)*(q + 1)**2*(q + 4)
Let g(n) = 945*n**2 + 941*n + 44. Let q(y) = -316*y**2 - 313*y - 15. Let m(x) = -3*g(x) - 8*q(x). Factor m(z).
-(z + 1)*(307*z + 12)
Let x(d) = -d**4 - d**3 + 3*d**2 + d - 1. Let q(n) = 20*n**4 - 1136*n**3 - 1224*n**2 + 5776*n - 3452. Let y(s) = q(s) + 16*x(s). Factor y(t).
4*(t - 289)*(t - 1)**2*(t + 3)
Let o(a) be the third derivative of -a**6/24 + 31*a**5/12 + 355*a**4/8 + 555*a**3/2 - 2693*a**2. Solve o(w) = 0 for w.
-3, 37
Let h(f) be the third derivative of -f**5/12 - 205*f**4/12 - 1480*f**3/3 + 2566*f**2. Let h(c) = 0. Calculate c.
-74, -8
Let m be 2/(-25)*(-29750)/4760. Factor m*u + 0 + 1/2*u**2.
u*(u + 1)/2
Let j be (-1)/3*(-10 - 20). Let y be (-15)/j*-2 + 2 + -5. Factor -2/13*p**4 + 0*p + y - 4/13*p**3 - 2/13*p**2.
-2*p**2*(p + 1)**2/13
Determine v, given that 0*v + 16/9*v**2 - 350/9*v**4 + 0 + 172/9*v**3 = 0.
-2/25, 0, 4/7
Let m(g) = 2*g**2 + 42*g - 32. Let l be m(-22). Let k be ((-3)/l)/((-159)/7844). Factor 4/3 + 4/3*w**5 - 9*w + 53/3*w**2 + w**4 - k*w**3.
(w - 1)**3*(w + 4)*(4*w - 1)/3
Let m be 9*(-2)/(-8)*(-32)/(-24). Let d(z) be the first derivative of -28/3*z**m - 16*z - 32*z**2 + 12. Factor d(y).
-4*(y + 2)*(7*y + 2)
Let y(a) = a**2 + a - 94. Let c be y(-10). Let j be (-7)/c - 12/(-12). Suppose 7/4*u**2 + j*u + 1/4*u**3 + 5/4 = 0. Calculate u.
-5, -1
Let j = -67 + 65. Let f be 76/19*(-1 - (j - 34)). Factor -n - 141*n**3 + 3*n**2 + f*n**3 - n**2.
-n*(n - 1)**2
Let y(u) be the first derivative of 3*u**4/16 - 6*u**3 - 3*u**2/2 + 72*u + 7708. Let y(g) = 0. What is g?
-2, 2, 24
Let f = 293/22 - -552/11. Let l = f + -629/10. Factor l*s**2 - 3/5 + 0*s.
3*(s - 1)*(s + 1)/5
Let y be (-289)/(-5) + 1/5. Let s = 115 - y. Determine p so that 16*p**2 + 9*p - s*p + 11*p**2 - 12 = 0.
-2/9, 2
Let a be 230/(-30) + 19 + (-3 - 6). Factor 5/3*k - 2/3 + a*k**2.
(k + 1)*(7*k - 2)/3
Suppose -9*h = 37*h + 1840. Let q be h/340 - (-2)/17. Determine f so that -3/2*f**3 + 0*f + 0*f**2 + q = 0.
0
Let p(g) be the third derivative of 0 - 323*g**2 - 1/48*g**4 - 1/15*g**5 + 2/3*g**3 + 1/240*g**6 + 0*g. Suppose p(u) = 0. Calculate u.
-1, 1, 8
Let i(z) = -342*z - 3758. Let c be i(-11). Suppose -196/3*y**2 - 10/3*y**c - 48 + 106/3*y**3 - 152*y = 0. Calculate y.
-1, -2/5, 6
Let u(b) be the second derivative of 2*b**6/35 - 297*b**5/140 + 675*b**4/28 - 1325*b**3/14 - 1125*b**2/14 + 569*b. What is m in u(m) = 0?
-1/4, 5, 15
Find a, given that -43*a**2 + 9*a**3 + 336*a + 20*a**3 + 5*a**3 + 2880 - 33*a**3 = 0.
-5, 24
Find k such that 146/13*k**3 + 80000/13 + 10328/13*k**2 + 2/13*k**5 - 76/13*k**4 + 53600/13*k = 0.
-4, 25
Let f(x) be the first derivative of 9*x**4/7 - 46*x**3/7 - 12*x**2/7 + 629. Suppose f(p) = 0. Calculate p.
-1/6, 0, 4
Solve 729147 - 1364*k + 3*k**2 + 2359*k + 1963*k = 0 for k.
