 Let -2*p**5 + 157*p**3 - s*p**3 + 0*p**5 + p**5 = 0. Calculate p.
-1, 0, 1
Let s(n) be the second derivative of 0*n**2 - 7/120*n**5 - 1/18*n**3 + 0 - 4*n + 1/8*n**4. Factor s(m).
-m*(m - 1)*(7*m - 2)/6
Let b be (10/(-6))/(-4 - (-114)/36). Factor -7 - 1 - 6*q + q**3 + 5*q**2 + 2*q**2 - 4*q**b.
(q - 2)*(q + 1)*(q + 4)
Let t(x) be the third derivative of x**6/30 + 11*x**5/90 + x**4/9 - 7*x**3/6 + 23*x**2. Let g(l) be the first derivative of t(l). Factor g(n).
4*(n + 1)*(9*n + 2)/3
Let m be (2 - 2) + 1*(-28)/(-77). Let g(u) = -u + 2. Let h be g(-2). Factor -m*r + 26/11*r**2 + 46/11*r**h + 0 - 54/11*r**3 - 14/11*r**5.
-2*r*(r - 1)**3*(7*r - 2)/11
Let g(a) be the first derivative of -9 + a**4 + 4/3*a**3 - 4*a**2 + 0*a. Factor g(n).
4*n*(n - 1)*(n + 2)
Suppose o = 40 - 10. Let n = o - 30. Factor n*v**2 + 4/5*v**3 - 2/5*v + 0*v**4 + 0 - 2/5*v**5.
-2*v*(v - 1)**2*(v + 1)**2/5
Let g = 31 + -12. Let z = -17 + g. What is k in z*k + 10 + 2*k**2 - 12 - 4*k + 2*k**3 = 0?
-1, 1
Let i be -12 + (-17)/(-1) - 15/3. Let x(t) = t**3 - 4*t**2 - 3*t - 7. Let c be x(5). Factor i - 9/2*v**4 + 0*v - 27/4*v**5 - 3/4*v**c + 0*v**2.
-3*v**3*(3*v + 1)**2/4
Let i = -173 + 177. Let n(g) be the first derivative of 2 - 2*g**4 - 4/5*g**5 + i*g + 0*g**3 + 4*g**2. Suppose n(v) = 0. What is v?
-1, 1
Let w(p) = 2*p**4 + 7*p**3 - 5*p**2 - 7*p. Let r(k) = 2*k**3 + 4*k**3 - 99*k**2 + 2*k**4 - 6*k + 95*k**2. Let l(i) = -3*r(i) + 2*w(i). Factor l(s).
-2*s*(s - 1)*(s + 1)*(s + 2)
Let l be (2 + -2 - (1 + -1))/(-5). Factor -2/11*v**4 + 4/11*v**3 + 0 + l*v + 0*v**2.
-2*v**3*(v - 2)/11
Let s(n) = n**2 - 253*n + 3841. Let t be s(16). Suppose t*i**5 - 301/2*i**4 + 4*i + 123*i**3 - 38*i**2 + 0 = 0. Calculate i.
0, 2/7, 1/2, 2
Let a = -8/641 + 697/4487. Solve 0 - 5/7*i**5 + 0*i - 3/7*i**3 - a*i**2 + 9/7*i**4 = 0.
-1/5, 0, 1
Factor 15/8*v**3 + 1/8*v**4 + 17/8*v + 0 - 33/8*v**2.
v*(v - 1)**2*(v + 17)/8
Let a be (-7)/28*0 + 144/30. Let -12/5*k**2 - 28/5*k + a = 0. Calculate k.
-3, 2/3
Suppose 5*s + 3*r = 1, 4*s + 8*r - 20 = 12*r. Factor 5/2*v**3 + 10 + 20*v + 25/2*v**s.
5*(v + 1)*(v + 2)**2/2
Let m be 16/(-60)*(68/(-24) - -2). Factor -8/9*n**2 - 2/3*n + 0 - m*n**3.
-2*n*(n + 1)*(n + 3)/9
Let m(d) = -3*d**5 - 18*d**3 - 3*d**2 + 19*d. Suppose -2*c = -24 + 8. Let y(t) = -5*t**5 - 27*t**3 - 4*t**2 + 28*t. Let h(l) = c*m(l) - 5*y(l). Factor h(v).
v*(v - 3)*(v - 1)*(v + 2)**2
Let h(n) = n**2 - 13*n + 42. Let v be h(4). Suppose s - 8 = -v. Suppose -4/9*z**s + 0 - 2/9*z**3 + 2/3*z = 0. Calculate z.
-3, 0, 1
Let p = -1609 + 1609. Let o(q) be the third derivative of -8*q**2 + p - 1/15*q**3 - 1/20*q**4 - 1/50*q**5 - 1/300*q**6 + 0*q. What is s in o(s) = 0?
