 given that 488/7*s - 2876/7*s**2 - 16/7 + 322*s**3 + 9360/7*s**4 + 3726/7*s**5 = 0.
-2, -1, 1/23, 2/9
Let h be (13 - 10)/(-1 - 14/(-8)). Let t be (2 + (-4)/h)*2. Factor -6*v**3 - t*v + 0*v + 2*v**4 + 29*v**2 - 23*v**2.
2*v*(v - 1)**3
Let c be 8 + (-416)/117 + 34/(-51). Suppose 2/9*w**5 - 4/3*w + 0 + c*w**2 + 2/3*w**4 - 10/3*w**3 = 0. Calculate w.
-6, 0, 1
Let k(q) be the second derivative of -4*q**5/25 - 71*q**4/5 - 1306*q**3/15 - 60*q**2 + 1666*q. Let k(z) = 0. Calculate z.
-50, -3, -1/4
Let y(o) be the first derivative of -o**4/8 + o**3/6 + o**2/2 + 1995. Factor y(k).
-k*(k - 2)*(k + 1)/2
Let u be (2 + (-26)/8)/(315/(-126)*(-6)/(-48)). What is z in 7/4*z**3 - 23/4*z**2 + 4 - 2*z + 7/4*z**u + 1/4*z**5 = 0?
-4, -1, 1
Let b = 596 + -594. Factor 5 - 55*d + 2*d**b + 10 - 11*d + 3 + 46.
2*(d - 32)*(d - 1)
Let p = -264 - -272. Factor 853*j + 15*j**4 - 3*j**5 - 431*j - p*j**3 + 21*j**2 - 428*j - 19*j**3.
-3*j*(j - 2)*(j - 1)**3
Let z(j) be the second derivative of 2*j**6/15 - 3*j**5 + 68*j**4/3 - 64*j**3 - 2635*j. Factor z(q).
4*q*(q - 8)*(q - 4)*(q - 3)
Let u(b) be the first derivative of 1/3*b**4 + 34 + 4*b**2 + 0*b - 20/9*b**3. Factor u(w).
4*w*(w - 3)*(w - 2)/3
Suppose -1388*i = -1375*i - 26. Let j(t) be the second derivative of 1/48*t**3 + 0 - 1/160*t**5 + 1/16*t**i - 1/96*t**4 - 7*t. Determine q, given that j(q) = 0.
-1, 1
Let y = 8677/101 - 15031/202. Factor -7 - y*q + 10*q**3 + 137/2*q**2.
(q + 7)*(4*q + 1)*(5*q - 2)/2
Let f(l) be the first derivative of -8/9*l**3 + 0*l - 231 + 1/3*l**4 + 0*l**2. Determine m so that f(m) = 0.
0, 2
Let x(p) be the third derivative of 1/210*p**7 - 1/60*p**5 + 1/40*p**6 + 0 - 1/336*p**8 + 7*p**2 + 0*p**3 - 3*p - 1/12*p**4. Find i, given that x(i) = 0.
-1, 0, 1, 2
Factor -6*m - 81 + 15*m**4 - 27*m**3 + 10*m**2 + 58 + 23 - 3*m**5 + 11*m**2.
-3*m*(m - 2)*(m - 1)**3
Let j = -222357/5 + 44473. Suppose 0 = 2*l - 4*y + 8, -3*y = 2*l - l - 16. Suppose 16/5*w + 6/5*w**2 - 2/5*w**l - 4/5*w**3 + j = 0. What is w?
-2, -1, 2
Suppose 3*v = p + 9, -4*v - 26 = 3*p - 38. Let z be 10320/960 - (10 + p). Find o, given that -1/8*o**2 - 5/8*o + z = 0.
-6, 1
Let j = 26 - 24. Suppose 6*v**3 + 45*v - v**3 + 54*v**j - 104*v**2 = 0. Calculate v.
0, 1, 9
Factor 3/7*z**2 - 108/7 - 15*z.
3*(z - 36)*(z + 1)/7
Let i(j) = 490*j - 16. Let l be i(3). Factor 1449*t - 6*t**2 + t**2 - l*t.
-5*t*(t + 1)
Factor 0 + 85*v - 65/2*v**3 - 1095/2*v**2.
-5*v*(v + 17)*(13*v - 2)/2
Let j(v) be the first derivative of 40 + 3/16*v**2 + 9/8*v - 1/12*v**3. Factor j(m).
-(m - 3)*(2*m + 3)/8
Suppose 45319 = 34*z + 2479. Let j = z - 1260. Let j - 3/5*u**2 + 3*u = 0. Calculate u.
0, 5
Let c(v) = -5*v**4 - 4*v**3. Suppose f = -4*u + 113, -7 = -2*f + 3. Let b(j) = -3*j**4 + 25*j**3 + j**4 - u*j**3. Let w(y) = -11*b(y) + 6*c(y). Factor w(s).