-493
Factor 1/2*p**4 + 60 + 34*p - 9*p**2 - 9/2*p**3.
(p - 10)*(p - 3)*(p + 2)**2/2
Let o(d) be the second derivative of -13*d**5/4 - 595*d**4/12 - 305*d**3/3 - 40*d**2 + 952*d. Factor o(j).
-5*(j + 1)*(j + 8)*(13*j + 2)
Let a(v) = -v**2 - 2. Let y(s) = -29*s + 2872 + s**2 - 128*s - 83*s. Let o(p) = -4*a(p) + y(p). Factor o(t).
5*(t - 24)**2
Let f(g) be the first derivative of 3/16*g**4 - 7*g**3 + 0*g + 81/8*g**2 + 33. Determine o, given that f(o) = 0.
0, 1, 27
Let d be -2 + (19 - (-4 + 2)) + (-31)/(-31). Let j(v) be the first derivative of 4*v**4 + v**2 - d + 32/5*v**5 - 14/3*v**3 + 0*v. Determine o so that j(o) = 0.
-1, 0, 1/4
Let s(j) be the first derivative of -j**6/90 + 19*j**5/30 - 3*j**4 + 4*j**3/3 + 3*j + 49. Let q(v) be the third derivative of s(v). Find u such that q(u) = 0.
1, 18
Solve 10*o + 8*o**5 + 29*o**4 + 42*o**4 + 55*o**2 + 74*o**3 - 7*o**2 - 29*o**4 - 2*o = 0 for o.
-2, -1, -1/4, 0
Let c be (5 + (-7 - -1))/((-4)/2322). Let w = c + -578. Suppose 5*d**2 - w*d**3 + 0 - 5/2*d = 0. Calculate d.
0, 1
Let p(h) be the second derivative of -14*h**6/75 + h**5 - h**4/3 - 10*h**3/3 + 24*h**2/5 + 295*h. Suppose p(r) = 0. What is r?
-1, 4/7, 1, 3
Suppose 0*u + 69/8*u**2 + 3/8*u**5 + 141/8*u**3 + 0 + 75/8*u**4 = 0. Calculate u.
-23, -1, 0
Let z(j) = -5*j**2 - 65*j - 552. Let v(f) = 41*f**2 + 519*f + 4418. Let m(d) = 6*v(d) + 50*z(d). Suppose m(r) = 0. Calculate r.
-21, -13
Let l(j) = 30*j + 38 + 9 + 28 + 55. Let t be l(-4). Let 8*u**2 + 0 - 8/5*u - t*u**3 = 0. What is u?
0, 2/5
Suppose 888*n + 217 = 895*n. Factor -n*m + 14*m**2 - 5*m**2 - 80 - 19*m - 14*m**2.
-5*(m + 2)*(m + 8)
Let p(f) = 19*f**3 - f**2 + 8*f - 8. Let k be p(1). Let v be 2/(12/k)*2/12. Find y such that v*y**2 + 1 - 3/2*y = 0.
1, 2
Let h(s) = 97*s**2 - 31*s - 3. Let u be h(5). Factor -u + 2267 - 16*x - x**2.
-x*(x + 16)
Factor 69*o**3 - o**5 + 39*o**4 + 2397757*o**2 + 4*o**5 - 2397724*o**2.
3*o**2*(o + 1)**2*(o + 11)
Solve 140*n**4 - 7815 + 8135 + 560*n - 484*n**2 - 7*n**3 - 33*n**3 - 156*n**2 - 25*n**5 = 0.
-2, -2/5, 2, 4
Determine k, given that 0 - 9/8*k**5 + 9/2*k**2 - 3*k**4 + 21/8*k**3 + 0*k = 0.
-3, -1, 0, 4/3
Let h(c) = -10*c - 7. Let k = 1792 + -1793. Let j be h(k). Solve 2/11*z**2 + 0 + 0*z**j - 2/11*z**4 + 0*z = 0.
-1, 0, 1
Let i(u) be the second derivative of -u**7/1260 + 7*u**6/360 + 2*u**5/15 + 14*u**4 - 17*u. Let j(c) be the third derivative of i(c). Factor j(w).
-2*(w - 8)*(w + 1)
Let l(n) be the third derivative of -n**6/24 + 3*n**5/2 - 20*n**4 + 320*n**3/3 + 127*n**2 - 2*n - 2. Suppose l(b) = 0. Calculate b.
2, 8
Solve 445*f - 40 + 387*f + 1 - f**3 - 743*f - 43*f**2 - 6 = 0.
-45, 1
Let b = 4027803/2 - 2013901. Find p, given that -34 - 16*p + b*p**2 = 0.