-1
Suppose -n = 4*y + 3, -3*n + 2*n = -4*y - 13. Let d be 8 + -2 + y - 4. Find l, given that -2/3*l**5 + 0 + 0*l**2 - 2/3*l**4 + 0*l + d*l**3 = 0.
-1, 0
Solve m**4 + 27 + 3*m**5 + 11*m**3 - 45*m + 19*m**3 - 16*m**2 - 22*m**4 + 12*m**3 + 10*m**2 = 0.
-1, 1, 3
Let c(h) be the third derivative of -h**6/60 + 2*h**5/15 + 5*h**4/12 + h**2 + 8*h. Find p such that c(p) = 0.
-1, 0, 5
Let h(a) be the third derivative of -625*a**8/448 - 425*a**7/56 - 35*a**6/2 - 89*a**5/4 - 17*a**4 - 8*a**3 - 66*a**2 + 4. Find w such that h(w) = 0.
-1, -4/5, -2/5
Let b(k) be the second derivative of 7*k**6/75 + 17*k**5/100 - k**4/10 - 7*k**3/30 + k**2/5 + 237*k. Let b(v) = 0. What is v?
-1, 2/7, 1/2
Suppose -p = -4, 2*y + 3 + 5 = 2*p. Solve 1/4*r**5 + 1/2*r**4 + 0 + 0*r**2 + y*r + 1/4*r**3 = 0.
-1, 0
Let k(v) be the first derivative of 4*v**3/3 - 7*v**2/2 + 12*v + 8. Let p be k(5). Find y, given that y**2 - p + 77 + 3*y = 0.
-3, 0
Solve -3/4*m**3 - 4*m**2 - 15/4*m + 9/2 = 0.
-3, 2/3
Let b(u) be the first derivative of u**5/40 + u**4/18 - u**3/36 - u**2/6 + 15*u + 3. Let p(t) be the first derivative of b(t). Determine z so that p(z) = 0.
-1, 2/3
Let y(t) be the first derivative of t**5/15 + t**4/3 + t**3/3 - 2*t**2/3 - 4*t/3 + 80. Solve y(o) = 0 for o.
-2, -1, 1
Let m(b) = 10*b**2 - 5*b. Let k be m(1). Let j(s) be the first derivative of 0*s + 3/10*s**k - 3/2*s**2 - 3/2*s**3 - 10 + 0*s**4. Determine u so that j(u) = 0.
-1, 0, 2
Let c(a) be the third derivative of -a**8/1512 - a**7/945 + a**6/108 - a**5/90 + 9*a**2 - 4. Let c(w) = 0. Calculate w.
-3, 0, 1
Suppose 5*t - 5*u - 530 = -480, -u = -6*t + 25. Factor -2/5 + 1/5*d**t + 2/5*d**2 - 1/5*d.
(d - 1)*(d + 1)*(d + 2)/5
Let k(i) = 52*i**2 + 676*i + 624. Let x(w) = -8*w**2 - 104*w - 96. Let g(l) = 5*k(l) + 32*x(l). Factor g(s).
4*(s + 1)*(s + 12)
Let p(g) be the second derivative of -2*g**6/15 - 7*g**5/5 - 7*g**4/3 + 10*g**3 - 274*g. Solve p(h) = 0 for h.
-5, -3, 0, 1
Let k = -10 - -18. Let x be (0 - (0 - -4)) + k. Find r, given that -15*r**2 + 141*r**3 - 205*r**3 + x - 49*r**2 + 4*r = 0.
-1, -1/4, 1/4
Let s(i) = 375*i + 10130. Let f be s(-27). Factor -2/5*l**2 + 0*l + 2/5*l**4 - 2/5*l**3 + 2/5*l**f + 0.
2*l**2*(l - 1)*(l + 1)**2/5
Factor 45/2*r - 27/2 - 39/8*r**2 - 3/8*r**4 - 15/4*r**3.
-3*(r - 1)**2*(r + 6)**2/8
Determine n so that 5*n**2 - 14/5*n - 24/5 - 1/5*n**4 + 3*n**3 - 1/5*n**5 = 0.
-3, -2, -1, 1, 4
Let o(j) = -17*j**2 - 34*j - 13. Suppose -5*a - 7 = 13. Let w(v) = 52*v**2 + 101*v + 38. Let c(u) = a*w(u) - 11*o(u). Suppose c(q) = 0. Calculate q.
-1, -3/7
Let q(s) be the first derivative of 3/14*s**4 + 1/7*s**2 + 14 + 8/21*s**3 + 0*s. Factor q(n).
2*n*(n + 1)*(3*n + 1)/7
Factor -9/4*p + 1/4*p**3 + 3/4*p**2 + 5/4.
(p - 1)**2*(p + 5)/4
Let k(d) = 3*d**2 + 2. Let f(n) = -7*n**2 + n - 5. Let c(u) = -u**2 + u + 25. Let l be c(6). Let z(a) = l*k(a) - 2*f(a). Factor z(m).
