51. Determine y, given that 33/4*y - 9/2 - 3*y**r - 3/4*y**3 = 0.
-6, 1
Let s = 832/17913 - -1/853. Let t(h) be the first derivative of 2/7*h - 4/21*h**3 + 2/35*h**5 - 7 + 1/7*h**2 + s*h**6 - 1/7*h**4. Determine w so that t(w) = 0.
-1, 1
Let i(c) be the first derivative of 4*c**3/27 + 4*c**2/3 + 20*c/9 + 29. Factor i(t).
4*(t + 1)*(t + 5)/9
Solve -5*z**3 + 4*z**5 - 26*z - 8*z**2 + 20*z**4 - 12 + 29*z**3 - 2*z = 0 for z.
-3, -1, 1
Suppose 0 = 171*f + 120*f - 582. Solve -2/19*q**3 + 6/19 + 2/19*q - 6/19*q**f = 0 for q.
-3, -1, 1
Determine n, given that 11*n - n**2 + 3*n - 14 + 16*n - 21*n = 0.
2, 7
Factor -16/21*k**3 + 0*k + 2/3*k**2 + 2/21*k**4 + 0.
2*k**2*(k - 7)*(k - 1)/21
Let d(h) = 24 + 36 + 7*h**2 - 6 - 2*h**2 + 35*h. Let w(s) = 2. Let n(m) = -d(m) + 2*w(m). Factor n(k).
-5*(k + 2)*(k + 5)
Suppose -45*l + 90 = -27*l. Let a(f) be the third derivative of 0 + 0*f**3 + 1/75*f**6 + 0*f**4 + 0*f + 3*f**2 - 1/150*f**l. Factor a(r).
2*r**2*(4*r - 1)/5
Let z be ((-3)/5)/(39/(-130)). Factor 2 + 4*n + 6*n**2 + 17*n**z - 21*n**2.
2*(n + 1)**2
Suppose 3 = 5*r + 4*u, 13*u + 3 = 12*u. Factor -1/8*v**5 - 5/8*v**2 + 0 + 1/4*v + 3/8*v**r + 1/8*v**4.
-v*(v - 1)**3*(v + 2)/8
Determine g so that 32/7*g - 2/7*g**2 - 128/7 = 0.
8
Suppose 2*z - 2*z + 5*z = 0. Suppose 0 = 4*n - 5*d + 3*d - 10, -4*d - 14 = -5*n. Factor -2/7*q + 2/7*q**n + z.
2*q*(q - 1)/7
Let t(n) = 15*n**4 + 45*n**3 + 50*n**2 - 5. Let y(j) = -8*j**4 - 23*j**3 - 26*j**2 + 3. Let f(w) = -3*t(w) - 5*y(w). Determine g so that f(g) = 0.
-2, 0
Let h(l) = 2*l**3 - 2*l**2 + l + 5. Let n(a) = -a - 1. Let t(j) = 2*h(j) + 22*n(j). Solve t(w) = 0.
-1, 3
Let n(b) be the third derivative of b**5/60 - 11*b**4/6 + 14*b**3 + 237*b**2. Let n(k) = 0. What is k?
2, 42
Let t(n) = 1. Suppose -5*a + 9 = -1. Let r(g) = 3*g - g**3 + 0*g - 1 - 6*g + 3*g**a + 0*g**2. Let p(o) = 3*r(o) + 6*t(o). Factor p(b).
-3*(b - 1)**3
Let k(p) be the first derivative of p**3/9 + 5*p**2/2 + 26*p/3 + 104. Determine c so that k(c) = 0.
-13, -2
Let h(s) be the second derivative of -s**6/255 + s**5/34 - 3*s**4/34 + 7*s**3/51 - 2*s**2/17 + s - 24. Factor h(t).
-2*(t - 2)*(t - 1)**3/17
Let i be -2*-6*2/8. Let x be (-2)/(-1) + (i - 3). Suppose 8*q**4 - 30*q**3 + 10*q**5 - 30*q**5 - 5*q**x - 53*q**4 = 0. Calculate q.
-1, -1/4, 0
Let t be ((-58)/(-5))/((-12)/45). Let f = 45 + t. Factor -f*i**2 + 2 + 1/2*i**3 + 0*i.
(i - 2)**2*(i + 1)/2
Find j, given that 5/4*j**3 + 1 - 1/4*j**4 - 3/4*j**2 - 5/4*j = 0.
-1, 1, 4
Let j(x) = 12*x**4 - 20*x**3 + 10*x**2 + 2. Let p(w) = -w**5 - 24*w**4 + 39*w**3 - 19*w**2 - 5. Let h(k) = -10*j(k) - 4*p(k). Let h(r) = 0. Calculate r.
0, 1, 2, 3
Factor -9/4*q - 7/2 - 1/4*q**2.
