rmine y so that c(y) = 0.
-1, 1
Let f(h) be the first derivative of h**6/80 - h**5/10 + h**4/4 + 5*h**2/2 - 7. Let x(z) be the second derivative of f(z). What is g in x(g) = 0?
0, 2
Let a(o) be the first derivative of o**3/3 + 5*o**2/2 - 6*o + 14. Factor a(s).
(s - 1)*(s + 6)
Let a = -27 - -57/2. Let z = 11 - 8. Suppose z - 3*b**3 - a*b - 15/2*b**2 = 0. Calculate b.
-2, -1, 1/2
Let b(c) = 7*c**2 + 13*c + 1. Let h(f) = -3*f**2 - 6*f - 1. Let p(g) = -6*b(g) - 15*h(g). Factor p(s).
3*(s + 1)*(s + 3)
Let z(g) be the first derivative of g**4/4 + 3*g**3/2 + 3*g**2 - 2*g - 3. Let l(j) be the first derivative of z(j). Factor l(o).
3*(o + 1)*(o + 2)
Suppose i = 5*i. Let u = 88 - 85. Determine g, given that i*g - 1/2*g**5 - 1/2*g**4 + 1/2*g**u + 1/2*g**2 + 0 = 0.
-1, 0, 1
Suppose -10*z - 38*z**2 - 42*z**2 - 30*z - 5 = 0. Calculate z.
-1/4
Factor 1/2*p**3 + 0*p + 0 + 2*p**2.
p**2*(p + 4)/2
Suppose -51 = -6*x - 3. Let z(s) be the third derivative of -1/180*s**5 + 1/360*s**6 - 1/1008*s**x + 0 + 0*s**3 - s**2 + 0*s**4 + 0*s + 1/630*s**7. Factor z(w).
-w**2*(w - 1)**2*(w + 1)/3
Let a(x) be the third derivative of -x**5/20 - x**4/2 + 11*x**2. Find k such that a(k) = 0.
-4, 0
Factor 2/3*h + 2/9*h**2 - 4/9 + 2/9*h**4 - 2/3*h**3.
2*(h - 2)*(h - 1)**2*(h + 1)/9
Factor 3*q**3 - 24 + 2*q**2 + 36*q - 25*q**2 + 5*q**2.
3*(q - 2)**3
Suppose 3*b - 13 = -4. Factor 2/3*x**4 + 4/3*x**b - 2/3*x**5 + 2/3 - 2/3*x - 4/3*x**2.
-2*(x - 1)**3*(x + 1)**2/3
Let v = 4499/252 - 124/7. Let k(y) be the second derivative of 0*y**2 - 2*y + 1/9*y**3 + 1/90*y**6 + 1/20*y**5 - 1/126*y**7 - v*y**4 + 0. Factor k(p).
-p*(p - 1)**3*(p + 2)/3
Let l(u) be the second derivative of 0 + 0*u**3 + 6*u + 1/12*u**4 + 1/30*u**6 + 0*u**2 + 1/10*u**5. Factor l(r).
r**2*(r + 1)**2
Let i(t) be the second derivative of 0*t**4 + 1/180*t**6 + 0 + 1/240*t**5 - 2*t - 1/3*t**3 + 0*t**2. Let v(x) be the second derivative of i(x). Factor v(d).
d*(4*d + 1)/2
Suppose -3*x = -5 - 4. Let j be ((-4)/(-6))/((-2)/(-24)). Let d(u) = 60*u**2 - 6*u - 4. Let n(g) = -20*g**2 + 2*g + 1. Let o(w) = j*n(w) + x*d(w). Factor o(k).
2*(2*k - 1)*(5*k + 2)
Suppose 4*i = -8 + 16. Factor 2/5*n + 2/5*n**i - 4/5.
2*(n - 1)*(n + 2)/5
Determine n so that -2*n**2 - 8 + 8 - 16 - 18*n = 0.
-8, -1
Determine v, given that 23 - v**2 + 22 - 45 - 13*v = 0.
-13, 0
Solve -4/9*w**4 - 2/9*w**3 + 2/3*w**2 - 2/9 + 2/9*w = 0 for w.
-1, 1/2, 1
Suppose 5*j - 14 = -4*i, -5*j + 4*j + 4 = 2*i. Let y(a) be the first derivative of 0*a + 2/9*a**3 + 0*a**2 - 2/15*a**5 + 0*a**4 - j. Solve y(q) = 0 for q.
-1, 0, 1
Let m = 67/6 - 11. Let i(o) be the first derivative of -3/8*o**2 + 2 - 3/20*o**5 + m*o**3 + 1/24*o**6 + 1/8*o**4 + 1/4*o. Factor i(r).
