255 - k**5/17 + 31*k**4/102 - 10*k**3/17 + 311*k. Factor s(f).
2*f*(f - 5)*(f - 3)*(f - 2)/17
Let c(f) = -f**2 - 2*f + 2. Let t be c(-2). Suppose -2*r - r + t*a = 8, 2*r - 12 = -3*a. Determine w, given that r - 3/7*w**2 + 0*w + 1/7*w**3 = 0.
0, 3
Let a(p) = p**5 - p**4 + p**2 - 2*p. Let y(x) = -9*x**5 - 42*x**4 - 234*x**3 - 342*x**2 - 135*x. Let t(l) = -6*a(l) - y(l). Factor t(q).
3*q*(q + 1)**2*(q + 7)**2
Let h(a) be the first derivative of 0*a**2 + 0*a**5 + 2/15*a**6 + 5 - 1/4*a**4 + 1/6*a**3 + 5*a. Let j(g) be the first derivative of h(g). Factor j(r).
r*(r + 1)*(2*r - 1)**2
Let w = 34 - 32. Factor -m**w + 2 - 7*m**2 - 14 + 5*m**2 - 12*m.
-3*(m + 2)**2
Suppose -2*w + 0*w + 4 = -4*m, 0 = -w + 3*m + 1. Suppose -2*g = -2 - w. Factor -5*r + 5*r - 3*r**g + 12*r**4.
3*r**3*(4*r - 1)
Let b(y) be the first derivative of -y**3/6 - 26*y**2 + 105*y/2 - 54. Determine w so that b(w) = 0.
-105, 1
Let x(q) be the third derivative of q**8/30240 - q**6/3240 + q**4/4 + 15*q**2. Let t(r) be the second derivative of x(r). Factor t(u).
2*u*(u - 1)*(u + 1)/9
Let j(d) = d**3 - 8*d**2 + 10*d - 17. Let k be j(7). Let z(m) = -9*m**2 - 34*m - 25. Let w(b) = -26*b**2 - 101*b - 75. Let l(a) = k*w(a) - 11*z(a). Factor l(t).
-5*(t + 1)*(t + 5)
Let d(a) = 8*a**2 - 5*a + 3. Let p(o) = -65*o**2 + 40*o - 25. Let c(s) = -6*s + 41. Let z be c(11). Let q(f) = z*d(f) - 3*p(f). Suppose q(v) = 0. Calculate v.
0, 1
Factor 64 - 12*p - 24*p**3 - 40*p - 12*p + 34*p**3 + 2*p**4 - 12*p**2.
2*(p - 2)*(p - 1)*(p + 4)**2
Let o(y) be the second derivative of -23*y + 0 + 0*y**2 + 1/70*y**5 + 1/21*y**4 + 0*y**3. Solve o(w) = 0.
-2, 0
Let i(p) be the second derivative of -p**5/120 + p**4/4 - 3*p**3 - 7*p**2 - 3*p. Let u(m) be the first derivative of i(m). Factor u(t).
-(t - 6)**2/2
Let v(t) be the first derivative of -t**5 - 15*t**4/2 + 40*t**3/3 + 15*t**2 - 35*t - 412. Find s such that v(s) = 0.
-7, -1, 1
Let v(l) be the third derivative of 25*l**2 + 0*l**3 + 0 - 11/360*l**5 - 1/24*l**4 + 0*l. Find m such that v(m) = 0.
-6/11, 0
Let v(t) be the third derivative of -t**5/15 - 13*t**4/6 - 44*t**3/3 - 224*t**2. Factor v(q).
-4*(q + 2)*(q + 11)
Let j(u) = -40*u**5 - 4*u**4 - 8*u**3 + 7*u**2 - 2*u**4 - u**3 - 3 + 44*u**5. Let c(a) = a**3 - a**2 + 1. Let z(x) = 3*c(x) + j(x). Let z(t) = 0. What is t?
-1, 0, 1/2, 2
Let o(l) be the third derivative of l**5/48 - 35*l**4/24 + 45*l**3/8 + 55*l**2. Factor o(v).
5*(v - 27)*(v - 1)/4
Let s(d) be the second derivative of d**5/40 + 3*d**4/16 - d**3 + 12*d**2 + 19*d. Let l(u) be the first derivative of s(u). Factor l(p).
3*(p - 1)*(p + 4)/2
Let a = -12265 - -12265. Factor -2*j**2 + 8/5*j**3 + a + 2/5*j.
2*j*(j - 1)*(4*j - 1)/5
Suppose -6*o + 4*o = 4*s - 8, 0 = o + 3*s - 5. Find x, given that -2*x**2 + 95*x - 37*x**o + 30 + 4*x**2 = 0.
