*i**z - i**2. Let u(g) = g + 1. Let h(t) = 2*f(t) - 2*u(t). Factor h(o).
-2*o*(o - 1)*(o + 1)
Let j(r) be the first derivative of -5*r**4/12 - 35*r**3/3 - 100*r**2 - 500*r/3 + 161. Let j(s) = 0. Calculate s.
-10, -1
Let k(n) be the third derivative of 0*n + 1/90*n**5 - 1/9*n**4 - 5*n**2 + 0*n**3 + 0. Factor k(m).
2*m*(m - 4)/3
Let y be 4/(-8)*(-7 + 12/4). Let c(g) be the first derivative of 1/16*g**4 + 1/4*g + 3/8*g**y + 1/4*g**3 + 7. Factor c(k).
(k + 1)**3/4
Let g(a) be the third derivative of -a**5/180 + 25*a**4/72 - 11*a**3/3 - 610*a**2. Determine k, given that g(k) = 0.
3, 22
Let t be 6/30 - 38/(-10). Let y be -4 + 3 + (1 - (-4)/18). Determine r so that 0*r + 2/9*r**2 - y*r**t + 0*r**3 + 0 = 0.
-1, 0, 1
Let j(n) = -n**3 + 10*n**2 - 26*n + 7. Let v be j(5). What is l in 0 + 1/2*l + 1/2*l**4 - 1/2*l**v - 1/2*l**3 = 0?
-1, 0, 1
Let b(d) = -d**3 - 14*d**2 - 106*d - 216. Let y(l) = 3*l**3 + 40*l**2 + 317*l + 648. Let x(z) = 14*b(z) + 4*y(z). Suppose x(s) = 0. Calculate s.
-6
Suppose 12 = -16*t + 19*t. Let x(j) be the first derivative of 0*j + 6/25*j**5 + 3 + 0*j**2 + 1/2*j**t + 4/15*j**3. Suppose x(r) = 0. What is r?
-1, -2/3, 0
Let d(v) be the third derivative of 0 + 0*v**4 - 1/42*v**8 + 0*v**3 + 0*v - 1/30*v**5 - 3/35*v**7 - 1/10*v**6 - 3*v**2. Factor d(u).
-2*u**2*(u + 1)**2*(4*u + 1)
Let w be 32/(-18)*134/804*18/(-4). Find d, given that 2/3 - 2*d + 2/3*d**5 - 2*d**4 + 4/3*d**3 + w*d**2 = 0.
-1, 1
Let m(d) be the second derivative of -d**8/420 + d**7/210 + d**3/6 - 12*d. Let r(g) be the second derivative of m(g). Let r(u) = 0. Calculate u.
0, 1
Let v(j) = -56*j**4 - 280*j**3 - 332*j**2 + 174*j - 18. Let w(q) = q**4 - q. Let y(u) = -v(u) - 6*w(u). Factor y(a).
2*(a + 3)**2*(5*a - 1)**2
Let r(f) be the first derivative of f**6/20 + 5*f**5/16 + 17*f**4/24 + 17*f**3/24 + f**2/4 + 20*f - 3. Let s(u) be the first derivative of r(u). Factor s(a).
(a + 1)**2*(a + 2)*(6*a + 1)/4
Let r(f) = -10*f**4 + 1110*f**3 - 20160*f**2 - 6845*f - 5. Let c(b) = -11*b**4 + 1109*b**3 - 20161*b**2 - 6845*b - 4. Let v(g) = 5*c(g) - 4*r(g). Factor v(q).
-5*q*(q - 37)**2*(3*q + 1)
Let 10/21*m**2 + 16*m - 136/21 = 0. What is m?
-34, 2/5
Let s(m) be the third derivative of 0 + 0*m**5 + 1/784*m**8 + 0*m + 0*m**3 - 1/280*m**6 + 0*m**7 + 0*m**4 - 6*m**2. Factor s(j).
3*j**3*(j - 1)*(j + 1)/7
Let k = 1/1843 - -3675/20273. Find w such that 0*w - 8/11*w**3 - k*w**2 + 0 = 0.
-1/4, 0
Let r(l) = 4*l**2 - 5*l - 6. Let w(x) = -5*x**2 + 5*x + 7. Let a(p) = 4*r(p) + 3*w(p). Let c be a(6). Find m, given that 1/5 + 3/5*m + 3/5*m**2 + 1/5*m**c = 0.
-1
Let c(s) = 2*s**2 + 36*s + 160. Let m(r) = 4*r**2 + 72*r + 319. Suppose 14 = -14*f + 21*f. Let x(w) = f*m(w) - 5*c(w). Factor x(p).
