4/7*a**2 + 4/21*a**3 + 15 - 1/42*a**4. Let h(o) be the first derivative of m(o). Factor h(c).
-2*(c - 2)*(c + 1)*(c + 2)/7
Factor -68/13 + 2/13*u**2 + 30/13*u.
2*(u - 2)*(u + 17)/13
Let x be (-786)/2620*(75/27 + -5). Factor 20/3*l - x*l**2 + 22/3.
-2*(l - 11)*(l + 1)/3
Find r such that 2/5*r**2 - 888/5*r + 0 = 0.
0, 444
Let t(r) be the first derivative of -1/12*r**6 + 1/8*r**4 + 0*r + 0*r**5 + 0*r**2 + 0*r**3 - 24. Factor t(l).
-l**3*(l - 1)*(l + 1)/2
Suppose -57*w + 37*w + 25 = -15. Let h(g) be the first derivative of 0*g + 3/4*g**4 - 27 + 0*g**3 - 3/2*g**w. Factor h(n).
3*n*(n - 1)*(n + 1)
Suppose 5*i + 2*c - 10 = 0, -2*i - 18 = c - 21. Let h(f) be the first derivative of 3*f**2 + i*f + 2/3*f**3 + 5. What is g in h(g) = 0?
-2, -1
Let u(y) be the second derivative of -35152*y**2 - 13/2*y**4 - 676*y**3 - 3 + 6*y - 1/40*y**5. Factor u(l).
-(l + 52)**3/2
Let y be (-19 - (-1089)/57)*(-19)/(-1). Let b(r) be the second derivative of 23*r + 0 + 5*r**y + 1/50*r**5 + r**3 - 3/10*r**4. Solve b(m) = 0 for m.
-1, 5
Let p(d) be the third derivative of -13*d**7/126 - 275*d**6/72 + 595*d**5/36 + 4975*d**4/72 + 115*d**3/3 - 10576*d**2. Find c such that p(c) = 0.
-23, -1, -2/13, 3
Let i(q) = -q**2 - 21*q - 31. Let d be (-1)/(3 - (-20)/(-7)). Let g be i(d). Factor -140*f**2 + 20*f + g*f**2 + 69*f**2.
-4*f*(f - 5)
Let p = 180 - 167. Let s(d) = 2*d**2 - 32*d + 81. Let r be s(p). Factor 4/5*u**r + 8/5 + 4*u + 16/5*u**2.
4*(u + 1)**2*(u + 2)/5
Let s(k) = -k**3 - k**2 - 1. Let n be s(-2). Factor 1479*r**4 - 1499*r**4 - 28*r**2 - 36*r**n - 4*r**5 + 0*r**5 - 8*r.
-4*r*(r + 1)**3*(r + 2)
Suppose 21*f - 194 - 37 = 0. Factor -f*s - 2633*s**3 + 26*s + 2628*s**3 - 10*s**2.
-5*s*(s - 1)*(s + 3)
Let w be ((-92)/(-14))/((-8)/(-56)). Suppose y = d - 12, -5*d + w = y + y. What is m in 4*m**2 - 12*m**2 - d*m - 25 + 7*m**2 = 0?
-5
Determine g so that -2/13*g**5 - 1208/13*g**3 - 1670/13*g + 248/13*g**4 + 2156/13*g**2 + 476/13 = 0.
1, 2, 119
Suppose 251*m - 454 - 299 = 0. Let n(u) be the third derivative of -5/24*u**4 + 0*u - 1/42*u**7 + 1/24*u**6 + 0*u**m - 25*u**2 + 1/12*u**5 + 0. Factor n(z).
-5*z*(z - 1)**2*(z + 1)
Let b(z) = z**3 - 62*z**2 + 69*z. Let w(o) be the second derivative of 3*o**5/20 - 41*o**4/4 + 23*o**3 + o + 13. Let v(a) = 9*b(a) - 4*w(a). Factor v(c).
-3*c*(c - 1)*(c + 23)
Let o(x) be the second derivative of -x**7/560 + x**6/120 - x**5/80 + x**3/6 + 31*x**2 - 14*x + 2. Let u(p) be the second derivative of o(p). Solve u(w) = 0.
0, 1
Suppose 2/3*l**3 + 120 + 56/3*l**2 + 138*l = 0. What is l?
-15, -12, -1
Find s such that -3993 - 224*s + 1174 - s**2 - 9725 = 0.
-112
Let l = 2018475/11 - 183497. Determine z, given that l*z**2 + 2/11*z**5 - 8/11*z + 0 + 6/11*z**3 - 8/11*z**4 = 0.
-1, 0, 1, 2
Let g be ((-16)/(-90))/(4 + 72/(-20)). Let l(k) = -2*k**2 + 65*k + 35. Let s be l(33). Factor -g*c - 2/9*c**s + 0.
