**6/140 - 5*h**5/42 - h**4/7 + 4*h**3/21 - 19*h**2/2 + 9. Let m(d) be the second derivative of c(d). Factor m(n).
-2*(n + 1)*(n + 2)*(9*n - 2)/7
Solve 19/2*t**2 - t**3 + 5*t + 0 = 0 for t.
-1/2, 0, 10
Solve 15*q**2 - 4800 - 4560*q - 66*q**2 - 3*q**3 + 121*q**2 + 167*q**2 = 0.
-1, 40
Let w = 5086 + -66116/13. Factor w*v - 2/13 + 4/13*v**2.
2*(v + 1)*(2*v - 1)/13
Let x = -3841/52 - -2166/13. Let j = x + -92. Factor -3/8*q**2 + 9/8*q - j.
-3*(q - 2)*(q - 1)/8
Let u = 443/468 - 3/52. Let g(d) be the first derivative of -u*d + 3 + 2/27*d**3 + 1/3*d**2. Let g(l) = 0. What is l?
-4, 1
Let p(w) = 3*w**3 + 29*w**2 + 33*w + 11. Let s(o) = -20*o**3 - 205*o**2 - 230*o - 75. Let n(t) = 15*p(t) + 2*s(t). Determine a, given that n(a) = 0.
-3, -1
Solve -4/9*p**5 + 46/9*p**3 - 10/9*p**4 + 0*p - 20/9*p**2 + 0 = 0.
-5, 0, 1/2, 2
Let s(f) be the second derivative of -2/9*f**3 - 7 + 1/5*f**2 + 7/90*f**4 + 5*f. Factor s(d).
2*(d - 1)*(7*d - 3)/15
Let 12*p**4 - 272*p + 8*p**4 + 664*p**2 + 336*p**3 + 191*p**3 - 136*p**2 - 155*p**3 = 0. Calculate p.
-17, -2, 0, 2/5
Let b = -67019/7 - -9575. Let -2/7*c**2 + b*c - 4/7 = 0. Calculate c.
1, 2
Factor 46/3*o - 9*o**2 + 13/6*o**3 - 1/6*o**4 - 28/3.
-(o - 7)*(o - 2)**3/6
Let z(g) = 3*g**3 + g - 9. Let m(f) = 4*f**3 - 10. Suppose 3*r + 57 - 18 = 0. Let l = 18 + r. Let x(q) = l*m(q) - 6*z(q). Factor x(a).
2*(a - 1)**2*(a + 2)
Let x(v) be the second derivative of 0 + v**2 + 1/2*v**3 + 1/12*v**4 + 15*v. Suppose x(g) = 0. What is g?
-2, -1
Factor 0 - 2/5*k**3 - 16/5*k**2 - 14/5*k.
-2*k*(k + 1)*(k + 7)/5
Let x be (135/(-20) - 1) + 5. Let u = -9/4 - x. Let -1/2*g**4 + 1 - 3/2*g**3 - u*g**2 + 3/2*g = 0. Calculate g.
-2, -1, 1
Let h(l) be the first derivative of l**6/15 - l**5/5 - l**4/2 + 8*l**3/3 - 4*l**2 + 25*l - 25. Let q(x) be the first derivative of h(x). Factor q(b).
2*(b - 2)*(b - 1)**2*(b + 2)
Let u(y) be the third derivative of 1/7*y**3 + 0*y - 12*y**2 - 1/42*y**4 + 0 - 8/105*y**5. Suppose u(m) = 0. Calculate m.
-1/2, 3/8
Let j(g) be the third derivative of -g**6/72 + g**5/8 - 5*g**4/12 - 8*g**3/3 - 29*g**2. Let x(h) be the first derivative of j(h). Factor x(u).
-5*(u - 2)*(u - 1)
Let p = 3781/10104 - -1/1263. Factor 3/4*t + 3/8 - 3/4*t**3 + 0*t**2 - p*t**4.
-3*(t - 1)*(t + 1)**3/8
Let f be (14/6)/(1 - 4/6). Let y be 4*f/(-28) + 3. Factor -1/2*n - 1/6*n**y + 0.
-n*(n + 3)/6
Let q = 2/71 + -289/12780. Let b(p) be the third derivative of -1/45*p**5 - 1/36*p**4 - q*p**6 + 0*p**3 + 0 + 0*p + 4*p**2. Factor b(h).
-2*h*(h + 1)**2/3
Let q = -2/15 + 44/105. Let r(n) be the first derivative of -2 - q*n**4 - 5/7*n**2 + 22/21*n**3 - 4/7*n. Suppose r(w) = 0. What is w?