-(q + 2)*(q + 7)/4
Let b(z) be the first derivative of z**5/540 + z**4/54 - 5*z**3/54 + 11*z**2/2 - 2. Let r(y) be the second derivative of b(y). Factor r(u).
(u - 1)*(u + 5)/9
Let i(u) be the third derivative of u**6/300 - u**4/15 - 13*u**2 - 4. Suppose i(c) = 0. What is c?
-2, 0, 2
Let g(x) be the second derivative of 27*x**4/20 - 29*x**3/10 + 3*x**2/5 + 112*x - 3. Suppose g(c) = 0. Calculate c.
2/27, 1
Let g(h) be the first derivative of h**5/12 - 35*h**4/24 + 5*h**3 - 3*h**2 + 14. Let c(t) be the second derivative of g(t). Suppose c(q) = 0. Calculate q.
1, 6
Let v(m) be the second derivative of -2*m**7/21 + 10*m**6/3 - 42*m**5 + 490*m**4/3 + 3430*m**3/3 - 14406*m**2 - 2*m - 277. Factor v(i).
-4*(i - 7)**4*(i + 3)
Let o(w) be the third derivative of 2*w**7/105 - w**6/3 + 29*w**5/60 + 61*w**4/24 + 3*w**3 - 56*w**2. Find z, given that o(z) = 0.
-1/2, 2, 9
Let j(c) be the second derivative of -7*c**6/165 + c**5/22 + 5*c**4/11 - 20*c**3/33 - 8*c**2/11 - 101*c. Find u such that j(u) = 0.
-2, -2/7, 1, 2
Let i(c) = -30*c - 1108. Let g be i(-37). Factor 10/7*l + 4/7 - g*l**2.
-2*(l - 1)*(7*l + 2)/7
Let 2/11*s**3 - 8/11*s + 0 - 6/11*s**2 = 0. Calculate s.
-1, 0, 4
Suppose -14 = -4*y + 10. Factor -8*t**5 + 13*t**5 - y*t**3 + t**3.
5*t**3*(t - 1)*(t + 1)
Let l(t) be the first derivative of 9/2*t**2 + t**3 - 6 + 0*t. Factor l(u).
3*u*(u + 3)
Let k(d) be the first derivative of 0*d - 3/7*d**2 + 3/7*d**3 - 3/28*d**4 + 33. Let k(p) = 0. Calculate p.
0, 1, 2
Suppose 5*n + 5*f - 35 = 0, f = -0*n - 5*n + 23. Factor -5*w - 10*w**3 + 0 + 10*w**2 - 4*w**5 + 3*w**5 + 2*w**4 + 3*w**n + 1.
-(w - 1)**5
Suppose 5*b + 11 = 6*b. Suppose -3*a + 3 = -6*a, -a = 3*h - b. Factor -4*v**5 + h*v**3 + 0*v**5 + 4*v**4 + 0*v**5 - 4*v**2.
-4*v**2*(v - 1)**2*(v + 1)
Let 0 + 4/7*o**3 - 2/7*o**4 + 22/7*o**2 - 24/7*o = 0. What is o?
-3, 0, 1, 4
Let f(p) be the first derivative of -10/13*p**2 - 2/39*p**3 - 50/13*p + 2. Factor f(t).
-2*(t + 5)**2/13
Let b be 36/(-4) - (-4 + 1). Let s = b - -8. Solve -5*v + 6*v**s - 1 - 1 + v = 0.
-1/3, 1
Suppose 4*y = -2*i - 3*i + 27, 2*y + 2*i - 14 = 0. Find w, given that 5*w**4 + 0 + 0 - 28*w**3 + y*w**2 + 15*w**4 = 0.
0, 2/5, 1
Suppose 4*b - 28 = -8. Suppose 0 = b*l - 5 - 10. Factor -l*y**2 + 3*y**3 + 5*y**3 + y**4 - 4*y**4 - 2*y**3.
-3*y**2*(y - 1)**2
Let d(i) be the first derivative of -3*i**6/2 + 6*i**5 - 9*i**4 + 6*i**3 - 3*i**2/2 - 73. Factor d(g).
-3*g*(g - 1)**3*(3*g - 1)
Suppose -5*a - 15 = -0*a. Let q be (16 - (1 + 0)) + a. Factor -17 - 5*h**2 + 3*h**2 + q*h - 1.
-2*(h - 3)**2
Let j(z) = -5*z**4 + z**3 - 18*z**2 + 14*z + 2. Let f(m) = -3*m**4 + m**3 - m**2 - m + 1. Let n(p) = 2*f(p) - j(p). Factor n(k).
-k*(k - 4)*(k - 1)*(k + 4)
Factor 8*r**2 + 4*r**4 + 26/3*r**3 + 2/3*r**5 + 0 + 8/3*r.