-2*(p + 9)**2
Let g be ((-6)/5)/((-21)/(-140)). Let s be 8/(-5)*-2*(-1)/g. Solve 2/5 - 2/5*v**2 + s*v - 2/5*v**3 = 0 for v.
-1, 1
Factor 375/2*d - 3/4*d**4 + 0*d**3 + 0 + 225/4*d**2.
-3*d*(d - 10)*(d + 5)**2/4
Determine c, given that 15/2*c - 1/2*c**2 + 0 = 0.
0, 15
Suppose 4*r + c = 2*c + 10, -5*r + 18 = -4*c. Suppose r*i - 9 + 5 = 0. Factor -20/23*f + 2/23*f**i + 50/23.
2*(f - 5)**2/23
Let c be (-9)/(-6)*-1*-2. Let x(d) be the first derivative of -2 + 4*d + 2/3*d**c + 3*d**2. Suppose x(w) = 0. Calculate w.
-2, -1
Let c(q) = 0*q - q - 2 + 2*q. Let f be c(6). Factor 11*g**3 + 2*g**3 - 6*g**f - 12*g**2 + 2*g**3 + 0*g**3 + 3*g.
-3*g*(g - 1)**2*(2*g - 1)
Factor 23*n**3 + 142*n**2 + 19*n**3 - 35*n**2 - 2915*n + 16*n**3 - 59*n**3 + 2809.
-(n - 53)**2*(n - 1)
Let i(a) be the third derivative of 4*a**2 - 7/6*a**3 + 0*a - 1/8*a**4 - 1/120*a**6 + 1/20*a**5 + 0. Let b(t) be the first derivative of i(t). Factor b(f).
-3*(f - 1)**2
Let f(w) = 5*w**2 + 5*w + 6. Let t be f(-2). Suppose 7*z - t = -2. Factor -2/3*g**z - 1/3*g + 0.
-g*(2*g + 1)/3
Determine v, given that -6 - 4*v - 2/3*v**2 = 0.
-3
Suppose 28 = 14*g + 28. Factor 0*t**2 + g + 0*t + 2/9*t**3.
2*t**3/9
Let u(o) be the first derivative of -o**8/4200 + o**7/2100 + 4*o**3 + 5. Let n(r) be the third derivative of u(r). Determine i, given that n(i) = 0.
0, 1
Let y(f) = -3*f**2 + 368*f - 240. Let w be y(122). Solve 0*p**w + 3/8*p + p**2 + 3/4*p**3 + 0 - 1/8*p**5 = 0.
-1, 0, 3
Let u(d) be the first derivative of d**6/15 + 6*d**5/25 - 9*d**4/2 - 70*d**3/3 - 315. Suppose u(f) = 0. Calculate f.
-5, 0, 7
Solve 9/4 + 21/4*x + 3/4*x**3 + 15/4*x**2 = 0.
-3, -1
Factor 6*t**4 - 20*t**4 + 8*t**3 - 20*t**2 + 3*t**4 + 5*t**4 + 15*t**3 - 4*t.
-t*(t - 2)**2*(6*t + 1)
Find a such that 294*a**3 - 2*a**5 + 48*a + 318*a**2 + 34*a**3 + 263*a**3 + 38*a**5 + 357*a**4 = 0.
-8, -1, -2/3, -1/4, 0
Let v(q) be the third derivative of -q**8/3360 + q**6/360 + 11*q**4/24 - 4*q**2. Let d(c) be the second derivative of v(c). Factor d(u).
-2*u*(u - 1)*(u + 1)
Let d(o) be the second derivative of o**6/40 - 7*o**5/20 + 11*o**4/8 - 5*o**3/2 - 33*o**2/2 - 40*o. Let s(p) be the first derivative of d(p). Factor s(b).
3*(b - 5)*(b - 1)**2
Let t(r) be the second derivative of -r**5/12 - 5*r**4/12 + 5*r**3/2 + 9*r**2/2 - 21*r. Let z(p) be the first derivative of t(p). Factor z(o).
-5*(o - 1)*(o + 3)
Let s(v) be the second derivative of v + 1/14*v**4 - 1/70*v**5 + 2/7*v**2 - 8 + 5/21*v**3 - 1/105*v**6. Determine t so that s(t) = 0.
-1, 2
Let y be (-3)/((-105)/334) + (-62)/155. Let b = y + -9. Factor 32/7*p + b*p**4 + 24/7*p**2 + 16/7 + 8/7*p**3.
(p + 2)**4/7
Let t be 78988/(-279) - (-1)/9. Let v = t - -287. Let 0 - 2/3*b**2 + 2/3*b**v - 2/3*b + 2/3*b**3 = 0. Calculate b.
