he first derivative of g(t). Let s(n) = 0. Calculate n.
-1, 0, 4
Let d(p) be the third derivative of -1/540*p**6 + 0 - 1/945*p**7 + 0*p**3 + 1/108*p**4 + 0*p + 4*p**2 + 1/270*p**5. Factor d(t).
-2*t*(t - 1)*(t + 1)**2/9
Suppose v + 44*k + 3 = 45*k, -5*v - 3 = -3*k. Factor 8 - 4*g**v - 15/2*g**2 + 4*g - 1/2*g**4.
-(g - 1)*(g + 1)*(g + 4)**2/2
Suppose -u + 7 + 24 = 5*d, -5*u = -3*d + 13. Let c(n) be the third derivative of 1/150*n**d + 7*n**2 + 0*n + 0*n**5 + 0 - 1/30*n**4 + 0*n**3. Factor c(q).
4*q*(q - 1)*(q + 1)/5
Let w(i) be the first derivative of 3*i**5/5 - 45*i**4/2 + 157*i**3 + 1530*i**2 + 3468*i + 381. Suppose w(y) = 0. What is y?
-2, 17
Let y(g) be the first derivative of g**8/2520 + g**7/630 - g**6/180 - 2*g**5/45 - g**4/9 - 11*g**3/3 - 1. Let r(n) be the third derivative of y(n). Factor r(x).
2*(x - 2)*(x + 1)**2*(x + 2)/3
Let i(w) be the third derivative of w**8/120960 - w**6/4320 - w**5/10 + 14*w**2. Let r(l) be the third derivative of i(l). What is j in r(j) = 0?
-1, 1
Let b(f) be the third derivative of f**6/30 + f**5/15 - 8*f**4/3 - 32*f**3/3 + 14*f**2 + 4*f. Let b(v) = 0. What is v?
-4, -1, 4
Let r(j) be the first derivative of -3*j**4/4 + 12*j**3 - 54*j**2 + 154. Let r(x) = 0. What is x?
0, 6
Let f(n) be the second derivative of -n**7/126 + 2*n**6/45 - n**5/12 + n**4/18 + 7*n. Determine g, given that f(g) = 0.
0, 1, 2
Let i = -13 - -18. Let h be (0*(-2)/6)/(i - 3). What is a in h - a**2 + 2/5*a = 0?
0, 2/5
Let c = 1/111 - -35/222. Let l = 13/2 - 6. Solve -c*d**2 - 1/3 + l*d = 0.
1, 2
Let k be 1*(-3)/((-12)/(-20)). Let s be ((-5)/(-2))/k + 135/70. Factor -2/7*j**4 + 8/7*j**3 + 0 - s*j**2 + 4/7*j.
-2*j*(j - 2)*(j - 1)**2/7
Let v(b) be the third derivative of -b**8/110880 - b**7/6930 - b**6/990 + 7*b**5/30 + 9*b**2. Let p(x) be the third derivative of v(x). Solve p(w) = 0 for w.
-2
Let m(n) be the second derivative of -125*n**5/4 + 1625*n**4/4 - 4225*n**3/2 + 10985*n**2/2 - 18*n. Let m(r) = 0. What is r?
13/5
Let w(s) be the second derivative of s**5/10 - 371*s**4/6 + 34595*s**3/3 - 34225*s**2 - 262*s. Factor w(h).
2*(h - 185)**2*(h - 1)
Let 4/5 - 14/5*w**2 + 2*w = 0. What is w?
-2/7, 1
Let r(o) be the first derivative of -75*o**4/4 + 30*o**3 + 54*o**2 + 24*o + 130. Factor r(d).
-3*(d - 2)*(5*d + 2)**2
Let a be (3/27)/((-12)/(-72)). Let w(i) be the first derivative of 0*i - 4/5*i**5 + 0*i**4 + 0*i**2 + 0*i**3 + 4 - a*i**6. Factor w(y).
-4*y**4*(y + 1)
Let d be 3 + (8/6 - 5/15). Let m(b) be the second derivative of 1/30*b**d + 0 + 1/15*b**3 - 1/75*b**6 + 0*b**2 - 1/50*b**5 - b. Factor m(c).
-2*c*(c - 1)*(c + 1)**2/5
Let f(n) be the second derivative of -n**10/52920 - n**9/26460 + n**8/11760 + n**7/4410 + n**4/2 + 12*n. Let m(j) be the third derivative of f(j). Factor m(b).
-4*b**2*(b - 1)*(b + 1)**2/7
Let m be (24/(-10))/(18/(-150)). Let f be (-36)/(-24) - 26/m. Let f*v**4 - 9/5*v + 0 + v**3 + 3/5*v**2 = 0. Calculate v.