-1/4, 1, 2
Suppose -3*u + 24 = -5*a, 23 = 4*u - 5*a - 4. Suppose -u*n + 40 = 2*n. Let -5 + 2 - n*i**2 - 14*i + 4*i - 1 - 2*i**3 = 0. What is i?
-2, -1
Let m = -4329 - -4331. Factor 0 + 3*j + 3/2*j**m.
3*j*(j + 2)/2
Let i(f) be the second derivative of -f**3/6 - 5*f**2/2 - 6*f. Let a be i(-10). Factor 4*t - 4 + 4*t + 0 - a*t**2 + 3*t**3 - 2*t**3.
(t - 2)**2*(t - 1)
Suppose 2/21*l**2 - 316/7*l + 37446/7 = 0. What is l?
237
Let -9*x - 206*x**2 + 110*x**2 + 279*x**2 - 83*x - 18*x**3 + 235*x**2 = 0. Calculate x.
0, 2/9, 23
Let h(l) be the second derivative of -l**5/60 - 7*l**4/36 - 7*l**3/18 + 5*l**2/2 - 49*l. Factor h(z).
-(z - 1)*(z + 3)*(z + 5)/3
Find q, given that 576/5 + 1/5*q**2 + 48/5*q = 0.
-24
Let w(h) be the second derivative of -h**4/6 - 79*h**3/3 - 78*h**2 - 429*h. Factor w(x).
-2*(x + 1)*(x + 78)
Let n = 134/33 + -3328/825. Let f(r) be the third derivative of 1/300*r**6 + 2/15*r**3 + 1/12*r**4 + n*r**5 + 0 + 6*r**2 + 0*r. Solve f(m) = 0 for m.
-2, -1
Let y be -64 - 9/((-18)/(-4)). Let s = 331/5 + y. Solve -s + 0*g + 1/5*g**2 = 0.
-1, 1
Let a(f) be the third derivative of 11*f**2 + 0*f + 1/21*f**4 + 0 + 1/21*f**3 - 1/42*f**5. Factor a(r).
-2*(r - 1)*(5*r + 1)/7
Let v(q) be the second derivative of -q**7/378 + 131*q**6/135 - 17161*q**5/180 - 2*q - 385. Factor v(j).
-j**3*(j - 131)**2/9
Suppose 2 - 4 = -p. Determine u so that 22*u + 0 + 2*u - 3 - 32*u**p - 16*u**2 = 0.
1/4
Let i(v) = 4*v**2 - v - 1. Let l be i(-1). Suppose -l*c + 6 = -2. Let -y**2 + 2*y**3 + 4*y**2 - 3*y**4 - 4*y**2 + c*y**4 = 0. What is y?
0, 1
Let b be (-2)/(-16) - -1735*11/2200. Factor -8/5*z**2 + 8*z**3 - b*z + 4/5*z**5 - 4 + 28/5*z**4.
4*(z - 1)*(z + 1)**3*(z + 5)/5
Let d(x) be the second derivative of -4/7*x**3 - 1/28*x**4 - 24/7*x**2 - 18*x + 0. Let d(u) = 0. Calculate u.
-4
Let l(k) be the third derivative of 0*k**4 - 3/98*k**7 + 0 + 8*k**2 + 0*k + 0*k**3 + 9/784*k**8 - 1/140*k**5 + 1/40*k**6. Factor l(p).
3*p**2*(p - 1)*(3*p - 1)**2/7
Let w = 996 - 996. Let k(v) be the third derivative of 3*v**2 - 1/30*v**6 + 0 + 2/15*v**5 + 0*v**3 + w*v - 1/6*v**4. Find s such that k(s) = 0.
0, 1
Let z be ((-1 - 13) + 2)*3/(-9). Solve -3*i**z + 3*i**3 + 7*i**2 + 131*i - 4*i**2 - 131*i - 3*i**5 = 0.
-1, 0, 1
Let g(l) be the first derivative of l**6/10 - 9*l**5/25 - 3*l**4/4 + 3*l**3 + 6*l**2/5 - 36*l/5 - 305. Suppose g(r) = 0. What is r?
-2, -1, 1, 2, 3
Let i(y) be the third derivative of -y**8/2352 + y**7/490 + 16*y**2 + 10*y. What is n in i(n) = 0?
0, 3
What is i in 90/7 + 3/7*i**2 - 33/7*i = 0?
5, 6
Let b be (6/4)/(9/96). Let v = b - 14. Factor -12*a + 4*a**2 - v*a**2 + a**2 + 12.
3*(a - 2)**2
Let x(i) be the third derivative of i**5/5 - 19*i**4/6 + 56*i**3/3 + 260*i**2. Determine y, given that x(y) = 0.
7/3, 4
Let p(w) be the first derivative of 8*w**2 + 11 - 20/3*w**3 + 2*w**4 - 4*w. Factor p(b).