-1, 0, 1
Let p(r) = 52*r + 1200. Let y be p(-23). Factor 0 + 0*u - 1/8*u**3 + 1/8*u**y + 0*u**2.
u**3*(u - 1)/8
Let r(a) be the third derivative of a**7/630 - a**6/72 - 47*a**5/180 - 13*a**4/24 + 5*a**3 - 572*a**2. Let r(i) = 0. Calculate i.
-3, 1, 10
Let m(x) be the second derivative of x**4/32 - x**3/4 + 9*x**2/16 - 64*x. Factor m(b).
3*(b - 3)*(b - 1)/8
Let m(q) be the second derivative of 5*q**4/24 + 25*q**3/12 + 15*q**2/2 + 117*q. Factor m(t).
5*(t + 2)*(t + 3)/2
Let v be ((-5)/(-10))/(2/20). Suppose -v*r = -x + 3, -5*x + 1 = -2*r - 14. Factor 0*h + 3/4*h**3 + 0 + 3/4*h**5 - 3/2*h**4 + r*h**2.
3*h**3*(h - 1)**2/4
Factor -1/11*d**3 + 27/11*d - 14/11 - 12/11*d**2.
-(d - 1)**2*(d + 14)/11
Factor 1/2*o + 2 - 1/4*o**2.
-(o - 4)*(o + 2)/4
Suppose -56*b + 126*b + 128*b - 396 = 0. Suppose 0 + 3/5*n - 1/5*n**b = 0. Calculate n.
0, 3
Find q, given that -14/9*q**3 + 10/9*q**4 + 16/9*q - 8/9 - 2/9*q**5 - 2/9*q**2 = 0.
-1, 1, 2
Let n(o) = -o**3 - 15*o**2 + 27*o + 176. Let z be n(-16). Solve -2/3*q**2 + 1/3*q**3 + 8/3*q**4 + 0*q + z + 5/3*q**5 = 0.
-1, 0, 2/5
Let i(m) be the second derivative of m**6/960 - m**5/80 + m**4/16 + 8*m**3/3 - 19*m. Let b(d) be the second derivative of i(d). Find g, given that b(g) = 0.
2
Let t(b) = -b**2 + 6*b + 6. Suppose x = 6*x + q - 31, -2*q + 20 = 3*x. Let v be t(x). Factor v*h**2 - 2*h + 2*h**3 - 4*h**2 - 2 + 0*h**2.
2*(h - 1)*(h + 1)**2
Let p(v) be the first derivative of v**7/147 - v**6/35 + 3*v**5/70 - v**4/42 + 15*v + 20. Let o(q) be the first derivative of p(q). What is y in o(y) = 0?
0, 1
Let c be 0/(-4 - 25/(-5)). Let x(m) be the second derivative of 3*m + 1/60*m**5 + 0*m**2 + c*m**4 + 0 - 1/18*m**3. Factor x(p).
p*(p - 1)*(p + 1)/3
Let p(y) be the third derivative of 0*y - 1/60*y**5 - 1/70*y**7 + 0 + 0*y**3 + 10*y**2 - 1/24*y**6 + 1/24*y**4. Factor p(b).
-b*(b + 1)**2*(3*b - 1)
Let v(i) = 65*i**3 + 2*i**2. Let g be v(1). Let o = 269/4 - g. Factor -1/2*l**2 - 1/4*l**3 + 0 - o*l.
-l*(l + 1)**2/4
Factor -2/7*c**3 + 0*c + 40/7*c**2 + 0.
-2*c**2*(c - 20)/7
Let h(s) = 4*s**4 + 4*s**3 - 8*s**2 - 12*s. Let u(k) = 4*k**4 + 3*k**3 - 9*k**2 - 13*k. Let z(i) = 5*h(i) - 4*u(i). Factor z(v).
4*v*(v - 1)*(v + 1)*(v + 2)
Suppose -3*x = -2*z + 6, -x = -5*z - 4*x + 15. Suppose 6*f**5 + 15*f**2 + 21*f**z + f**3 + 3*f + 11*f**3 + 21*f**4 - 6*f**3 = 0. Calculate f.
-1, -1/2, 0
Let z = 11610 + -58048/5. Find j, given that z*j**3 + 0 - 2/5*j + 0*j**2 = 0.
-1, 0, 1
Let g be (-2961)/(-658) - 1/(-2). What is j in 15/7*j**2 - 15/7*j**g - 60/7*j + 75/7*j**3 - 12/7 - 3/7*j**4 = 0?
-2, -1, -1/5, 1, 2
Let b(h) be the third derivative of 0*h**4 + 8*h**2 + 0 + 0*h + 0*h**3 + 0*h**6 - 1/80*h**5 + 1/280*h**7. Factor b(k).
3*k**2*(k - 1)*(k + 1)/4
Let l(s) be the first derivative of -s**6/21 - 248*s**5/35 - 484. Factor l(k).
-2*k**4*(k + 124)/