3 - 8*h**2 - 72*h + 184. Let g(y) = y**3 - 11*y**2 - 70*y + 182. Let r(b) = 5*a(b) - 4*g(b). Factor r(l).
(l - 4)**2*(l + 12)
Let a(q) be the third derivative of -q**6/60 - 5*q**5/3 - 143*q**4/3 + 1352*q**3/3 - 414*q**2. Let a(b) = 0. What is b?
-26, 2
Let g(l) be the third derivative of l**11/1164240 - l**9/70560 - l**8/35280 + 2*l**5/15 + 11*l**2. Let k(z) be the third derivative of g(z). Factor k(r).
2*r**2*(r - 2)*(r + 1)**2/7
Let g(k) = -5*k**3 - 6*k**2 - 2*k. Let c(n) = n**3 + n**2 + n + 1. Let f(u) = -4*c(u) - g(u). Let p be f(-2). Let p + 0*j - 2/11*j**2 = 0. Calculate j.
0
Let p(h) be the third derivative of -h**5/3 + 85*h**4/24 + 35*h**3/2 + 23*h**2 - 5. Solve p(a) = 0 for a.
-1, 21/4
Let d(g) = -g**2 - g - 1. Suppose 6 = o + 4*y - 4, y = 4*o - 6. Let u(l) = -8*l**2 - 12*l - 7. Let n(t) = o*u(t) - 18*d(t). Determine q so that n(q) = 0.
1, 2
Let y be (-4*21/630)/(2/(-10)). Let -y*k + 0*k**2 + 2/3*k**3 + 0 = 0. What is k?
-1, 0, 1
Factor -1/8*g**4 + 0*g + 3/2*g**3 - 11/8*g**2 + 0.
-g**2*(g - 11)*(g - 1)/8
Let d**4 + 1139*d - 20*d**3 + 4*d**5 + 3*d**4 - 1123*d - 20*d**2 + 16 = 0. Calculate d.
-2, -1, 1, 2
Let l = 497/2358 - -3/262. Let c(i) be the first derivative of l*i**2 + 0*i + 2/27*i**3 + 1. Find p such that c(p) = 0.
-2, 0
Let v(y) = y**5 - 10*y**4 + 7*y**3 - 4*y**2 - 3*y - 1. Let t(c) = -c**5 + 9*c**4 - 7*c**3 + 3*c**2 + 4*c. Let s(f) = -5*t(f) - 4*v(f). Factor s(p).
(p - 2)**2*(p - 1)**2*(p + 1)
Solve 12*h + 9/4*h**2 + 16 = 0 for h.
-8/3
Let g(y) = 1203*y - 2404. Let v be g(2). Find j, given that -4*j - 14/3*j**4 - 58/3*j**v + 0 - 20*j**3 = 0.
-3, -1, -2/7, 0
Let y be 18/8 + -5 + (-95)/(-20). Find x, given that 0*x**y - 9 + 3*x**3 - 3*x - 11*x**3 + 5*x**2 + 7*x**3 = 0.
-1, 3
Let v be (-15)/30*(3 - 11). Factor 125/2*c**4 - 25/2*c**3 + 26*c - 45*c**2 - v.
(c + 1)*(5*c - 2)**3/2
Factor 32*o**3 - 2*o**4 - 2*o - 14*o**2 - 16*o**3 - 4*o + 6*o.
-2*o**2*(o - 7)*(o - 1)
Let d = -1/992 + 1991/6944. Suppose 0 + 2/7*b - 4/7*b**4 + 4/7*b**2 - d*b**5 + 0*b**3 = 0. Calculate b.
-1, 0, 1
Suppose -130*g - 33*g**2 - 22*g**2 - 4198*g**4 + 4193*g**4 + 70*g**3 = 0. What is g?
-1, 0, 2, 13
Let s be (-1)/4 - (-165)/20. Let g = s - 5. Solve -9*f - 12 - 3*f**2 - g*f + 0*f = 0 for f.
-2
Let m(z) = 953*z - 4761. Let t be m(5). Factor 0*q + 0 - 1/2*q**t + 3/2*q**2 - q**3.
-q**2*(q - 1)*(q + 3)/2
Let j(m) be the first derivative of -1/3*m**3 + 9*m - 1/3*m**4 + 1/10*m**5 + 2*m**2 + 11. Let p(t) be the first derivative of j(t). Factor p(v).
2*(v - 2)*(v - 1)*(v + 1)
Suppose 2*a - 22 = -4*i, -5*i = -3*a - 0*i + 22. Suppose -24 = -14*z + 4. Factor -24*k**3 + a*k**5 + 12*k**4 - k**2 + 17*k**z - 11*k**5.
-2*k**2*(k - 2)**3
Find m, given that 126 + 554/7*m**2 + 228*m - 152/7*m**3 + 8/7*m**4 = 0.
