5, 1, 4
Let w(l) be the third derivative of l**8/896 + l**7/560 - l**6/64 - l**5/160 + l**4/8 - l**3/4 + 63*l**2. Factor w(a).
3*(a - 1)**3*(a + 2)**2/8
Let v(a) be the first derivative of a**4/32 - 23*a**3/24 + 11*a**2/8 + 347. Factor v(q).
q*(q - 22)*(q - 1)/8
Let f = 118 + -122. Let n be 36/(-98)*(f - (-7 + 10)). Find c, given that 2/7*c**2 - 12/7*c + n = 0.
3
Suppose -66 = -313*u + 302*u. Solve u - 3/4*d**3 - 9*d + 9/2*d**2 = 0 for d.
2
Let y(d) = -d**2 + 7*d + 1. Let w be y(8). Let h = -1 - w. Factor -2/3*a**4 - 4/3 - 14/3*a - 10/3*a**3 - h*a**2.
-2*(a + 1)**3*(a + 2)/3
Suppose -u + 11*u - 200 = 0. Factor 8*s - 18 + 46 + 2*s**2 - u.
2*(s + 2)**2
Let m(i) be the third derivative of i**6/300 - i**5/6 - 9*i**4/10 + 497*i**2 - 1. Find d, given that m(d) = 0.
-2, 0, 27
Factor -56*j + 0*j**5 + 2*j**5 - 8*j**4 + 32*j**2 + 10*j + 14*j.
2*j*(j - 2)**3*(j + 2)
Let h(d) be the third derivative of -d**9/15120 - d**8/2520 + 3*d**5/20 + 9*d**2. Let a(p) be the third derivative of h(p). What is n in a(n) = 0?
-2, 0
Let u(o) = -o**2 - 2*o - 1. Let q(w) = 3*w**2 + 8*w + 2. Let n(h) = -q(h) - 4*u(h). Let k be n(-1). Factor 0*t**2 + 1/2*t**k + 1 - 3/2*t.
(t - 1)**2*(t + 2)/2
Let j = 1661 - 1659. Solve -243*h**j + 54*h - 4 + 729/2*h**3 = 0.
2/9
Let i(t) be the third derivative of t**6/40 + t**5/4 - 13*t**4/8 + 7*t**3/2 - 94*t**2. Factor i(u).
3*(u - 1)**2*(u + 7)
Suppose 5*o = 5*c, 2*c + 8 = 3*c + 3*o. Factor 12*t**3 - 16*t**c + 4*t**5 - 3*t**4 - 16*t - 6*t**4 + 25*t**4.
4*t*(t - 1)*(t + 1)*(t + 2)**2
Let m(r) = -r**4 - 2*r**2 + r + 1. Let o(p) = 3*p**4 - 3*p**3 + 8*p**2 - 4. Let a(d) = -12*m(d) - 3*o(d). Find w such that a(w) = 0.
-2, 0, 1
Let t = -15 - -17. Factor -37*x**t - 2*x**5 + 16*x**2 - 2*x + 21*x**2 + 4*x**3.
-2*x*(x - 1)**2*(x + 1)**2
Let n(l) be the third derivative of -l**6/120 + l**5/4 - 25*l**4/8 - l**3/6 - 11*l**2. Let t(g) be the first derivative of n(g). Solve t(r) = 0 for r.
5
Let u(q) be the second derivative of -q**5/4 + 95*q**4/12 - 200*q**3/3 - 250*q**2 - 3*q + 1. Find f, given that u(f) = 0.
-1, 10
Let b(g) be the second derivative of -g**7/210 + 17*g**6/150 + 9*g**5/50 + 25*g + 9. Factor b(t).
-t**3*(t - 18)*(t + 1)/5
Let b = -439/48240 + 8/603. Let y(f) be the third derivative of 0*f + 1/160*f**6 - b*f**5 - 1/32*f**4 + 0 - 11*f**2 + 1/24*f**3. Solve y(h) = 0.
-1, 1/3, 1
Let a(p) be the third derivative of -p**5/30 - 43*p**4/12 - 14*p**3 + 140*p**2. Determine k so that a(k) = 0.
-42, -1
Let v(d) be the third derivative of -d**7/1155 + d**6/60 + 13*d**5/110 + 41*d**4/132 + 14*d**3/33 - 2*d**2. Find g, given that v(g) = 0.
-1, 14
Factor -128/7 - 2/7*a**2 - 32/7*a.
-2*(a + 8)**2/7
Let y(l) be the first derivative of 0*l**2 + 5/38*l**4 - 216/19*l - 2/19*l**5 + 12 - 1/57*l**6 + 30/19*l**3. Factor y(z).