4*(b - 1)**2*(2*b - 1)
Suppose 2*k - 7 = -4*w + 23, -4*w = -2*k + 14. Factor 14*j - 3 - k - 5*j**2 - 29*j + 4.
-5*(j + 1)*(j + 2)
Let q(u) = u**2 + 2*u. Let t(p) = 11*p**2 + 204*p. Let v(i) = -18*q(i) + 2*t(i). Factor v(x).
4*x*(x + 93)
Let l(u) = -u**3 + 18*u**2 + u + 5. Let r be l(18). Find o, given that 3 + 40*o**3 - 4*o**2 + 3*o - r*o**3 - 20*o**3 + o**2 = 0.
-1, 1
Let z(p) be the third derivative of -p**7/1680 - p**6/480 + p**5/96 + p**4/32 + 169*p**2. Solve z(l) = 0 for l.
-3, -1, 0, 2
Let i(j) be the first derivative of -3 + 3*j**2 - 1/2*j**3 - 2*j**4 - 3/4*j**5 - 4*j. Let u(g) be the first derivative of i(g). Solve u(d) = 0.
-1, 2/5
Let u = -1251 - -1254. Let v(k) be the second derivative of -2/21*k**7 - 13/5*k**5 - 8/3*k**u + 0*k**2 + 0 - 5*k + 4/5*k**6 + 4*k**4. Let v(m) = 0. Calculate m.
0, 1, 2
Suppose -16*l**4 - 20*l**2 + 6*l + 12*l**2 + 9*l**2 - 96*l**3 = 0. Calculate l.
-6, -1/4, 0, 1/4
Let m be ((-11)/(44/24))/(-3). Factor 0*z**2 - 4 + 3*z**m + 5*z**3 - 4*z**3.
(z - 1)*(z + 2)**2
Find s such that 0 - 3*s**3 + 9/4*s**4 + 3/4*s**2 + 0*s = 0.
0, 1/3, 1
Suppose 0*w + 2*k = 4*w - 2, 0 = -3*w - 5*k + 21. Suppose 269*t = 267*t + 4. Let i - 15*i**2 + 3*i**t + 11*i**w = 0. What is i?
0, 1
Suppose 148*q**2 + 20 + 215*q**2 - 303*q**2 + 20*q**3 - 75*q = 0. What is q?
-4, 1/2
Let i = 47/498 + 6/83. Let c(g) be the first derivative of 0*g + 1/4*g**2 + 10 + i*g**3. Factor c(j).
j*(j + 1)/2
Let 30*u**2 - 76*u + 250*u**4 - 20*u**3 - 255*u**4 + 256*u + 135 = 0. What is u?
-3, -1, 3
Let h(n) be the second derivative of n**5/10 - 7*n**4 + 196*n**3 - 2744*n**2 - 173*n. Factor h(m).
2*(m - 14)**3
Let u(w) be the second derivative of 1/14*w**5 + 2/21*w**3 + 0*w**2 + 1/6*w**4 - 21*w + 0. Factor u(n).
2*n*(n + 1)*(5*n + 2)/7
Let y be (-485)/194*(-4)/35 + (-34)/(-28). Factor 27/2*n + 0 - 9*n**2 + y*n**3.
3*n*(n - 3)**2/2
Let g(k) be the second derivative of -k**5/35 + 20*k**4/21 + 2*k**3/21 - 40*k**2/7 - 2*k - 61. Factor g(n).
-4*(n - 20)*(n - 1)*(n + 1)/7
Suppose -8 = -2*h + 10. Suppose -2*l + h = 3. Factor -62*a**5 - 30*a**2 - 63*a + 13*a**4 - 4*a**4 + 18*a**l - 27 + 59*a**5.
-3*(a - 3)**2*(a + 1)**3
Let o be 7/(7/2) + -3. Let z(p) = p**2 + p. Let x be z(o). Factor x*g**3 + 2*g + 4 + 2*g**3 - 4*g**2 - 4.
2*g*(g - 1)**2
Suppose 2*a + 43 - 43 = 0. Let t(r) be the second derivative of -8*r**2 + a + 10*r + 0*r**3 + 1/3*r**4. Factor t(y).
4*(y - 2)*(y + 2)
Let y(j) = j**2 + 2. Let x(u) = 136*u + 800. Let f(t) = -t - 1. Let m(z) = 24*f(z) + x(z). Let s(n) = -m(n) - 4*y(n). Solve s(d) = 0.
-14
Let n(l) be the third derivative of l**7/15120 + l**6/4320 + 3*l**4/8 - 10*l**2. Let b(x) be the second derivative of n(x). Factor b(c).
c*(c + 1)/6
Let f(d) = -5*d**3 + 37*d**2 - 55*d + 27. Let n(q) be the first derivative of -5*q