2*r*(r + 1)**2*(r + 2)**2/3
Let o(t) be the first derivative of -t**6/90 - t**5/5 - 3*t**4/2 + 32*t**3/3 - 31. Let y(z) be the third derivative of o(z). Let y(n) = 0. Calculate n.
-3
Let o(w) = 7*w**2 + 552*w + 38098. Let p(z) = z**2 + 2. Let v(c) = o(c) - 5*p(c). What is x in v(x) = 0?
-138
Suppose -a = -2*d + 20, 3*a + 5*d - 36 = 5*a. Let z be a/15 + 2 - (2 - 2). Factor -4/15*f + 0 + z*f**2.
2*f*(f - 2)/15
Let c(z) be the third derivative of 0*z**4 + 0*z + 19*z**2 + 1/120*z**6 + 0*z**3 + 1/20*z**5 + 0. Factor c(m).
m**2*(m + 3)
Let g(q) be the second derivative of q**5/30 - 5*q**4/18 - 4*q**3 - 532*q. Factor g(z).
2*z*(z - 9)*(z + 4)/3
Let k(v) be the third derivative of -20*v**2 + 1/15*v**4 + 0 + 0*v + 1/150*v**5 + 1/5*v**3. Factor k(c).
2*(c + 1)*(c + 3)/5
Let m(a) be the first derivative of -1715*a**6/6 - 3724*a**5 + 3745*a**4/4 + 11930*a**3/3 + 2110*a**2 + 440*a - 425. Find j such that m(j) = 0.
-11, -2/7, 1
Let v(l) = l**2 - 10*l + 24. Let y be v(4). Let i be (-60)/(-10) + -2 + -1. Suppose y + 0*a + 7/8*a**i - 1/4*a**2 + 9/8*a**4 = 0. What is a?
-1, 0, 2/9
Let a(h) = -h**2 - 9*h + 90. Let x be a(-15). Solve -2*p**2 + x - 10/7*p**3 - 6/7*p - 2/7*p**4 = 0 for p.
-3, -1, 0
Factor -313 - 105*o + 12*o**2 + 105 - 199*o.
4*(o - 26)*(3*o + 2)
Let i(o) be the first derivative of o**7/210 + o**6/60 - o**4/12 - o**3/6 - 15*o**2/2 + 11. Let l(b) be the second derivative of i(b). Factor l(j).
(j - 1)*(j + 1)**3
Let w(o) be the first derivative of -3*o**4/8 - o**3 + 15*o**2/4 + 9*o - 52. Factor w(a).
-3*(a - 2)*(a + 1)*(a + 3)/2
Let v(w) be the third derivative of 0*w**4 + 1/90*w**5 - 1/9*w**3 + 0 - 15*w**2 + 0*w. Find r, given that v(r) = 0.
-1, 1
Let c(u) be the third derivative of -u**8/6720 + u**7/3360 + u**3/6 - 8*u**2. Let x(f) be the first derivative of c(f). Factor x(m).
-m**3*(m - 1)/4
Let u(j) be the second derivative of -j**5/60 - j**4/3 - 461*j. Suppose u(z) = 0. Calculate z.
-12, 0
Let n(p) be the second derivative of p**6/90 + p**5/15 + p**4/6 + 7*p**3/6 - 11*p. Let m(i) be the second derivative of n(i). Factor m(f).
4*(f + 1)**2
Suppose d - 4*a = 13, -22 = -5*d + d + a. Let r(y) = 4*y**2 - 19*y - 5. Let p be r(d). Factor 1/6*s**2 + p*s + 1/6*s**4 + 1/3*s**3 + 0.
s**2*(s + 1)**2/6
Let s(a) be the third derivative of a**6/30 - 7*a**5/60 - a**4/12 + 3*a**2 - 12. Suppose s(k) = 0. Calculate k.
-1/4, 0, 2
Let j(b) be the first derivative of -2/39*b**3 + 0*b - 1/13*b**2 - 23. Find o, given that j(o) = 0.
-1, 0
Factor 2/9*x - 4/9*x**2 + 0*x**3 - 2/9*x**5 + 4/9*x**4 + 0.
-2*x*(x - 1)**3*(x + 1)/9
Factor 13 + 1/4*f**3 - 12*f + 9/4*f**2.
(f - 2)**2*(f + 13)/4
Suppose 4*q = 3*z + 31, 3*q = 6*z - 5*z + 27. Let c(f) = 15*f**2 - 30*f + 30. Let w(s) = -s**2 + s - 1. Let l(t) = q*w(t) + c(t). Suppose l(n) = 0. What is n?
2
Let t be (2/4)/(2*(-1)/(-28)). Let -1 - 4*n