)
Let n = 16375 - 114581/7. Factor 8*g**2 + 8/7 + 16/7*g**4 - n*g**3 - 2/7*g**5 - 34/7*g.
-2*(g - 4)*(g - 1)**4/7
Let o(k) = 330*k**2 + 1590*k + 2. Let t(g) = -g**3 + 887*g**2 + 4770*g + 7. Let x(s) = 7*o(s) - 2*t(s). Factor x(p).
2*p*(p + 3)*(p + 265)
Let f(b) be the first derivative of 1/12*b**3 - 5/4*b**2 - 65 + 25/4*b. Factor f(i).
(i - 5)**2/4
Factor 187*c**3 - 185*c**3 - 34*c**2 + 10*c**2 - 8*c**2 - 202*c - 168.
2*(c - 21)*(c + 1)*(c + 4)
Let i(r) be the second derivative of -9*r**4/4 + 277*r**3/2 + 93*r**2 + 10971*r. Suppose i(p) = 0. Calculate p.
-2/9, 31
Let y(w) be the second derivative of 13/12*w**4 + 9/2*w**3 - 14 - 6*w + w**2. Factor y(x).
(x + 2)*(13*x + 1)
Let b be (-76)/(-5 - -24) - 33*(-10)/75. Determine q, given that 0 - b*q**2 + 0*q = 0.
0
Let z(c) = -c**4 + c**3 + 1. Let f(s) = -4*s**4 - 6*s**3 - 15*s**2 - 7*s + 3. Let y = 140 - 143. Let d(w) = y*z(w) + f(w). Factor d(a).
-a*(a + 1)**2*(a + 7)
Let v = -4956 - -163550/33. Let a(w) be the first derivative of 0*w**4 + 1 + 0*w + 0*w**2 + v*w**3 - 2/55*w**5. Factor a(r).
-2*r**2*(r - 1)*(r + 1)/11
Let c be (16/28)/(-9 + 130/14). Let i(n) be the second derivative of 15*n - 1/6*n**3 + 0 + 1/3*n**c + 1/36*n**4. Factor i(x).
(x - 2)*(x - 1)/3
Let x = -1233 - -25894/21. Let w(n) be the third derivative of -1/35*n**5 - 14*n**2 - x*n**4 + 2/735*n**7 + 0 + 0*n**6 + 0*n + 0*n**3. Solve w(g) = 0.
-1, 0, 2
Let n(c) be the second derivative of 2*c**7/63 + c**6/90 - 17*c**5/15 + 127*c**4/36 - 22*c**3/9 - 10*c**2/3 + 7*c + 30. Solve n(r) = 0.
-5, -1/4, 1, 2
Let t(f) = -25*f**3 - 26*f**2 + 684*f + 672. Let i(o) = 4*o**3 + 4*o**2 - 114*o - 112. Let g(k) = -26*i(k) - 4*t(k). Factor g(a).
-4*(a - 8)*(a + 1)*(a + 7)
Let y be -2 + 3/12 + (-45)/(-12). Suppose 0 = 5*z - y*x + 3, 3*z - 4*x + 0 = -13. Factor -2*p + 3*p**2 + 4 - z - 4*p.
3*(p - 1)**2
Let t = 261701/5 - 51999. Let o = 342 - t. Factor -4/5*z**3 - o*z**4 + 0 + 4/5*z**5 + 0*z + 4/5*z**2.
4*z**2*(z - 1)**2*(z + 1)/5
Suppose s = -1146*d + 1149*d - 22, -6*s = 132. Factor -1/5*m**3 - 1/5*m**4 + 2*m**2 - 8/5*m + d.
-m*(m - 2)*(m - 1)*(m + 4)/5
Let w = 21 - 21. Suppose 4*l + 0*l - 24 = w. Suppose -15*k + 15*k**3 + l - 1 - 6*k**2 + k**2 = 0. Calculate k.
-1, 1/3, 1
Let l(c) be the first derivative of c**4/14 + 38*c**3/21 + 103*c**2/7 + 330*c/7 + 1719. Factor l(o).
2*(o + 3)*(o + 5)*(o + 11)/7
Suppose 5/4*t**5 + 7598567/4*t + 26645*t**3 - 1143574 - 1564799/2*t**2 - 629/2*t**4 = 0. What is t?
1, 8/5, 83
Let r(n) be the third derivative of -27*n**2 + 20/9*n**3 - 41/18*n**4 + 0 - 2*n + 4/45*n**5. Factor r(c).
4*(c - 10)*(4*c - 1)/3
Suppose 34 = 3*p + 2*b, -4*p - 11803*b = -11806*b. Suppose p*q**2 - 10/3*q - 14/3*q**4 - 4/3 + 10/3*q**3 = 0. Calculate q.
