2 - 13*v**7/147 - 29*v**6/60 + 349*v**5/210 - 16*v**4/7 + 12*v**3/7 - 265*v**2. Find z such that s(z) = 0.
-2, 3/5, 2/3, 1
Suppose 0 = 3*s - 5*x, 4*s + 4*x = 3*s + 17. Suppose -222 = -s*u - 62. Let 8*t + 6*t**2 + 100 - 2*t**2 + u*t = 0. What is t?
-5
Let d = -7/529 + 46573/1587. Factor -1/6 + 7/3*g + 86/3*g**3 + 32/3*g**5 - 73/6*g**2 - d*g**4.
(g - 1)**2*(4*g - 1)**3/6
Let s(j) = -12*j - 27. Let a be s(-3). Suppose -10*p + a*p = -3. Determine f so that 4/5*f**p + 0 - 6/5*f**5 + 2/5*f - 8/5*f**2 + 8/5*f**4 = 0.
-1, 0, 1/3, 1
Determine q so that 0*q**3 + 3/5*q**2 - 2/5*q - 1/5*q**4 + 0 = 0.
-2, 0, 1
Let o(a) be the third derivative of 0*a**3 + 1/80*a**6 + 0 + 0*a - 21*a**2 + 0*a**4 + 1/60*a**5 + 1/420*a**7. Factor o(n).
n**2*(n + 1)*(n + 2)/2
Let z(y) = -9*y**2 + 11*y - 12. Let o(h) = 20*h**2 - 20*h + 25. Let m(u) = -2*o(u) - 5*z(u). Factor m(r).
5*(r - 2)*(r - 1)
Factor -20/17*d + 6/17*d**2 + 16/17.
2*(d - 2)*(3*d - 4)/17
Let l(o) be the third derivative of o**6/260 + 19*o**5/390 + 11*o**4/52 + 3*o**3/13 + 3*o**2 + o. Factor l(s).
2*(s + 3)**2*(3*s + 1)/13
Let o(z) be the second derivative of -19*z - 1/45*z**6 + 8/3*z**2 + 1/9*z**4 + 1/10*z**5 + 0 - 4/3*z**3. Determine a so that o(a) = 0.
-2, 1, 2
Let d(x) be the first derivative of -5*x**4/4 - 20*x**3 + 65*x**2/2 + 164. Factor d(o).
-5*o*(o - 1)*(o + 13)
Let x = 1843 + -1841. Factor 3/4*q**x + 3*q + 3.
3*(q + 2)**2/4
Let w(r) = 12*r**4 + 12*r**3 - 18*r**2 - 9*r + 6. Let p(h) = -23*h**4 - 22*h**3 + 34*h**2 + 17*h - 11. Let t(i) = -3*p(i) - 5*w(i). Solve t(u) = 0.
-1, 1/3, 1
Let z(q) = -2*q**3 - q**2 + 2*q + 1. Suppose 3*s - 6 = 3*k - k, -4*s = -5*k - 1. Let n(h) = -h**3 - h**2 + h + 1. Let r(y) = k*z(y) - 7*n(y). Factor r(g).
(g - 1)*(g + 1)*(g + 4)
Let n(o) = -6 - 3*o + 0*o + 5*o. Let g be n(6). Let -g*f**2 + 3*f - f**2 - 7*f**4 - 4*f**2 - 5*f - 16*f**3 = 0. Calculate f.
-1, -2/7, 0
Let t(j) be the first derivative of 1 + 10/21*j**3 + 3/14*j**4 - 4/21*j**6 - 2/7*j**5 + 1/7*j**2 + 0*j. Solve t(m) = 0.
-1, -1/4, 0, 1
Factor 14*q**2 - 42/5*q**3 + 11/5*q**4 - 1/5*q**5 - 53/5*q + 3.
-(q - 5)*(q - 3)*(q - 1)**3/5
Let b(l) be the first derivative of 6*l**5/25 + l**4/2 - 2*l**3/3 - l**2 + 4*l/5 - 214. What is h in b(h) = 0?
-2, -1, 1/3, 1
Suppose w + 15 = -2*w, -5*p + w = -25. Let s(c) be the second derivative of -c**3 + 2/3*c**p + 0 + 2/3*c**2 - 1/6*c**5 - 4*c. Solve s(i) = 0 for i.
2/5, 1
Let o be 8 - 3 - (-6)/(-2). Let s(a) be the first derivative of -4 - 1/8*a**o - 1/12*a**3 + 1/2*a. Factor s(u).
-(u - 1)*(u + 2)/4
Suppose 0 = -2*l - 4*g - 14, 0*g = 2*l - 4*g - 26. Suppose -24*y + 4*y + y**l + 4*y**3 = 0. Calculate y.
