. Let l be c(-6). Let h = l + -8. Let k(r) = h*t(r) - 85*v(r). Factor k(m).
5*(m + 3)*(3*m + 1)
Determine b, given that 32/21*b**4 - 54/7*b + 0 - 96/7*b**2 - 92/21*b**3 - 2/21*b**5 = 0.
-1, 0, 9
Let m(d) be the second derivative of d**7/630 + 23*d**6/180 + d**4/2 - d**3/6 - 146*d - 1. Let l(h) be the third derivative of m(h). Let l(z) = 0. Calculate z.
-23, 0
Let d(m) be the second derivative of -3*m**5/40 + 6129*m**4/8 - 12521547*m**3/4 + 25581520521*m**2/4 + 2755*m. Factor d(u).
-3*(u - 2043)**3/2
Suppose 192/5 + 24/5*p**3 - 64/5*p**4 + 352/5*p**2 - 100*p - 4/5*p**5 = 0. What is p?
-16, -3, 1
Suppose -4*h - 10*v + 54 = -13*v, -v = -5*h + 73. Factor h*n + 3/2*n**2 - 33/2.
3*(n - 1)*(n + 11)/2
Suppose 322*i + 646*i + 55*i = 2046. Let 128/3*v + 70/3*v**i - 32/3 + 3*v**3 = 0. What is v?
-4, 2/9
Let 2049/5*t - 252/5*t**2 + 3/5*t**3 - 360 = 0. Calculate t.
1, 8, 75
Let h(p) be the second derivative of p**7/12600 - 3*p**5/200 - 17*p**4/12 + 2*p**3/3 - 146*p. Let l(y) be the third derivative of h(y). Factor l(a).
(a - 3)*(a + 3)/5
Let w(g) be the third derivative of -g**8/1344 + 4*g**7/21 + g**6/160 - 239*g**5/120 - 10*g**4/3 - 5*g**2 - g - 313. Suppose w(m) = 0. What is m?
-1, 0, 2, 160
Let i(o) = 32*o**2 + 44*o - 17. Let r(w) = -11*w**2 - 14*w + 6. Let u be -2 - (6/(-12)*10 - -9). Let g(z) = u*i(z) - 17*r(z). What is h in g(h) = 0?
-26/5