-1, -2/7, 1
Let j(c) be the second derivative of -5*c + 0*c**3 + 0*c**4 + 2/45*c**5 - 2/45*c**6 + 0*c**2 + 0 + 2/189*c**7. Let j(n) = 0. What is n?
0, 1, 2
Let b = -9222 + 9227. Let x(u) be the first derivative of 32*u - b*u**4 - 40*u**2 + 33 + 22*u**3 + 2/5*u**5. Let x(i) = 0. What is i?
1, 4
Let u = 218 + -214. Let k be 9*((5 - (-237)/(-27)) + u). What is y in -3/2*y**k - y - y**3 - 1/4*y**4 - 1/4 = 0?
-1
Let f = 203 + -200. Factor -128*p**2 - 3*p - p**3 - 2*p + 0*p**f - 2 + 124*p**2.
-(p + 1)**2*(p + 2)
Let n(p) be the first derivative of p**8/420 + p**7/35 - p**6/90 - p**5/5 - 127*p**3/3 + 131. Let q(k) be the third derivative of n(k). Factor q(i).
4*i*(i - 1)*(i + 1)*(i + 6)
Solve 33*k + 0 + 3/2*k**2 = 0 for k.
-22, 0
Let -1/3*o**3 - 3*o + 22/3 - 4*o**2 = 0. What is o?
-11, -2, 1
Let i(c) be the second derivative of 0*c**6 - 62*c + 0*c**2 + 0*c**3 + 0*c**4 - 1/42*c**7 + 0 + 1/20*c**5. Determine r so that i(r) = 0.
-1, 0, 1
Suppose 2*j - 479*y - 18 = -473*y, -5*j = -5*y - 15. Factor j + 1/2*v**2 + 7/2*v.
v*(v + 7)/2
Let x = 84 - 81. Determine o so that -7*o**3 + 7*o**2 - 16*o + 12 + o**3 + 0*o**2 + 5*o**x = 0.
2, 3
Let v(d) be the second derivative of -11/15*d**4 + 12/5*d**3 + 1/25*d**5 + 0*d**2 + 62*d + 0. Suppose v(y) = 0. What is y?
0, 2, 9
Let u(f) be the first derivative of f**7/105 - f**6/60 - f**5/15 + 75*f**2/2 - 202. Let s(x) be the second derivative of u(x). Factor s(l).
2*l**2*(l - 2)*(l + 1)
Let c(v) be the third derivative of -v**7/420 - 7*v**6/720 + v**5/20 - v**4/18 - 330*v**2. Find s such that c(s) = 0.
-4, 0, 2/3, 1
Let l be ((-11000)/(-150) + -72)/((-2)/(-16)). Factor l + 146/3*u**2 + 6*u**4 - 112/3*u - 28*u**3.
2*(u - 1)**2*(3*u - 4)**2/3
Let w = -294 + 324. Factor -12*v**3 + w*v**2 - 35*v**2 + 7*v**3.
-5*v**2*(v + 1)
Factor -24/11*g + 10/11*g**2 + 2/11*g**3 - 72/11.
2*(g - 3)*(g + 2)*(g + 6)/11
Let w(s) be the first derivative of -1/2*s**3 + 0*s**2 + 5/16*s**4 + 1/10*s**5 - 1/24*s**6 - 24 + 0*s. Find q, given that w(q) = 0.
-2, 0, 1, 3
Let m(o) = -14*o**4 - 26*o**3 - 126*o**2 + 204*o + 278. Let g(j) = -4*j**4 - 9*j**3 - 42*j**2 + 68*j + 93. Let s(l) = 20*g(l) - 6*m(l). What is i in s(i) = 0?
-3, -1, 2, 8
Let v(a) = 2*a**3 + 8*a**2 + 4*a. Let p(b) = -2*b**3 - b**2 - 2*b. Let h be (-8)/6*(2 + 63/(-18)). Let n(z) = h*p(z) + v(z). Let n(c) = 0. Calculate c.
0, 3
Let s(d) be the second derivative of -1/72*d**4 - 10/3*d**3 - 5 - 9*d - 300*d**2. Factor s(p).
-(p + 60)**2/6
Suppose 0 = 57*g - 68*g + 198. Suppose 1 = -n + 3*k, 3 - g = -5*n - 5*k. Factor -2/25 - 8/25*x**n + 2/5*x.
-2*(x - 1)*(4*x - 1)/25
Find w, given that -1/2*w**2 - 990 + 1981/2*w = 0.
1, 1980
Let x(j) be the second derivative of -j**6/180 - j**5/20 + j**4/3 - 31*j**3/6 - j + 60. Let a(q) be the second derivative of x(q). Factor a(y).