-2, 0, 2
Let g(u) = -11*u**3 + 531*u**2 + 3*u. Let c(x) = 145*x**3 - 6905*x**2 - 40*x. Let a(m) = -3*c(m) - 40*g(m). What is y in a(y) = 0?
0, 105
Let o(r) be the second derivative of 4/9*r**2 + 1/90*r**6 + 7/18*r**4 + 2/3*r**3 + 9 + r + 19/180*r**5. Factor o(j).
(j + 2)**3*(3*j + 1)/9
Let l(z) be the third derivative of 0*z**3 - 1/40*z**6 + 0 + 15*z**2 + 0*z**4 + 1/20*z**5 + 0*z. Solve l(y) = 0 for y.
0, 1
Let b(d) be the third derivative of -d**5/420 - 23*d**4/168 + 4*d**3/7 - d**2 - 86*d. Determine k so that b(k) = 0.
-24, 1
Let h be (-10)/(-4) - (-75)/150 - (-6)/(-2). What is a in 1/2*a**2 + 3/2*a + h = 0?
-3, 0
Let y(k) be the first derivative of 1/12*k**4 - 2/3*k - 7 - 1/6*k**2 + 2/9*k**3. Factor y(n).
(n - 1)*(n + 1)*(n + 2)/3
Let z(r) = -r**4 - r**3 - 4*r**2 - r - 1. Let p(s) = -16*s**4 + 48*s**3 - 44*s**2 - 72*s - 12. Let h(m) = -p(m) + 12*z(m). Factor h(u).
4*u*(u - 15)*(u - 1)*(u + 1)
Let y be (-67 - 20/(-5))*(-1)/3. Let m be 6/y + (-1)/(-21). Determine a so that 0*a - m + 1/3*a**2 = 0.
-1, 1
Let o = -11 + 14. Suppose 4*b + b - 6 = u, -3*b = o*u - 18. Suppose -6*a**2 - 7*a - a**b + 19*a + 3*a**2 = 0. Calculate a.
0, 3
Let l(g) = 16*g**3 - 26*g**2 - g - 11. Let k = 56 + -52. Let i(v) = 3*v**3 - 5*v**2 - 2. Let n(f) = k*l(f) - 22*i(f). Solve n(w) = 0.
0, 1, 2
Let a(f) be the third derivative of f**7/6300 - f**6/300 + 3*f**5/100 + f**4/24 - 9*f**2. Let s(c) be the second derivative of a(c). Factor s(k).
2*(k - 3)**2/5
Let f(b) be the second derivative of 3/40*b**5 + 1/8*b**3 - 1/6*b**4 + 17*b + 0*b**2 + 0 + 0*b**6 - 1/168*b**7. Factor f(g).
-g*(g - 1)**3*(g + 3)/4
Let y = -17 + 20. Suppose -w = 3*m + y, 2*w + 2*m + 1 = 3. Suppose -27 + 3*t**3 + 6*t**2 + 4*t**3 - 3*t - 33*t + 5*t**w - 3*t**4 = 0. Calculate t.
-1, 3
Let l(a) be the first derivative of -2*a**3/27 + 16*a**2/9 - 10*a/3 - 84. Factor l(d).
-2*(d - 15)*(d - 1)/9
Suppose g + 3 - 61 = -5*l, 5*l + 4*g - 52 = 0. Suppose l = 4*u - 0. Factor 2*y**3 - 8*y**3 + y**3 + 2*y**2 + 3*y**u.
-2*y**2*(y - 1)
Suppose 5*v - 257 = -7. Suppose v = f + 4*f. Factor 4 + 4*n + 8*n + 4*n + f*n**2 + 7*n**4 + n**5 + 15*n**2 + 19*n**3.
(n + 1)**3*(n + 2)**2
Let q be 16/56*1/2. Factor 4/7*j**4 + q*j**5 + 0 + 4/7*j**2 + 1/7*j + 6/7*j**3.
j*(j + 1)**4/7
Let w(i) be the first derivative of 5*i**4/16 - 25*i**3/6 + 115*i**2/8 - 35*i/2 + 363. Solve w(a) = 0.
1, 2, 7
Solve 970*s - 47*s**2 + 52*s**2 + 9538 + 55070 + 360*s + 23837 = 0 for s.
-133
Let g = -37731/172 - -650/43. Let k = 205 + g. Factor k*o**2 - 1/4*o**3 + 0 - 1/2*o.
-o*(o - 2)*(o - 1)/4
Let k(u) be the third derivative of -u**7/525 - u**6/60 - 4*u**5/75 - u**4/15 - 2*u**2 + 12*u. Suppose k(l) = 0. Calculate l.
-2, -1, 0
Factor -8*a - a**2 + 2*a**4 + 4*a**3 - 5 - 7*a**2 + 11 + 4*a.