(r - 1)**4*(r + 1)/4
Factor -1/3*w**2 + 1/3*w**3 + 0 + 1/3*w**4 + 0*w - 1/3*w**5.
-w**2*(w - 1)**2*(w + 1)/3
Let z(w) = -10*w**2 + 17*w + 15. Let i(p) = 5*p**2 - 9*p - 8. Let b(c) = -11*i(c) - 6*z(c). Let b(r) = 0. What is r?
-2/5, 1
Let o(h) = 3*h**3 - 9*h**2 - 6*h - 6. Let x(p) = -p**2 - 1. Let r(q) = -o(q) + 6*x(q). Factor r(w).
-3*w*(w - 2)*(w + 1)
Let w(c) be the second derivative of -9*c**7/1400 + c**6/600 + c**5/300 + c**3/3 - 2*c. Let y(l) be the second derivative of w(l). Find n such that y(n) = 0.
-2/9, 0, 1/3
Factor -5*r**3 + 8*r**2 + 5*r + 5*r**3 - 4*r**4 - r - 4 + 4*r**5 - 8*r**3.
4*(r - 1)**3*(r + 1)**2
Let q(g) be the third derivative of -g**9/15120 + g**8/4200 - g**7/4200 + 5*g**3/6 - 6*g**2. Let r(v) be the first derivative of q(v). Factor r(s).
-s**3*(s - 1)**2/5
Determine o so that -2*o**4 + 5*o**3 + 48*o - 32 - 5*o**3 - 2*o**2 - 12*o**3 = 0.
-4, 1
What is f in 0*f**3 + 1/6*f**5 + 0 - 1/6*f + 1/3*f**2 - 1/3*f**4 = 0?
-1, 0, 1
Suppose -5*y - 2 = -2*b, -4*y = b - 3*y - 1. Let k(m) be the first derivative of 0*m**5 + 0*m + 3/20*m**4 + b - 1/10*m**6 + 0*m**2 + 0*m**3. Factor k(g).
-3*g**3*(g - 1)*(g + 1)/5
Factor -2/3*l**3 + 0 + 2/3*l + 0*l**2.
-2*l*(l - 1)*(l + 1)/3
Let m = -9 + 12. Factor -4*u**3 - m*u**3 + u**2 + 3*u**3 + u + 2*u**2.
-u*(u - 1)*(4*u + 1)
Let l(h) be the first derivative of h**4/14 - 2*h**3/21 - 10. Find c such that l(c) = 0.
0, 1
Let j(d) be the second derivative of 0*d**2 + 1/20*d**5 + 4*d + 1/6*d**3 + 0 - 1/6*d**4. What is r in j(r) = 0?
0, 1
Factor 10/17*x**2 + 4/17*x + 2/17*x**4 + 8/17*x**3 + 0.
2*x*(x + 1)**2*(x + 2)/17
Let k(p) be the second derivative of 4*p + 0*p**2 + 0*p**3 + 1/70*p**5 + 1/42*p**4 + 0. Factor k(s).
2*s**2*(s + 1)/7
Suppose 2*i + 24 = 6*i. Let b(y) be the second derivative of -y + 1/7*y**2 + 1/7*y**4 - 4/21*y**3 + 1/105*y**i + 0 - 2/35*y**5. Factor b(r).
2*(r - 1)**4/7
Let o be (-25)/(-30) + 2/(-6). Suppose r - i = -2*r + 13, -5*r + i = -19. Let o*q**2 + 3/4*q - 3/4*q**r - 1/2 = 0. Calculate q.
-1, 2/3, 1
Let k(i) be the third derivative of i**6/480 + i**5/80 + i**4/32 - 2*i**3/3 + 4*i**2. Let s(p) be the first derivative of k(p). Factor s(d).
3*(d + 1)**2/4
Suppose x = 5*x - 2*w - 76, 2*x + 2*w = 32. Suppose x*o + 2/3*o**3 - 18 - 6*o**2 = 0. Calculate o.
3
Let v(d) be the third derivative of -1/2*d**3 - 6*d**2 + 1/20*d**6 + 0*d + 0*d**5 - 1/4*d**4 + 1/70*d**7 + 0. Factor v(f).
3*(f - 1)*(f + 1)**3
Let c(h) = -h**3 - h**2 - h - 45. Let g be c(0). Let a = g - -45. Find j, given that j**2 - 1/2*j - 1/2*j**3 + a = 0.
0, 1
Let p(q) be the third derivative of -q**5/20 + q**4/2 - 2*q**3 - 7*q**2. Factor p(f).
-3*(f - 2)**2
Determine t so that 9*t + 28*t - 5*t + 4*t**2 + 64 = 0.
-4
Let h(n) = 32*n**3 + 19*n**2 - 11*n - 11. Let c(z) = 16*z**3 + 10*z**2 - 6*z - 6. Let b(i) = 11*c(i) - 6*h(i). Determine t so that b(t) = 0.