-2*c*(c + 2)/9
Let j be 1655 - 1709 - (-975)/18. Factor -5/6*b**2 - 2/3*b + 10/3 + j*b**3.
(b - 5)*(b - 2)*(b + 2)/6
Let s be 8/(-12)*-3*2. Suppose 2*z = -3*f + 12, -20*z = -16*z - 2*f - 8. Factor 8*a**3 + 3*a + 7*a**z - 11*a**2 + 26*a**2 + 5*a**s + 2*a.
5*a*(a + 1)**3
Let x be (-23)/5 - 16/((-480)/150). Determine p, given that 2/5*p**4 + 0 + x*p**2 - 4/5*p**5 + 12/5*p**3 - 4/5*p = 0.
-1, 0, 1/2, 2
Factor -5*u**3 - 134*u + 1199*u - 1210*u**2 + 2816*u**2 - 1266*u**2.
-5*u*(u - 71)*(u + 3)
Suppose 38988/5 + 2223*l + 3/5*l**3 + 354/5*l**2 = 0. What is l?
-57, -4
Let h = 1109/23 - 5269/115. Let 3/5*g**5 - 3/5*g**4 + h*g**2 - 18/5*g**3 + 0 + 24/5*g = 0. What is g?
-2, -1, 0, 2
Suppose -24*s + 39 = -11*s. Factor 6 + 6*p**s + 16 - 10 - 6*p**2 - 14*p + 2*p**4.
2*(p - 1)**2*(p + 2)*(p + 3)
Let i(l) be the first derivative of -10/3*l**3 + 1/2*l**5 + 5/4*l**4 - 10*l**2 - 1/6*l**6 + 13 + 37*l. Let x(w) be the first derivative of i(w). Factor x(z).
-5*(z - 2)**2*(z + 1)**2
Let a = -52 - -66. Suppose 8 = 2*f + 34*m - 35*m, 0 = -2*f + 4*m + a. Factor 6/13*p**2 - 6/13 - 2/13*p**f + 2/13*p.
-2*(p - 3)*(p - 1)*(p + 1)/13
Let n be (-708)/(-8)*8/9. Let d = n - 1640/21. Determine t, given that 2/7*t**5 + 4/7*t**2 + 0 - d*t**4 - 2/7*t + 0*t**3 = 0.
-1, 0, 1
Let g(m) be the third derivative of -m**5/480 - 59*m**4/192 + 1559*m**2. Factor g(s).
-s*(s + 59)/8
Let h(n) be the first derivative of n**5/150 - n**4/36 - 2*n**3/45 + n**2/2 + 17*n - 128. Let f(l) be the second derivative of h(l). Find b such that f(b) = 0.
-1/3, 2
Suppose -4*j = 5*o - 2769, o = -j + 6*o + 711. Let z be (1 + (-5)/2)*j/(-18). Factor -60*a**4 + z*a**4 + 3*a**2 - a**3 + 5*a**2 - 5*a**3.
-2*a**2*(a - 1)*(a + 4)
Let z = 34666 + -34662. Factor -2900/3*t**2 - 5000 - 11000/3*t - 1/6*t**5 - 120*t**3 - 43/6*t**z.
-(t + 3)*(t + 10)**4/6
Suppose 0 + 125/4*g**4 - 175*g - 5/4*g**5 - 435/4*g**3 - 1265/4*g**2 = 0. What is g?
-1, 0, 7, 20
Let a be (18 - 4768/336) + 8/(-7). Factor -3/2*x**4 - 5/6*x**2 + 0 + a*x**3 - 1/3*x.
-x*(x - 1)**2*(9*x + 2)/6
Let d(u) = -u**3 - 7*u**2. Let h be d(-7). Suppose -12*o + 19*o - 14 = h. Factor -4 - 1/4*g**2 - o*g.
-(g + 4)**2/4
Suppose 276*w - 274*w - 8 = 0. Let s(v) be the first derivative of 5/8*v**w + 1/2*v**3 + 2*v - 3*v**2 - 35. Factor s(o).
(o - 1)*(o + 2)*(5*o - 2)/2
Factor 2/3*a - 140/9 + 2/9*a**2.
2*(a - 7)*(a + 10)/9
Let z(s) be the first derivative of s**6/6 + 56*s**5/5 + 1048. Determine j, given that z(j) = 0.
-56, 0
Let l = -55 - -79. Suppose l + 16 = 10*i. Determine y, given that -2660*y**i + 2658*y**4 + 0*y**3 + 12*y**3 = 0.
0, 6
Let s(m) be the first derivative of 56 - 4/25*m**5 - 32/5*m**3 - 8/5*m**4 - 64/5*m**2 - 64/5*m. Find b, given that s(b) = 0.