2*(a - 1)**2*(a + 1)*(a + 3)
Let m(a) be the third derivative of -a**8/336 + 47*a**7/1470 - 7*a**6/60 + 13*a**5/105 + a**4/7 + 169*a**2. Find g, given that m(g) = 0.
-2/7, 0, 2, 3
Factor 3*r**3 - 6*r + 690 - 15*r**2 - 690 - 12*r.
3*r*(r - 6)*(r + 1)
Let z(f) be the first derivative of f**6/36 - 7*f**5/30 + 3*f**4/8 + 7*f**3/18 - 5*f**2/6 - 278. Suppose z(i) = 0. What is i?
-1, 0, 1, 2, 5
Let o = -111 + 113. Let s(j) be the first derivative of 0*j**o + 7/20*j**4 + 1/30*j**6 + 0*j + 5 - 1/5*j**5 - 1/5*j**3. Factor s(a).
a**2*(a - 3)*(a - 1)**2/5
Let o be (2 + -1 + -2)*-1. Let n(y) = -4*y**2 + 3*y - 1. Let v(m) = -m - 1. Let s(x) = o*n(x) - v(x). Factor s(r).
-4*r*(r - 1)
Suppose -5*m - 7*m = 756. Let x = 66 + m. Factor 0 - 4/5*d**4 + 8/5*d + 18/5*d**x - 24/5*d**2.
-2*d*(d - 2)**2*(2*d - 1)/5
Suppose 4*g - 3*g = 5*a - 22, -a - 2*g = 0. Suppose 0 = -4*r + 8*r + 3*h - 14, 0 = -a*r + 4*h. Determine v so that 3/2*v**3 + 3*v**r + 3/2*v + 0 = 0.
-1, 0
Factor 2/3*h**3 + 2/3*h**4 + 0 - 2/3*h**2 - 2/3*h.
2*h*(h - 1)*(h + 1)**2/3
Let n be 5/(-2) - (-10 - -6). Let y(i) be the first derivative of -2*i - n*i**2 - 4 - 1/3*i**3. Factor y(q).
-(q + 1)*(q + 2)
Let l(k) = -15*k**3 + 156*k**2 - 333*k + 162. Let q(b) = 12*b**3 - 156*b**2 + 331*b - 162. Let n(c) = -5*l(c) - 6*q(c). Let n(v) = 0. What is v?
-54, 1
Let k(g) = -19*g**3 + 105*g**2 - 101*g + 15. Let o(r) = -r**3 + r. Let v(j) = k(j) + 6*o(j). Suppose v(x) = 0. What is x?
1/5, 1, 3
Let i(k) be the second derivative of -5*k**7/42 - 65*k**6/6 - 725*k**5/2 - 9975*k**4/2 - 33075*k**3/2 - 46305*k**2/2 + k - 16. Factor i(u).
-5*(u + 1)**2*(u + 21)**3
Let f(n) be the third derivative of 0 - 4*n**2 + 1/28*n**5 + 0*n - 1/70*n**6 + 1/490*n**7 + 0*n**3 - 1/28*n**4. Solve f(s) = 0 for s.
0, 1, 2
Let b(u) be the second derivative of -u**7/1470 + u**6/210 - u**5/140 - 6*u**2 + 10*u. Let j(y) be the first derivative of b(y). Factor j(a).
-a**2*(a - 3)*(a - 1)/7
Let d(o) be the first derivative of 48*o + 33/5*o**5 + 7 - 129/4*o**4 - 84*o**2 - 1/2*o**6 + 73*o**3. Factor d(x).
-3*(x - 4)**2*(x - 1)**3
Let y(c) be the third derivative of 0*c**5 + 0*c + 12*c**2 + 0 + 1/6*c**3 + 0*c**4 + 1/540*c**6. Let j(v) be the first derivative of y(v). Factor j(u).
2*u**2/3
Let w(p) be the third derivative of -p**6/24 - 5*p**5/6 - 2*p**2 + p. Let w(i) = 0. Calculate i.
-10, 0
Let q = -2 + -1. Let f be (6/9*q)/(-1). Suppose 6*j - 1 - 2*j - 4*j + j**f = 0. What is j?
-1, 1
Let d = -9249 + 18511/2. Factor 4*h**2 + d*h + 3 + 1/2*h**3.
(h + 1)**2*(h + 6)/2
Let n(z) be the first derivative of -z**4/8 - z**3/2 - z**2/2 + 107. Find w such that n(w) = 0.
-2, -1, 0
Let f be 2/(-6)*(18 - 15)*-3. Let a(v) be the second derivative of -95/4*v**5 - 15/2*v**4 + 0 + 14/3*v**f - v + 4*v**2 - 50/3*v**6. Let a(t) = 0. What is t?
-2/5, 1/4
Let o(w) be the third derivative of w**6/240 - 19*w**5/120 + 35*w**4/48 - 17*w**3/12 +