-1, 21/2
Let b(v) be the first derivative of -v**4 + 32*v**2 + 288. Factor b(o).
-4*o*(o - 4)*(o + 4)
Suppose -23*u = 35*u - 127 - 163. Suppose 0 + u*v**2 + 15/2*v**3 + 5/2*v**4 + 0*v = 0. Calculate v.
-2, -1, 0
Suppose 0 - 14 = -7*f. Factor -4*j**4 + 5*j**3 - f*j**2 + 4*j + 7*j**3 - 10*j**2.
-4*j*(j - 1)**3
Let h(g) = -2*g**3 - 152*g**2 - 150*g + 40. Let x be h(-75). Factor -x - 2/5*l**2 + 8*l.
-2*(l - 10)**2/5
Let i be 147/(-42) + (-8)/(-1). Factor -9/4*z**2 + i - 21/4*z.
-3*(z + 3)*(3*z - 2)/4
Let f be (-4847)/(-1572) + (-1)/12. Let s(x) be the first derivative of 7 + 0*x**f - x**4 + 0*x + 18/5*x**5 + 0*x**2. Factor s(u).
2*u**3*(9*u - 2)
Determine c, given that -52/3*c + 2/3*c**3 - 46/3*c**2 + 32 = 0.
-2, 1, 24
Determine b so that 93*b - 19*b**2 + 3*b**4 + 4*b**2 + 119*b + 6*b**3 - 230*b = 0.
-3, -1, 0, 2
Let d be (-54)/45*10/(-4). Suppose -c - 3*t - 2*t + d = 0, 5*c + 3*t - 15 = 0. Determine l so that -2/7*l**c + 0*l - 4/7*l**2 + 0 = 0.
-2, 0
Let g(k) be the third derivative of k**7/105 - k**6/6 + 4*k**5/5 + 5*k**4/6 - 25*k**3/3 - 296*k**2. Solve g(f) = 0 for f.
-1, 1, 5
Suppose 0 = 2*x - 4*s - 20, 40 = x - 2*s + 6*s. Solve 20*g**2 - 5*g**3 - 3*g - 6*g - x*g**4 + 14*g = 0 for g.
-1, -1/4, 0, 1
Let g(c) be the first derivative of 14*c**3/3 - 47*c**2 - 28*c + 74. Solve g(p) = 0.
-2/7, 7
Let w = -163 - -3261/20. Let d(k) be the first derivative of 0*k**2 + w*k**5 - 1/16*k**4 - 1/12*k**3 + 4 + 1/24*k**6 + 0*k. Solve d(h) = 0 for h.
-1, 0, 1
Let q be (-65)/9 + (-10)/(-45). Let g = q + 10. Factor -g*z**2 + 10*z + 7*z**2 - 2*z**3 - 4 - 8*z.
-2*(z - 2)*(z - 1)*(z + 1)
Let x(w) be the third derivative of 0 + 1/30*w**4 + 0*w**3 + 0*w + 1/100*w**6 - 1/30*w**5 + 2*w**2. Determine r, given that x(r) = 0.
0, 2/3, 1
Let o(r) be the second derivative of -r**6/150 - 17*r**5/50 + r**4/20 + 52*r**3/15 + 34*r**2/5 - 353*r. What is z in o(z) = 0?
-34, -1, 2
Let k(d) = -d**2 + 1. Let j(i) = -i**2 - 27 - 3 + 36*i**2 + 43*i - 3*i. Let q(l) = -j(l) - 30*k(l). Suppose q(b) = 0. What is b?
-8, 0
Let o(r) be the third derivative of 0 + 2/15*r**6 + 1/2*r**4 + 0*r - 7/15*r**5 + 0*r**3 + 8*r**2. Factor o(l).
4*l*(l - 1)*(4*l - 3)
Let s(o) = -3*o**3 + 536*o**2 - 353*o - 534. Let n be s(178). Suppose -1/2*c**2 - 1/2*c**3 + 3/8*c**5 + 5/8*c**4 + n*c + 0 = 0. Calculate c.
-2, -2/3, 0, 1
Suppose 10*v - 62 = -32. Let b(c) be the second derivative of 1/28*c**4 + c + 0*c**2 + 2/7*c**v + 0. Let b(p) = 0. Calculate p.
-4, 0
Suppose 15 = 3*v, -2*h + 4*v = 3*h - 130. Let d be 24/(-45)*h/(-40). Find s such that -1/5*s + 3/5*s**3 + d*s**2 + 0 = 0.
-1, 0, 1/3
Let q(i) be the third derivative of i**9/20160 + i**8/2240 + i**7/840 - i**5/6 + 8*i**2. Let a(j) be the third derivative of q(j). Find w such that a(w) = 0.