-2/7, 3
Let j = 600 + -91801/153. Let q = j + 311/765. Suppose -q*u**2 + 0*u + 2/5 = 0. What is u?
-1, 1
Suppose 5*b - 13 = f, -b + 2 = f - 3. Let h be f/8 - 71/(-4). Factor 12*i + 8*i**3 - 5 + 0 - h*i**2 + 3.
2*(i - 1)**2*(4*i - 1)
Let t(m) be the second derivative of -2*m**7/147 + 8*m**6/105 - m**5/35 - 10*m**4/21 + 8*m**3/21 + 16*m**2/7 - 121*m. Factor t(x).
-4*(x - 2)**3*(x + 1)**2/7
Let y(k) be the first derivative of 10*k**3 - 13*k**2 - 4*k + 13. Solve y(n) = 0 for n.
-2/15, 1
Suppose 2/5*h**2 + 0 - 144/5*h = 0. Calculate h.
0, 72
Let k be (-56)/(-84) + 26*(-4)/(-24). Factor 1/4*l - 1/6*l**2 - 1/6*l**3 - 1/12 + 1/4*l**4 - 1/12*l**k.
-(l - 1)**4*(l + 1)/12
Let b(x) = -x**3 + 19*x**2 + x - 16. Let m be b(19). Factor 3/7*w**m + 3/7*w**2 + 1/7*w + 1/7*w**4 + 0.
w*(w + 1)**3/7
Suppose 3/4*s**3 - 15/4*s**2 + 15/4 - 3/4*s = 0. Calculate s.
-1, 1, 5
Let j(v) = v**3 + 3*v**2 + v + 2. Let n be j(-3). Let i be 3 - (1 - 2)*n. Determine k so that -5*k**2 + 15*k + 5*k**2 + 3*k**i + 12 - 3*k = 0.
-2
Let j(l) be the third derivative of 19*l**7/840 + 69*l**6/160 + 217*l**5/120 - 61*l**4/8 + 3*l**3 - 96*l**2. Suppose j(x) = 0. What is x?
-6, 2/19, 1
Let b(i) be the second derivative of -i**6/3960 + i**5/220 + 2*i**3 - 18*i. Let p(q) be the second derivative of b(q). Factor p(o).
-o*(o - 6)/11
Let d = -304 + 306. Let q(g) be the first derivative of 1/2*g**d + 6 - 1/9*g**3 + 4/3*g. Let q(z) = 0. Calculate z.
-1, 4
Let b(q) be the third derivative of 4/75*q**5 + 4/15*q**3 - 1/150*q**6 + 0*q - q**2 + 0 - 1/6*q**4. Factor b(d).
-4*(d - 2)*(d - 1)**2/5
Suppose -4*t = 76 + 32. Let l be (3/t)/(18/(-216)). Solve 4/3*v**3 - l*v - 1/3 + 1/3*v**2 = 0.
-1, -1/4, 1
Let h(b) be the second derivative of -1/9*b**3 - 1/30*b**5 - 1/9*b**4 + 0 + 0*b**2 + 11*b. Find r, given that h(r) = 0.
-1, 0
Let o(a) be the third derivative of -a**8/336 + a**7/56 - a**6/36 + 3*a**3 - 17*a**2. Let p(g) be the first derivative of o(g). Factor p(k).
-5*k**2*(k - 2)*(k - 1)
Let v(u) be the second derivative of u**6/30 + u**5/10 + u**4/12 + 19*u - 1. Suppose v(c) = 0. Calculate c.
-1, 0
Determine j, given that 13*j**2 - 36*j - 27*j**2 - 56 + 10*j**2 = 0.
-7, -2
Let a(l) be the first derivative of 3*l**6/40 - l**5/8 - l**4/2 - 23*l**3/3 + 9. Let s(o) be the third derivative of a(o). Factor s(m).
3*(m - 1)*(9*m + 4)
Let y(a) = a**2 + 2*a - 3. Suppose 5*b = -2*c - 0*c - 26, 2*b + 11 = -c. Let i be y(b). Let 4*j**i - 4*j**3 - 2*j**4 + 14*j**4 - 12*j**5 = 0. Calculate j.
0, 1/2, 1
Suppose 0 = 7*c - 12*c + 10. Determine y, given that -4*y - 5*y**c - 3*y + 22*y - 5*y = 0.
0, 2
Suppose 0 = 2*g - 2 - 2. Determine j, given that g*j**2 + 0*j + j**2 - j + 0*j = 0.
0, 1/3
Suppose 180*y = 178*y + 10. Let w(s) be the first derivative of 1/2*s**4 - 3*s**2 + 0*s**3 - y - 4*s. Factor w(u).