-1/4, 0
Determine d so that 3*d**3 + 5*d**3 + d**3 + 6*d**2 - 3*d**5 = 0.
-1, 0, 2
Let p(k) be the first derivative of -k**6/135 - k**5/90 + k**4/108 + 3*k**2/2 - 3. Let h(q) be the second derivative of p(q). Suppose h(i) = 0. Calculate i.
-1, 0, 1/4
Factor 3/7*h**2 + 9/7*h + 0.
3*h*(h + 3)/7
Let b(g) = 7*g - 9. Let h be b(6). Let u be 0 - h/(-9) - 1. Factor -8/3*k + 4*k**2 + 2/3*k**4 - u*k**3 + 2/3.
2*(k - 1)**4/3
Let g be ((-4)/5)/(4/(-30)). Let q = 10 - g. Determine k so that k - 2 + 23*k**2 + 13*k**2 - k - 162*k**q = 0.
-1/3, 1/3
Factor 7*x + 0*x - 3*x - 8*x**2 + 10*x**2.
2*x*(x + 2)
Suppose t - 25 = 5*u, -5*t - 2*u + 0*u = 10. Let k be t/(0 + 1 - 0). Factor 2*n + k + 0 + 2*n**2.
2*n*(n + 1)
Let y = 63 - 61. Find f such that 0*f**y - 2/5*f + 2/5*f**3 + 0 = 0.
-1, 0, 1
Factor -5*l**3 + 4*l**4 - 4*l**4 - 3*l**4 + 8*l**3.
-3*l**3*(l - 1)
Let o(x) be the first derivative of 16*x**3 - x**6 - 13*x**4 - 3 - 11*x**2 + 4*x + 28/5*x**5. Solve o(r) = 0 for r.
2/3, 1
Suppose 7*r = 9*r - 4. Let d(y) be the third derivative of 0 + 0*y**3 + 1/600*y**6 + 1/120*y**4 + 1/150*y**5 - y**r + 0*y. Factor d(j).
j*(j + 1)**2/5
Let j(r) be the first derivative of -r**4/4 - 3*r**3 - 9*r**2/2 - 8*r - 5. Let v be j(-8). Factor -1/4*q**2 + 1/4 + v*q.
-(q - 1)*(q + 1)/4
Solve 27*t**3 + 216*t + 291/2*t**2 + 96 + 3/2*t**4 = 0 for t.
-8, -1
Let r(i) be the third derivative of i**8/504 + 2*i**7/315 - i**6/90 - 2*i**5/45 + i**4/36 + 2*i**3/9 - 28*i**2. Solve r(h) = 0 for h.
-2, -1, 1
Let r(k) be the third derivative of 1/3*k**5 + 0*k + 1/21*k**7 - 1/168*k**8 + 0 - 1/6*k**6 - 2*k**2 - 5/12*k**4 + 1/3*k**3. What is x in r(x) = 0?
1
Let z = -19 + 24. Let s(d) be the first derivative of 0*d - 2*d**2 - 2 + 2/3*d**3 + 2*d**z + 4*d**4. Factor s(o).
2*o*(o + 1)**2*(5*o - 2)
Let m(d) be the first derivative of -9*d**3/4 + 33*d**2/8 - 3*d/2 + 19. Determine h, given that m(h) = 0.
2/9, 1
Let y be -1 + 3 + (-1)/1. Let i = -4 - -6. Factor -1 + y - z**i.
-z**2
Let u(b) be the second derivative of -7*b**6/90 + 19*b**5/60 - 2*b**4/9 - 2*b**3/9 - 3*b. Factor u(c).
-c*(c - 2)*(c - 1)*(7*c + 2)/3
Factor 0*b - 1/4*b**4 + 0 - 1/2*b**3 - 1/4*b**2.
-b**2*(b + 1)**2/4
Let m(z) be the second derivative of 0*z**2 + 2*z + 0*z**4 - 1/10*z**5 + 0 + 0*z**3. Determine n so that m(n) = 0.
0
Let h(f) = -2*f + 18. Let p be h(8). Let j(t) be the first derivative of -4/3*t**3 + 0*t + 1/2*t**p - 4. Find b, given that j(b) = 0.
0, 1/4
Let u = 462/5 - 92. Let v = -1131/5 + 227. Factor -v*o - 2/5 - u*o**2.
-2*(o + 1)**2/5
Suppose b = 3*o - 7, -4*b - 8*o = -7*o - 11. Find u, given that -2/9 - 4/9*u - 2/9*u**b = 0.
-1
Let k(d) be the third derivative of 243*d**6/40 + 81*d**5/5 + 18*d**4 + 32*d**3/3 + 5*d**2. Factor k(h).
(9