-3, 0, 1
Let f(q) = 6*q**3 + 432*q**2 + 10336*q + 82944. Let s(h) = -2*h**3 - 144*h**2 - 3444*h - 27648. Let k(p) = 3*f(p) + 8*s(p). Factor k(m).
2*(m + 24)**3
Let i(v) be the third derivative of -1/30*v**3 + 0 - 7*v**2 + 1/300*v**5 + 0*v**4 + 0*v. Factor i(s).
(s - 1)*(s + 1)/5
Let h(c) be the second derivative of -2/15*c**6 + 0*c**3 - 4*c + 1/5*c**5 + 0*c**2 + 0*c**4 + 0. Factor h(m).
-4*m**3*(m - 1)
Suppose 0*i - 94 = -2*i. Factor -6*t - i*t**2 + 2*t + 43*t**2.
-4*t*(t + 1)
Let t be ((-8)/8)/((-1)/3). Suppose 7*u - t*u = 8. Factor 6*s + 1 + 3*s**u - 9 - 1.
3*(s - 1)*(s + 3)
Let f be ((-5)/(-60)*8)/((-107)/6). Let k = 154/1605 - f. Determine c, given that 4/15*c + 2/15*c**4 - 2/5*c**3 - k*c**2 + 0 + 2/15*c**5 = 0.
-2, -1, 0, 1
Let m be -12*((-22)/4)/11. Let y(i) be the first derivative of -m - 7/25*i**5 - 8/15*i**3 + 19/20*i**4 + 0*i - 2/5*i**2. Factor y(z).
-z*(z - 2)*(z - 1)*(7*z + 2)/5
Let a = -4952 - -4954. Factor 6 + 92/3*n**a + 6*n**4 - 32*n**3 + 32*n.
2*(n - 3)**2*(3*n + 1)**2/3
Suppose -25*n + 9*n + 27*n - 22 = 0. Determine z, given that -1/5*z**n - 3/5 - 4/5*z = 0.
-3, -1
Factor 4*m + 3 + 11*m + 9*m**3 + 0*m + 21*m**2.
3*(m + 1)**2*(3*m + 1)
Let c be ((-60 + 68)/(-8 - -2))/(8/(-9)). Suppose 3*t**3 - 3*t + 3/2*t**4 - c*t**2 + 0 = 0. Calculate t.
-2, -1, 0, 1
Let k = 176845/9 + -19649. Determine g so that g**2 + 11/9*g + 1/9*g**3 + k - 1/9*g**4 = 0.
-1, 4
Let p = -347763317/477 + 729064. Let x = 1/477 + p. Determine w so that 10/9*w - x + 2/9*w**3 - 8/9*w**2 = 0.
1, 2
Let o(l) = -l**2 - 9*l - 17. Let y be o(-4). Let j(u) be the second derivative of -7*u + 1/12*u**4 + 0 + 0*u**2 + 1/3*u**y. Determine i, given that j(i) = 0.
-2, 0
Suppose 2*a - 21 - 15 = 0. Suppose -5*u = -a + 3. Determine y so that -5*y**3 + 2*y**3 + 12*y - 2*y**u + 8 + y**3 = 0.
-1, 2
Let k(u) = 4*u**3 - 17*u**2 + 4*u + 2. Let p be k(4). What is r in 2/3*r + 4/3 - 2/3*r**p = 0?
-1, 2
Let z be -2 - 6/((-6)/5). Let y(f) be the first derivative of 0*f**2 - 1/10*f**4 + 2/15*f**z + 5 + 0*f. Find x, given that y(x) = 0.
0, 1
Let o(n) be the second derivative of n**7/42 - n**6/24 - n**5/4 + 25*n**4/24 - 5*n**3/3 - 7*n**2/2 + 5*n. Let z(c) be the first derivative of o(c). Factor z(x).
5*(x - 1)**3*(x + 2)
Let t(o) be the second derivative of o**6/210 + 2*o**5/35 + 5*o**4/28 - 2*o**3/21 - 10*o**2/7 + 56*o + 1. Factor t(z).
(z - 1)*(z + 2)**2*(z + 5)/7
Suppose 34*v - 2*u = 36*v + 8, -5*v + 4 = -u. Solve 3/2*m**2 + 1/2*m + v + 1/2*m**3 - 3/2*m**4 - m**5 = 0 for m.
-1, -1/2, 0, 1
Determine t, given that 0*t + 0 + 1/3*t**4 + 2*t**3 - 7/3*t**2 = 0.
-7, 0, 1
Let z(b) be the first derivative of -b**4/2 - 11*b**3/6 + 43*b**2/4 - 5*b - 54. Factor z(c).