-2*(z - 2)**2*(z + 3)**3/19
Let y(m) be the second derivative of 2/21*m**7 - 23*m + 0 + 0*m**2 + 0*m**3 + 2/15*m**6 + 0*m**4 + 0*m**5. Factor y(j).
4*j**4*(j + 1)
Let y(m) = m**3 + 3*m**2 - 2*m - 3. Let f be y(-3). Suppose f + 3 = 2*b. Solve 10*o**2 - 4*o**3 - 18 - 6*o + 6*o**b - 4*o**3 = 0 for o.
-1, 3
Factor 0 + 8*p**3 - 5/2*p**2 - p - 9/2*p**4.
-p*(p - 1)**2*(9*p + 2)/2
Let n be (2/636)/(10/1880). Let g = n + 4/53. Suppose -10/3*t**3 - g*t - 16/3*t**2 + 4/3 = 0. What is t?
-1, 2/5
Let i = 391 - 3909/10. Let p(k) be the first derivative of -1/2*k - i*k**5 + 3 - 1/2*k**4 - k**2 - k**3. Factor p(h).
-(h + 1)**4/2
Let o(k) = 4*k + 42. Let z be o(-11). Let u be (z/(-9))/((-14)/(-105)). Factor u*x**3 + 2/3*x + 0 + 7/3*x**2.
x*(x + 1)*(5*x + 2)/3
Factor 0 + 2/5*p**4 + 0*p + 4/5*p**3 - 6/5*p**2.
2*p**2*(p - 1)*(p + 3)/5
Let b(z) = z**2 - z - 1. Let c(j) = -2*j**3 + 45*j**2 - 201*j - 245. Let r(p) = -3*b(p) + c(p). Let r(f) = 0. Calculate f.
-1, 11
Let n(l) be the second derivative of l**4/6 - l**3 - 28*l**2 - 4*l + 10. Factor n(o).
2*(o - 7)*(o + 4)
Let l(z) be the third derivative of -z**7/120 - 3*z**6/160 + z**5/20 + z**4/24 - 2*z**2 + 126. Factor l(n).
-n*(n - 1)*(n + 2)*(7*n + 2)/4
Suppose 2*k + 3*k = 70. Let x = k + -2. Let 26*v - 11*v**2 - 12 - 7*v**2 + 3*v**3 + 10*v - x = 0. What is v?
2
Suppose -185*g + 204*g - 38 = 0. Find j such that 4/3*j - 10/3 - 2/15*j**g = 0.
5
Suppose 4*s - 4*q + 9*q + 7 = 0, -2*s + 3*q = -13. Let j(l) be the second derivative of 0 + 0*l**s + 6*l - 1/16*l**3 + 1/96*l**4. Factor j(k).
k*(k - 3)/8
Let t be (-2)/11 - 6/99*-3. Let f(n) be the second derivative of 1/20*n**5 + 0*n**4 + 0*n**3 + t*n**2 - 1/30*n**6 - n + 0. Determine h so that f(h) = 0.
0, 1
Let s(t) be the third derivative of t**6/120 + t**5/20 - 2*t**3/3 - 28*t**2 - 2. Factor s(i).
(i - 1)*(i + 2)**2
Let o(l) be the third derivative of l**7/2520 - l**6/720 - 7*l**4/12 - 30*l**2. Let d(k) be the second derivative of o(k). Solve d(g) = 0 for g.
0, 1
Suppose -3*h + 5*h + y = 5, 0 = -3*h - 17*y + 23. Find l, given that 13/4*l**h + 11/4*l - 1/2 = 0.
-1, 2/13
Factor -52/7 + 22/7*y + 2/7*y**2.
2*(y - 2)*(y + 13)/7
Factor -13/2*l**2 + 9/2*l**3 + 2*l + 0.
l*(l - 1)*(9*l - 4)/2
Suppose 2*a - 20 = -8*a. Factor 4*m**3 + 9*m - 19*m + 5*m**3 + 18 - 3*m**4 + 9*m**a - 23*m.
-3*(m - 3)*(m - 1)**2*(m + 2)
Suppose 0*u + u = 3*k - 4, -2*k + 20 = -5*u. Suppose 3*r - 11 - 19 = k. Let -9*g**3 + 3*g**2 - g**4 + r*g**4 - 7*g**5 + 4*g**5 = 0. What is g?
0, 1
Factor -27*v**4 - v**3 - 25*v**4 - v**3 - v**2 + 50*v**4 + 2*v + 3*v**2.
-2*v*(v - 1)*(v + 1)**2
Let q be (36/(-1824))/((-2)/(-56)). Let k = -1/19 - q. Determine h so that -1/3*h + k - 1/6*h**2 = 0.