-2*s**3*(4*s + 1)
Let -41*w**4 + 0*w**5 + 6*w**5 + 279*w**3 - 103*w**4 + 19680*w**2 - 3*w**5 - 19818*w**2 = 0. Calculate w.
0, 1, 46
Let z(j) be the third derivative of j**6/360 + 11*j**5/90 + 115*j**4/72 + 25*j**3/3 - 2600*j**2. Factor z(s).
(s + 2)*(s + 5)*(s + 15)/3
Factor 938 - 4688/5*b - 2/5*b**2.
-2*(b - 1)*(b + 2345)/5
Let n = 105380 - 105380. Factor -1/6*t**3 + n + 0*t - 1/3*t**2.
-t**2*(t + 2)/6
Let p(i) = 10*i**2 + 8*i + 36. Let j(c) = -8*c**2 - 9*c - 36. Let d be ((-6)/(13 - -5))/(2/(-30)). Let x(g) = d*p(g) + 6*j(g). Determine k so that x(k) = 0.
-2, 9
Suppose 147*d - 12 = 145*d. Let a be (d/8)/(7 - 287/56). Factor 0*u + 2/5 - a*u**2.
-2*(u - 1)*(u + 1)/5
Let q be (-6)/(-7)*(-1)/(25/(-525)). Let o(g) be the first derivative of q - 1/3*g**3 + 0*g + 0*g**2. Factor o(h).
-h**2
Let a = -44095 + 132289/3. Let -8*v - 28/3 + a*v**2 = 0. Calculate v.
-1, 7
Let b(v) be the third derivative of v**6/60 + 7*v**5/5 + 115*v**4/4 - 2116*v**3/3 + 2330*v**2. Suppose b(c) = 0. Calculate c.
-23, 4
Let p(f) be the first derivative of -3481*f**4/14 + 15812*f**3/21 - 1952*f**2/7 + 256*f/7 - 3581. Suppose p(q) = 0. What is q?
8/59, 2
Let k(g) be the second derivative of -g**7/147 - g**6/15 + 19*g**5/2 + 2711*g**4/42 - 113560*g**3/21 - 115600*g**2/7 - 1058*g + 1. Solve k(z) = 0.
-20, -1, 17
Find u, given that -26*u**2 - 480/7 + 25/7*u**3 + 512/7*u - 1/7*u**4 = 0.
2, 4, 15
Factor -1/2*p**2 + 57/2 - 8*p.
-(p - 3)*(p + 19)/2
Let x(k) = 3*k**2 - 13*k - 8. Let t be ((-15)/6)/((-5)/10). Let c(q) = -7*q**2 + 26*q + 13. Let z(d) = t*x(d) + 2*c(d). Solve z(r) = 0.
-1, 14
Let b be 395/9 - (189 - 146). Determine l so that -b*l + 0 + 2/9*l**3 + 8/9*l**4 - 32/9*l**2 = 0.
-2, -1/4, 0, 2
Suppose 41*v - 11135 = 3625. Let q be 80/v + -8*2/(-36). Suppose -1/6 + 2/3*a - 1/6*a**4 - a**2 + q*a**3 = 0. What is a?
1
Find p such that 2/7*p**3 - 2/7*p**2 + 0 - 24/7*p = 0.
-3, 0, 4
Let q = -49 + 60. Suppose 0 = -3*o + q + 1. Let -o + 4 - 2*k**2 + k**5 + 0 - k**3 + 2*k**4 = 0. What is k?
-2, -1, 0, 1
Let c(n) be the first derivative of 3/8*n**4 - n**3 + 0*n**2 + 0*n - 87. Factor c(t).
3*t**2*(t - 2)/2
Suppose -207*d = -472 - 149. Factor 14/15*i**d + 2/15*i**4 + 6/5*i + 0 + 2*i**2.
2*i*(i + 1)*(i + 3)**2/15
Let w(g) = -6*g - 24. Let u be w(-6). Find m such that 12*m**4 + 56*m**5 - 104*m**5 + 51*m**5 - u*m - 12*m**2 + 9*m**3 = 0.
-2, -1, 0, 1
Suppose 5*q = f, f + 168 - 174 = 2*q. Suppose -l - 4*l = 0. Factor -1/4*y**3 - 1/4*y + l - 1/2*y**q.
-y*(y + 1)**2/4
Let l(x) be the second derivative of x**4/12 + 17*x**3/2 + 205*x**2 + 5*x - 134. Factor l(m).
(m + 10)*(m + 41)
Let s = 287308 - 2015813/7. Let h = 669 + s. Suppose 1/7*w**2 + 169/7 + h*w = 0. What is w?