-(c - 2)*(c + 5)*(4*c - 1)/2
Let i(k) = 29*k - 2*k**3 - 9*k**2 + 3*k**3 - 39*k. Let x be i(10). Factor 0 + 2/11*f**4 + x*f**2 + 0*f + 2/11*f**3.
2*f**3*(f + 1)/11
Suppose 0 - 1/2*f**2 - 3*f = 0. What is f?
-6, 0
Let o(u) be the second derivative of -u**4/32 + 135*u**3/8 - 54675*u**2/16 + 4*u - 65. Factor o(a).
-3*(a - 135)**2/8
Let i(a) = -5*a**4 + 36*a**3 - 14*a**2 - 149*a - 160. Let w(m) = m**4 - 7*m**3 + 2*m**2 + 30*m + 32. Let k(d) = -2*i(d) - 11*w(d). Let k(z) = 0. Calculate z.
-2, -1, 4
Let h(r) be the third derivative of r**5/240 + 5*r**4/96 - 7*r**3/12 - 2*r**2. Determine i, given that h(i) = 0.
-7, 2
Let m(i) be the third derivative of -i**9/20160 + i**7/1680 + i**5/12 + 9*i**2. Let g(w) be the third derivative of m(w). Factor g(h).
-3*h*(h - 1)*(h + 1)
Let s(k) be the second derivative of 4*k**6/15 - 71*k**5/5 + 227*k**4 - 1802*k**3/3 + 578*k**2 - k + 240. Determine p so that s(p) = 0.
1/2, 1, 17
Let z(s) be the first derivative of 0*s**2 - 1/3*s**3 + 0*s - 1. Factor z(p).
-p**2
Let i be ((-9)/(-36))/(2/12). Factor 0 + 0*d + i*d**3 - 3*d**2.
3*d**2*(d - 2)/2
Let g be (3/(-6)*12)/(-2). Let h(k) be the second derivative of 1/40*k**5 + 0*k**g + 0*k**4 - 3*k - 1/20*k**6 - 1/21*k**7 + 0 + 0*k**2. Factor h(y).
-y**3*(y + 1)*(4*y - 1)/2
Let 21/8*a**2 - 5/4*a**3 - 27/2 + 1/8*a**4 + 9/2*a = 0. Calculate a.
-2, 3, 6
Suppose 0 = -2*u - 3*u + 40. Let p be u/((-9)/((-9)/2)). Factor l**5 + p*l**3 + 3*l - 7*l**5 - 10*l**3 + 9*l**5.
3*l*(l - 1)**2*(l + 1)**2
Let l be -21 - (21 - 3078/72). Factor 105/4*b + l*b**3 + 75/4 + 33/4*b**2.
3*(b + 1)*(b + 5)**2/4
Let u(y) be the third derivative of -y**6/280 - 11*y**5/140 - 19*y**4/28 - 20*y**3/7 + 602*y**2. Suppose u(r) = 0. What is r?
-5, -4, -2
What is d in -32/3 + 14/3*d + 1/3*d**2 = 0?
-16, 2
Let n be (-4 + 3)*(1 + -1)/(4/(-2)). Find p, given that 1/5*p**4 + 1/5*p + 1/10*p**3 + n - 1/2*p**2 = 0.
-2, 0, 1/2, 1
Suppose 23 = n + 2*u - 4*u, -5*n + 55 = 5*u. Determine s so that -n*s - 2*s**3 - 11*s + 30*s - 2*s**2 = 0.
-2, 0, 1
Let r(i) = -4*i - 18. Let y be r(-5). Factor 4*q - y*q**3 + 3*q**3 - 6*q**3 + q**3.
-4*q*(q - 1)*(q + 1)
Let v be ((5 - -1) + 0)*(-39)/(-312). Let t(z) be the first derivative of 1/2*z - v*z**2 - 1/8*z**4 + 1/2*z**3 + 3. Solve t(a) = 0.
1
Let t(p) be the third derivative of p**7/140 + 47*p**6/240 + 53*p**5/32 + 75*p**4/32 + 2*p**2 - 84*p. Factor t(z).
z*(2*z + 15)**2*(3*z + 2)/8
Let i be 2905/100 + (12 - 98/8). Suppose 3/5*v**4 + 68/5*v**3 + 337/5*v**2 + i - 552/5*v = 0. What is v?
-12, 1/3, 1
Factor 145*f + f**2 + 55*f + 9*f**2 - 9*f**2.
f*(f + 200)
Let t(o) be the first derivative of -o**5/30 + 11*o**4/12 + o**3/6 - 16*o**2/3 - 22*o/3 - 59. So