-3, 1
Let w = -14757/20 + 738. Let j(l) be the second derivative of 9*l - w*l**5 + 1/28*l**7 + 0 - 3/2*l**2 + 1/10*l**6 - 7/4*l**3 - l**4. Factor j(p).
3*(p - 2)*(p + 1)**4/2
Suppose 4*v + 8 = 0, -5*v - 14 = -2*c + 2. Factor 2*r**2 - 20*r - 6*r**c + r**3 + 18*r**2.
-5*r*(r - 2)**2
Let t(m) be the second derivative of 8*m**5/5 - 26*m**4/3 + 26*m**3/3 + 10*m**2 - 8*m. What is c in t(c) = 0?
-1/4, 1, 5/2
Let c be 4/(-5)*480/(-336). Find l such that 0 + 0*l - 2/7*l**5 - 4/7*l**2 - 10/7*l**3 - c*l**4 = 0.
-2, -1, 0
Find g, given that -41*g**3 - 3*g**4 + 8*g**4 - 128*g**3 + 9*g**3 = 0.
0, 32
Let g = 8539/8 + -1067. What is t in -g*t - 1/4 - 1/8*t**2 = 0?
-2, -1
Let h(y) be the first derivative of -y**6/6 - 253*y**5/5 - 21667*y**4/4 - 655451*y**3/3 - 1184908*y**2 - 2287148*y + 668. Determine a so that h(a) = 0.
-83, -2
Let x(a) be the second derivative of 7*a**5/120 - 3*a**4/8 - a**3/9 + 238*a. Suppose x(d) = 0. What is d?
-1/7, 0, 4
Suppose 129 - 137 = -4*t. Factor 5/7 - 6/7*q + 1/7*q**t.
(q - 5)*(q - 1)/7
Let j(f) be the third derivative of -f**7/1470 - f**6/70 - 29*f**5/420 - 3*f**4/28 + 121*f**2 + f. Determine n, given that j(n) = 0.
-9, -2, -1, 0
Suppose -4 = 5*k - 14. Factor 7*t**2 + t**2 - 2*t**3 - k*t**3.
-4*t**2*(t - 2)
Let n(o) be the first derivative of -1/120*o**6 - 7/3*o**3 + 2 + 0*o**2 + 1/20*o**5 + 0*o + 0*o**4. Let x(b) be the third derivative of n(b). Factor x(a).
-3*a*(a - 2)
Let t(x) be the third derivative of -1/1140*x**6 + 0*x + 0 + 0*x**4 + 0*x**3 + 23*x**2 - 8/1995*x**7 + 0*x**5 - 2/399*x**8. Let t(v) = 0. Calculate v.
-1/4, 0
Let w(b) be the second derivative of 3*b**5/20 + 623*b**4/16 + 6045*b**3/2 - 4563*b**2/2 - 66*b. Factor w(a).
3*(a + 78)**2*(4*a - 1)/4
Let h(r) = 2*r**5 - 3*r**4 + 20*r**3 - 14*r**2 + 5*r - 5. Let u(x) = -x**5 - x**3 + x**2 - x + 1. Let l(z) = -h(z) - 5*u(z). Suppose l(t) = 0. What is t?
-3, 0, 1
Let a = 16313/7 + -2335. Let g = a + 40/7. Suppose -g - 2/7*v**2 + 8/7*v = 0. Calculate v.
2
Let k(x) be the third derivative of x**8/30240 + x**7/7560 + x**5/30 - x**4/8 + 37*x**2 - 1. Let q(i) be the third derivative of k(i). Factor q(l).
2*l*(l + 1)/3
Find r such that -4/3*r**2 - 1/3*r**3 + 7/3*r + 10/3 = 0.
-5, -1, 2
Let f(j) be the third derivative of 0*j + 1/900*j**6 + 2/45*j**3 - 1/60*j**4 - 18*j**2 + 0*j**5 + 0. Determine y, given that f(y) = 0.
-2, 1
Factor -24 + 124/5*i - 4/5*i**2.
-4*(i - 30)*(i - 1)/5
Let k(a) be the second derivative of a**5/120 + a**4/4 + 5*a**3/3 + 14*a**2/3 + 8*a + 1. Factor k(f).
(f + 2)**2*(f + 14)/6
Suppose -38*f - 66 + 180 = 0. Let y(o) be the second derivative of 11*o + 0 + 1/28*o**4 + 3/140*o**5 + 1/210*o**6 + 1/42*o**f + 0*o**2. Factor y(g).
g*(g + 1)**3/7
Let o(k) be the first derivative of 2*k**6/21 - 4*k**5/5 - 2*k**4/7 + 272*k**3/21 - 16*k**2/7 - 640