-2, -1, 0
Let n(v) = 30*v**2 - 2225*v + 2125. Let u(a) = 5*a**2 - 371*a + 354. Let y(b) = 6*n(b) - 35*u(b). Let y(h) = 0. Calculate h.
1, 72
Let f(x) = 6*x**5 - 2*x**4 + x**3 + 2*x**2 + 15*x + 11. Let z(s) = 3*s**5 - s**4 + s**3 + s**2 + 8*s + 6. Let j(r) = -6*f(r) + 11*z(r). Solve j(k) = 0.
-1, -2/3, 0, 1
Solve -200 - 90*m - m**2 + 6*m**2 + 256*m - 76*m = 0.
-20, 2
Let n(x) = -4*x**3 + 18*x**2 - 30*x - 158. Let h(s) = 7*s**3 - 35*s**2 + 60*s + 323. Let z(d) = 6*h(d) + 11*n(d). Suppose z(l) = 0. What is l?
-5, 4
Let k(j) be the second derivative of 1/12*j**5 + 2/3*j**3 + 3/2*j**2 - 1/3*j**4 - 1/120*j**6 - 2*j + 0. Let s(h) be the first derivative of k(h). Factor s(p).
-(p - 2)**2*(p - 1)
Let -7/5*s**2 - 2/5 - 9/5*s = 0. What is s?
-1, -2/7
Let w(b) = -8*b - 30. Let d be w(-4). Factor 9*y**4 + 5*y**3 - 17*y**2 - 5*y + 5 + d*y**2 + y**4.
5*(y - 1)*(y + 1)**2*(2*y - 1)
Let x be 4/(-6) + (-68)/(-12). Let m be 4/((-12)/9) + 5. What is q in 7/4*q**m - q**x + 11/4*q**3 - 7/4*q - 1/2 - 5/4*q**4 = 0?
-2, -1, -1/4, 1
Let p(t) be the third derivative of -t**6/24 + t**5/12 + 5*t**4/6 - 10*t**3/3 - 2*t**2 - 13*t. Let p(b) = 0. Calculate b.
-2, 1, 2
Suppose 0 = -2*g + 3*c + 17, -14 = -5*g + 5*c + 26. Let -3*t**4 - 7*t - 2*t**3 + 2 + g*t**4 - 6*t**4 + 8*t**2 + t**5 = 0. What is t?
-2, 1
Let d(q) = q + 6. Let x be d(3). Solve 7*g**4 + 11*g**3 + 11*g**2 + x*g**2 + 9*g**3 - 2*g**4 = 0 for g.
-2, 0
Let c be (-6)/18 + (-436)/(-12). Factor -8*a - 8*a + 13*a**2 - a**5 - c*a**3 - 14*a**4 - 53*a**2 - a**5.
-2*a*(a + 1)*(a + 2)**3
Let q(a) = -a**3 - a**2 - 2. Let t be q(0). Let g be 1/(1/(-4)*t). Factor -4*r**3 - 6*r + 22*r**g - 41*r**3 + 2*r + 10*r**2 - 81*r**4.
-r*(r + 1)*(9*r - 2)**2
Let l(b) be the first derivative of 147*b**5/5 - 2772*b**4 - 2124*b**3 - 456*b**2 + 100. Solve l(s) = 0 for s.
-2/7, 0, 76
Let o(t) be the third derivative of t**9/10080 - t**8/4320 - t**7/3780 - 19*t**5/60 - 10*t**2. Let c(d) be the third derivative of o(d). Solve c(r) = 0 for r.
-2/9, 0, 1
Let y(m) be the second derivative of m**8/20160 + m**7/11340 - m**6/2160 - m**5/540 + 19*m**4/12 + 49*m. Let q(o) be the third derivative of y(o). Factor q(g).
(g - 1)*(g + 1)*(3*g + 2)/9
Suppose 0 = 3*o + 4*l + 2 + 17, 0 = -o - l - 4. What is g in -5*g**2 + 15/2*g**o + 0 - 5/2*g**4 + 0*g = 0?
0, 1, 2
Let y(d) = 2*d**4 - 3*d**3 + d**2. Let l(z) = 7*z**3 + 0*z**2 - z**2 - 3*z**4 - 3*z**3. Suppose 2 = -2*w + 10. Let s(o) = w*y(o) + 3*l(o). Factor s(v).
-v**2*(v - 1)*(v + 1)
Let n(h) be the second derivative of h**2 + 0*h**3 + 2*h + 0 - 1/210*h**5 - 1/420*h**6 + 1/42*h**4. Let a(f) be the first derivative of n(f). Factor a(v).
-2*v*(v - 1)*(v + 2)/7
Let t be (-3)/2*(1168/120 + -10). Let s(l) be the first derivative of 2/3*l**3 - t*l**5 + 0*l**4 + 0*l**2 - 