-2
Let o = 840308 - 840306. Factor 1 - 1/3*g**o + 2/3*g.
-(g - 3)*(g + 1)/3
Let u = 2125/42 - -955/42. Determine g so that u*g**2 - 14/3*g**3 - 832/3*g - 256/3 = 0.
-2/7, 8
Let x be (-150)/(-19) + -8 - 87465/(-76). Let z = x - 1150. Factor -z*f**2 + 0*f + 3/4.
-3*(f - 1)*(f + 1)/4
Let j(d) = 3*d**2 - 3*d - 8*d**3 + 0 - 11*d**2 + 3. Let q(i) = i**3 + i**2 + i - 1. Let r(z) = j(z) + 3*q(z). Let r(s) = 0. What is s?
-1, 0
Let v(i) be the first derivative of -5*i**4/4 - 74*i**3/3 + 285*i**2/2 - 54*i + 6868. Factor v(w).
-(w - 3)*(w + 18)*(5*w - 1)
Let i(b) = -131*b**3 + 1185*b**2 + 82*b - 8. Let t(c) = -785*c**3 + 7105*c**2 + 490*c - 50. Let p(a) = -25*i(a) + 4*t(a). Factor p(l).
5*l*(l - 9)*(27*l + 2)
Factor -2/17*s**3 + 74/17*s**2 + 1440/17 + 688/17*s.
-2*(s - 45)*(s + 4)**2/17
Let i(s) be the second derivative of -1/90*s**6 + 4/9*s**3 + 1/6*s**4 + 0 + 0*s**5 - 5/2*s**2 + 17*s. Let g(n) be the first derivative of i(n). Solve g(k) = 0.
-1, 2
Let y(h) = -11*h**3 - 26*h**2 + 111*h - 192. Let o(c) = -31*c**3 - 77*c**2 + 334*c - 571. Let i(d) = -6*o(d) + 17*y(d). Suppose i(s) = 0. Calculate s.
2, 9
Let -310*b - 2/3*b**3 - 932/3*b**2 + 0 = 0. Calculate b.
-465, -1, 0
Let y = 181 + -190. Let o(j) = j**2 + 16*j + 63. Let g be o(y). Solve g + 8/9*c - 10/9*c**3 + 16/9*c**2 = 0 for c.
-2/5, 0, 2
Factor 0*s + 0 - 60*s**2 - 2/5*s**4 - 302/5*s**3.
-2*s**2*(s + 1)*(s + 150)/5
Let c(z) = 4*z**2 - 63*z + 47. Let o be c(15). Factor 23*f**o + 16*f + 29*f**2 - 16 + f - 53*f**2.
-(f - 16)*(f - 1)
Suppose 8 = -22*k + 26*k. Determine a, given that -27*a**2 + 12 - 1175*a**3 + 16*a**4 - 1178*a**3 - 21*a**k + 14*a + 2359*a**3 = 0.
-2, -3/8, 1
Let k = 3833 + -3833. Let i(f) be the first derivative of 0*f - 4/7*f**2 + 0*f**3 - 1/21*f**6 + 5/14*f**4 + 22 + k*f**5. Determine p so that i(p) = 0.
-2, -1, 0, 1, 2
Let x(d) be the second derivative of d**5/170 + 3*d**4/34 + 2*d**3/17 - 16*d**2/17 - 1256*d. Factor x(m).
2*(m - 1)*(m + 2)*(m + 8)/17
Let i(x) be the third derivative of x**6/24 + 15*x**5/2 - 635*x**4/8 - 1175*x**3/3 - 2707*x**2. What is c in i(c) = 0?
-94, -1, 5
Determine v, given that -291*v**3 + 294*v**3 - 105*v + 147*v**2 - 108*v + 108 - 45*v**2 = 0.
-36, 1
Let s(d) = -3*d**3 - 2 + 157*d - 324*d + 154*d - 6*d**2. Let n(o) = -4*o**3 - 6*o**2 - 14*o. Let b(r) = -2*n(r) + 3*s(r). Factor b(c).
-(c + 1)*(c + 2)*(c + 3)
Let y(n) be the first derivative of 2*n**5/5 - 55*n**4/2 + 726*n**3 - 9317*n**2 + 58564*n + 1572. What is s in y(s) = 0?
11, 22
Let z(w) be the second derivative of 11*w**6/10 + 49*w**5/2 + 275*w**4/4 + 70*w**3 + 26*w**2 - 18*w - 28. Solve z(p) = 0 for p.
-13, -1, -2/3, -2/11
Suppose -34*r**4 + 11*r**4 + 37*r**5 - 138*r - 191*r**2 + 8 + 101*r