-2*(y - 1)*(y + 4)
Factor -28*k - 245*k**2 - 4/5.
-(35*k + 2)**2/5
Determine y, given that -740*y**3 + 7*y**2 - 22*y**2 - 25*y**5 - 387 + 2277 + 43*y**4 - 435*y**2 + 1485*y - 283*y**4 = 0.
-3, -2, 7/5
Let x(i) = i**3 - 109*i**2 + 292*i + 2756. Let n be x(106). Suppose 19*p - 18*p = 2. Solve 2/17*v**p + n + 22/17*v = 0 for v.
-11, 0
Let c = 44 + -42. Suppose -c = r - 2*r. Find m, given that 2*m - 2*m**r + 5*m**3 - 4*m - 6*m**4 + 0*m + 5*m**3 = 0.
-1/3, 0, 1
Solve 162 - 47*k**4 + 416*k**2 - k**5 - 205*k - 36*k**4 - 158*k**3 - 236*k + 105*k**4 = 0.
1, 2, 9
Let l(h) = 3*h**2 - h. Let m(z) = 6*z + 14*z**2 - 21 + 63 - 3*z + 13*z. Let i(s) = -4*l(s) + m(s). Factor i(d).
2*(d + 3)*(d + 7)
Let z(l) be the first derivative of 2*l**3/21 + l**2 + 141. What is s in z(s) = 0?
-7, 0
Let h(b) be the third derivative of b**7/1155 + 107*b**6/132 - 1073*b**5/330 + 179*b**4/44 - 6222*b**2. Determine x, given that h(x) = 0.
-537, 0, 1
Suppose -23 = 21*s + 922. Let f be (2256/(-47))/(s/2). Suppose -f*c**3 + 2/5*c**2 - 14/15*c**4 + 8/15 + 32/15*c = 0. Calculate c.
-2, -1, -2/7, 1
Suppose 4 = -26*q + 4*q + 24*q. Let p = -136 - -954/7. Factor 1/7*z**3 + 0*z + 0 - p*z**4 + 1/7*z**5 + 0*z**q.
z**3*(z - 1)**2/7
Let o(y) be the second derivative of 270*y**2 + 13/6*y**6 + 67/4*y**5 + 285/4*y**4 + 15 + 5/42*y**7 + 5*y + 180*y**3. Factor o(m).
5*(m + 2)**2*(m + 3)**3
Suppose -31*m**3 - 8474*m - 8455*m + 16888*m - 5*m**4 - 61*m**2 - 6 = 0. What is m?
-3, -2, -1, -1/5
Let b = 3127402/7 + -446771. Factor -v - 1/7*v**4 - b*v**2 + v**3 + 6/7.
-(v - 6)*(v - 1)**2*(v + 1)/7
Let r(m) = m**3 - 539*m**2 + 5822*m - 14863. Let a(c) = -25*c**3 + 14555*c**2 - 157195*c + 401305. Let i(l) = -3*a(l) - 80*r(l). Find y, given that i(y) = 0.
-119, 5
Let t(c) be the second derivative of 1/4*c**5 + 235/12*c**4 + 225/2*c**2 + 29*c - 3 + 455/6*c**3. Factor t(s).
5*(s + 1)**2*(s + 45)
Let r be -1*(5 - 10 - (37 - -3)). Factor 25*u**4 + 70*u**3 + 25*u**5 - r*u**5 + 15*u**5.
-5*u**3*(u - 7)*(u + 2)
Find l, given that 50*l**2 + 95729*l + 1450*l**2 + 165*l**4 - 94969*l + 910*l**3 - 5*l**5 = 0.
-2, -1, 0, 38
Let t(w) = w**2 + 22*w + 77. Let q be t(-11). Let c be (-2)/(-8) + -1*q/16. Suppose 2*o**2 - c*o + 4/3 - 1/3*o**3 = 0. What is o?
1, 4
Let l(t) = -4*t**2 - 3844*t + 2. Let u(o) = -47*o**2 - 42286*o + 23. Let w(d) = 23*l(d) - 2*u(d). Factor w(f).
2*f*(f - 1920)
Let s = -79 + 37. Let h = s + 61. Determine o so that 25*o + h*o - 14*o - 25 - 5*o**2 = 0.
1, 5
Factor 0 - 2/5*k**4 - 44*k**3 + 0*k + 2/5*k**5 + 0*k**2.
2*k**3*(k - 11)*(k + 10)/5
Let d(v) be the second derivative of 98*v - 43/30*v**3 + 0 - 1849/20*v**2 - 1/120*v**4. Factor d(j).
-(j + 43)**2/10
Let l be -7*2*(112 + -90). Let w = 619/2 + l. Factor w*f**3 + 0 + 1/2*f - 2*f**2.
f*(f - 1)*(