2*(u - 2)*(u + 1)**2
Let z(n) be the first derivative of -n**4/4 - 20*n**3/3 + 4*n + 7. Let j be z(-20). Determine p so that 4/3*p**2 + 8/3 - j*p = 0.
1, 2
Let 0*r**2 + 0 + 0*r + 6/11*r**3 - 6/11*r**4 = 0. Calculate r.
0, 1
Suppose 19 = 2*k + 5*j, -4*k + 12 = 3*j - 5. Solve -15*o**2 + 19*o**k - 7*o**2 + 12 = 0 for o.
-2, 2
Let d(o) be the second derivative of o**4/6 - 11*o**3 + 62*o**2 - 10*o. Let d(j) = 0. What is j?
2, 31
Let y = 14 - 4. Suppose -4*l - y + 18 = 0. Determine m, given that -3/2*m + 3/4*m**4 + 0*m**l + 3/2*m**3 - 3/4 = 0.
-1, 1
Find r, given that -59402*r - 4*r**3 - 1308*r**2 + 136141 - 33417*r - 2148022 - 3168235 - 49753*r = 0.
-109
Let t(c) be the third derivative of 35*c**6/24 + 13*c**5/3 + 5*c**4/2 - 9*c**2. Suppose t(n) = 0. What is n?
-6/5, -2/7, 0
Solve 0*c**4 + 3/4*c**5 + 9*c + 0 - 27/4*c**3 + 3*c**2 = 0 for c.
-3, -1, 0, 2
Let d(j) = 3*j - 13. Let c be d(5). Factor 7*r**4 + 5*r - 3*r**4 + 4 - 5*r - 8*r**c.
4*(r - 1)**2*(r + 1)**2
Let l(d) be the first derivative of -5*d**3/3 - 310*d**2 - 19220*d + 441. Factor l(x).
-5*(x + 62)**2
Factor -7*f**3 - 48*f - 2*f**2 - 34*f**2 + 210*f + 3*f**3 - 216 + 6*f**3.
2*(f - 12)*(f - 3)**2
Let z(m) be the second derivative of m**5/25 - 6*m**4/5 + 64*m**3/15 - 4*m + 2. Find w such that z(w) = 0.
0, 2, 16
Solve -2/11*k**2 - 88 + 8*k = 0.
22
Let v = 23001 + -22999. Factor -2/9*i**v + 0 + 0*i - 8/9*i**3.
-2*i**2*(4*i + 1)/9
Let f(z) be the first derivative of 0*z - 1 + 1/2*z**3 + 3/2*z**2. Solve f(g) = 0.
-2, 0
Factor 4*c**3 + 207 - 85 - 52*c**2 - 132*c + 58.
4*(c - 15)*(c - 1)*(c + 3)
Suppose 3*a - 21 = 3*d, 0*d - 2*d = -3*a + 18. Let h be 15/10 + 2/a. Suppose s**3 - s + 7/2*s**h - 7/2*s**4 + 0 = 0. Calculate s.
-1, 0, 2/7, 1
Let s(d) be the first derivative of d**3/3 + 15*d**2/2 + 26*d + 94. Let y be s(-13). Factor -1/2*h**2 + y*h + 0 - 11/4*h**3.
-h**2*(11*h + 2)/4
Let u(p) be the first derivative of 231852*p**3 - 3336*p**2 + 16*p + 392. Solve u(b) = 0 for b.
2/417
Let r(k) = 0*k + 0*k - 2*k + k**4 + k**5 + k**2 + 0*k + 4 + k**3. Let n(m) = m**5 + 2*m**4 + m**2 - m + 4. Let d(c) = 6*n(c) - 7*r(c). Factor d(f).
-(f - 2)**2*(f - 1)**2*(f + 1)
Let h(g) be the first derivative of 3/2*g**4 - 21/16*g**2 + 3 + g**3 + 3/8*g. Factor h(r).
3*(r + 1)*(4*r - 1)**2/8
Let g(v) be the second derivative of v**6/40 - v**5/10 + v**4/8 + 5*v**2 + 9*v. Let u(t) be the first derivative of g(t). Factor u(f).
3*f*(f - 1)**2
Let u(x) = -x - 5. Let n be u(-8). Let t(r) = 12*r - 20. Let v be t(2). Find i, given that -i**3 + i**v + 0*i**2 + 3*i - 6*i**2 + 2*i - 2 + n*i**2 = 0.
-2, 1
Suppose -205*h = -204*h - 126. Let m be (-10)/(-3)*(-27)/h*-7. Factor 4/9*k**4 + 2/9*k**m - 4