-2, 34
Let c(q) = -5*q**2 + q - 4. Let p be c(4). Let l be (64/p)/(2/(-15)). Let -5*r**2 + 2*r**2 + r**2 + l + 4*r = 0. Calculate r.
-1, 3
Factor -29/2 - 16/3*q - 1/6*q**2.
-(q + 3)*(q + 29)/6
Suppose -59*b**2 + 55/3*b**4 + 38/3*b**3 - 112/3 - 278/3*b + 2*b**5 = 0. Calculate b.
-8, -7/6, -1, 2
Let g(w) be the second derivative of w**4/3 + 256*w**3/3 + 8192*w**2 - 40*w + 13. Let g(t) = 0. What is t?
-64
Let j(r) be the first derivative of r**3/7 - 8361*r**2/14 - 8364*r/7 - 7107. Determine m, given that j(m) = 0.
-1, 2788
Let u(l) be the third derivative of -l**9/161280 + l**7/13440 - 29*l**5/30 + l**3/2 - 89*l**2. Let t(s) be the third derivative of u(s). Factor t(h).
-3*h*(h - 1)*(h + 1)/8
Let o be 0/((-2)/3*45/(-30)). Suppose -4*v = -5*l + 29, o = -2*l + 4*v + v + 15. Suppose 52*t**3 + 3*t - 3*t + t**4 - 53*t**3 - l*t**2 - 3*t = 0. Calculate t.
-1, 0, 3
Let z(b) = -b**3 + 69*b**2 - 52*b + 8543. Let u be z(70). Factor -1/4*r**u + 17/4*r**2 + 10 + 29/2*r.
-(r - 20)*(r + 1)*(r + 2)/4
Let g be (4/5)/((-4)/30). Let j(d) = -8*d**3 - d**2 - 4*d + 7. Let y(q) = -4*q**3 + 775*q - 3*q**3 - 779*q + 6. Let c(o) = g*y(o) + 5*j(o). Solve c(r) = 0.
1/2, 1
Let n(s) be the second derivative of 1/56*s**7 + 1/4*s**4 + 7/2*s**3 - 1 - 1/20*s**6 + 6*s**2 - 33/80*s**5 + 43*s. Solve n(l) = 0.
-2, -1, 2, 4
Let t = 244474/9 + -28216. Let o = t + 10646/9. Factor -2/3*f**2 - o + 56/3*f.
-2*(f - 14)**2/3
Let z be 2/(-3) + ((-39)/221 - (-57990)/10710). Solve -2/7*h**3 + 24/7 - z*h + 2*h**2 = 0 for h.
2, 3
Let u(m) be the third derivative of -m**6/300 - m**5/15 + 21*m**4/20 + 216*m**3/5 - 1264*m**2. Factor u(d).
-2*(d - 8)*(d + 9)**2/5
Let x(q) = q**3 - 21*q + 12*q**2 + 10*q**2 - 28*q**2 - 49 + 11*q**2. Let c be x(-7). Solve 220/7*b**4 - 16/7*b**2 + c + 16*b**5 + 0*b - 16/7*b**3 = 0 for b.
-2, -1/4, 0, 2/7
Suppose -288*m = -290*m - 12, -2*m + 18 = 5*u. Let t(k) be the first derivative of 1/30*k**u + 0*k - 1/10*k**4 + 1/10*k**2 + 0*k**5 + 28 + 0*k**3. Factor t(o).
o*(o - 1)**2*(o + 1)**2/5
Determine d so that 2/13*d**2 - 444/13*d + 24642/13 = 0.
111
Let x(p) be the second derivative of p**5/20 + p**4/8 - p**3 + 5*p**2 + p - 1. Let l(i) be the first derivative of x(i). Determine o, given that l(o) = 0.
-2, 1
Let i be 1*(-7 - -4)*-1. Suppose -24 = -i*u - 21. Factor -1/8*d**3 + 1/4*d**2 - u + 1/2*d.
-(d - 2)**2*(d + 2)/8
Suppose -12*f + 24*f - 84 = 0. Suppose b = -5*c + f, 3*b = 106*c - 109*c + 81. Factor -44/3*m**3 - 80/3*m + 16/3 + 7/3*m**4 + b*m**2.
(m - 2)**3*(7*m - 2)/3
Let w(m) be the first derivative of -m**6/2 - 54*m**5/5 - 213*m**4/4 - 78*m**3 + 4409. Find r such that w(r) = 0.
-13, -3, -2, 0
Let x = 633 + -641. Let i be ((-5)/x)/(4/144). Solve 5/2*b**4 - 5*b**2 + i + 10*b**3 - 30*b = 0 for b.
-3, 1
Suppose 126 = 5*t + 37*t. Let c(k) be the