-13
Let x(a) = -2*a**2 + 2*a. Let l be 6/(-15) + (-36)/(-15). Let o(g) = 0 + 0 - 2*g**2 + 5*g**2 - l*g. Let j(t) = -4*o(t) - 5*x(t). Suppose j(i) = 0. What is i?
-1, 0
Find l such that -8*l**2 + 14*l**2 - 355*l - 26 - l**2 + 716 = 0.
2, 69
Let o(v) be the second derivative of 37/4*v**3 - 65/16*v**4 + 21/80*v**5 + 0 + 11*v - 6*v**2. Let o(x) = 0. Calculate x.
2/7, 1, 8
Let n be ((-115)/(-23) + (-1528)/324)*6. Let j(d) be the first derivative of -15 - n*d**3 - 20/9*d**2 + 8/9*d - 1/3*d**4. Factor j(v).
-2*(v + 2)**2*(6*v - 1)/9
Let w(z) be the second derivative of -57*z + 10/3*z**3 + 16*z**2 + 1/6*z**4 + 0. Factor w(s).
2*(s + 2)*(s + 8)
Let f(y) be the third derivative of y**8/3024 - 5*y**7/378 + 11*y**6/180 + 1246*y**2. Factor f(c).
c**3*(c - 22)*(c - 3)/9
Let n(k) be the third derivative of -9/40*k**6 + 1/35*k**7 + 0 + 0*k + 1/2*k**5 - 24*k**2 + 0*k**3 - 3/8*k**4. Factor n(i).
3*i*(i - 3)*(i - 1)*(2*i - 1)
Factor -510 - 3/4*w**2 - 261/2*w.
-3*(w + 4)*(w + 170)/4
Let c(a) be the third derivative of -1/56*a**8 + 62 + 0*a + 0*a**4 + 0*a**5 + 38/315*a**7 - 2*a**2 - 2/45*a**6 + 0*a**3. Solve c(u) = 0 for u.
0, 2/9, 4
Suppose 34*q - 28*q = 54. Let v be q - (1 - (-432)/56). What is x in -v*x**4 - 32/7 - 80/7*x - 66/7*x**2 - 20/7*x**3 = 0?
-4, -1
Let f(j) be the first derivative of j**5/60 + j**4/24 - 23*j**2 + 37. Let t(a) be the second derivative of f(a). Factor t(i).
i*(i + 1)
Let h(y) be the first derivative of -y**7/1050 + y**5/300 + 69*y**2/2 - 108. Let i(n) be the second derivative of h(n). What is c in i(c) = 0?
-1, 0, 1
Let b(d) = -10*d - 56. Let h be b(-6). Factor 0*k**4 + k**h + 5 - 5*k**2 - 3*k**3 + 77*k - 74*k - 1.
(k - 4)*(k - 1)*(k + 1)**2
Let g(w) be the second derivative of 2*w + 7 + 1/21*w**2 - 1/63*w**4 - 1/105*w**5 + 1/315*w**6 + 1/63*w**3 + 1/441*w**7. Factor g(c).
2*(c - 1)**2*(c + 1)**3/21
Let p(t) = t**2 - 34*t + 42. Let n be p(33). Factor 11*i**2 - n*i - 18*i + 1 + 5 + i**2.
3*(i - 2)*(4*i - 1)
Let x(m) be the second derivative of m**6/60 - m**5/10 + m**4/6 - 73*m**2/2 + m. Let j(o) be the first derivative of x(o). Factor j(k).
2*k*(k - 2)*(k - 1)
Let 15360 + 28160*g + 1060/3*g**4 + 7820/3*g**3 - 73840/3*g**2 + 25/3*g**5 = 0. Calculate g.
-24, -2/5, 2, 4
Suppose a = -j + 25219, 0 = j - 4*j + 3*a + 75633. Factor -344605 - j*t - 615*t**2 + 67*t**3 + 67*t**3 - 139*t**3.
-5*(t + 41)**3
Suppose -15 = -3*i + 9*v - 8*v, 0 = -4*i - 4*v + 36. Factor 0*x**2 + 312*x**3 - 311*x**3 + i*x**2 + 3*x + 2*x.
x*(x + 1)*(x + 5)
Let z be 102/(-6) + 9193/348 + 6/(-8). Factor -z + 37/3*h + h**2.
(h + 13)*(3*h - 2)/3
Let n be (0 + -2)*(1 - (-22)/(-4)). Let m be (15/n)/(5/(-4)*-2). Factor -2*j**4 - m*j**3 + 22/3*j**2 + 2/3*j**5 - 8*j + 8/3.
2*(j - 2)*(j - 1)**3*(j + 2)/3
Solve 13*v + 19/3 + 7*v**2 + 1/3*v**3 = 0.
-19, -1