-m*(m + 2)
Let j(g) be the second derivative of 0*g**2 + 0*g**3 + 0 + 12*g + 1/4*g**4. Let j(k) = 0. Calculate k.
0
Factor -20/3*c**2 - 2*c**3 + 0 + 2/3*c**4 + 0*c.
2*c**2*(c - 5)*(c + 2)/3
Let o(v) = v**3 + 5*v**2 - v + 3. Let n be o(-5). Suppose 12 = 4*q, -19 = b - 5*q - n. Suppose 2*m**2 + b*m - 17*m + 12 + m**2 + m = 0. What is m?
2
Suppose -16/3*r**3 - 2/9*r**4 - 36*r**2 + 242/3 - 352/9*r = 0. Calculate r.
-11, -3, 1
Let u(m) = -5*m + 8. Let t be u(1). Factor -33*p + 4*p + 24*p**2 + 11*p + t.
3*(2*p - 1)*(4*p - 1)
Let p be 4/((-16)/246) - -5. Let r = p + 57. Determine z so that -1/2*z**2 + 0 + 1/2*z**4 - r*z**3 + 0*z + 1/2*z**5 = 0.
-1, 0, 1
Suppose 2*c + 0*c = -2*q - 2, -4*q = -4*c + 36. Factor -6*a + 6*a + 0 - 4 + c*a**2.
4*(a - 1)*(a + 1)
Factor 5*c**2 - 18*c**2 + 2*c**3 + 194*c + 235*c - 29*c**2 - 486 - 159*c.
2*(c - 9)**2*(c - 3)
Let z be (-14 + 1)*19/(-19). Let b = 16 - z. Solve 3/4*l**2 + 1/4*l**b - 1 + 0*l = 0 for l.
-2, 1
Let c = 450 - 446. Let d(s) be the first derivative of c*s + 1/12*s**3 + s**2 - 4. Determine i so that d(i) = 0.
-4
Let w(u) be the third derivative of -1/140*u**7 + 0 + 0*u**4 + 7*u**2 - 1/224*u**8 + 1/80*u**6 + 0*u**3 + 1/40*u**5 + 0*u. Factor w(l).
-3*l**2*(l - 1)*(l + 1)**2/2
Let i(m) = m**3 - 6*m**2 - 2*m + 8. Let b be i(6). Let y be 0/((-16)/(b + 8)). Solve 6*g + 2*g**2 + g**2 + y*g**2 = 0.
-2, 0
Let r(u) be the third derivative of u**6/360 - u**4/8 - 207*u**2. Suppose r(a) = 0. What is a?
-3, 0, 3
Let c(t) be the first derivative of 4*t**5/25 + 4*t**4/5 - 76*t**3/15 + 28*t**2/5 - 407. Let c(a) = 0. What is a?
-7, 0, 1, 2
Let a(n) be the second derivative of -n**4/12 - 5*n**3/3 - 3*n**2 + n. Let w be a(-9). Find r, given that -4 - r - 2*r + w - r**2 + r = 0.
-1
Suppose 148/11 - 2/11*t**2 - 70/11*t = 0. Calculate t.
-37, 2
Let r(l) be the second derivative of -5*l**8/336 + 2*l**7/35 - l**6/30 - 13*l**2/2 + 9*l. Let p(u) be the first derivative of r(u). Suppose p(q) = 0. What is q?
0, 2/5, 2
Let t be 6/4 - (-10 - (-10 - (-3)/6)). Suppose -3 = o - 5. Factor -8/5 + 16/5*v + o*v**t.
2*(v + 2)*(5*v - 2)/5
Suppose 7*b - 116 = 2*b + 2*n, -3*n = 5*b - 101. Let j be (-11)/b + (2 - 1). Factor -j*p**3 + 1/2 + 1/2*p - 1/2*p**2.
-(p - 1)*(p + 1)**2/2
Find b such that 176*b**4 + 11*b**5 - 37*b**3 + 22*b**5 - 1792*b + 5*b**3 - 1592*b**2 - 4*b**3 - 384 - 5*b**5 = 0.
-4, -1, -2/7, 3
Let f(r) = r**3 - 14*r**2 + 26*r - 20. Let z be f(12). Let p be (-1)/z - (58/(-8) - -3). Factor 1/3 - 4/3*a**2 - 2/3*a + 2/3*a**3 + a**p.
(a - 1)*(a + 1)**2*(3*a - 1)/3
Let y(z) = -z**4 + z - 1. Let o(u) = -4*u**5 - 11*u**4 + 4*u**3 + 8*u**2 + 5*u - 7. Suppose -5*g - 5 = -0. Let a(s) = g*o(s) + 5*y(s). Factor a(k).
2*(k - 1)*(k + 1)**3*(2*k - 1)
Let y be (-5 - -1)*(