/5 + 2*d**5/5 + 5*d**4/3 - 3*d**3 + 2*d**2 - 4*d. Factor z(j).
2*(j - 1)**3*(j + 1)*(5*j - 2)
Let y(w) be the first derivative of -3*w**4/4 + 3*w**2/2 + 9. Find n, given that y(n) = 0.
-1, 0, 1
Let r be 21/(-18)*24/(-42). Factor -r*l**3 + 2/3*l + 4/9 - 4/9*l**2.
-2*(l - 1)*(l + 1)*(3*l + 2)/9
Let q(h) be the second derivative of -h**5/50 - h**4/15 + 10*h. Determine b, given that q(b) = 0.
-2, 0
Let x(h) be the second derivative of -h**5/120 + h**4/18 - 5*h**3/36 + h**2/6 + 3*h. Factor x(n).
-(n - 2)*(n - 1)**2/6
Let w(l) = -l**3 - 2*l**2 + l + 2. Let u be w(1). Let d(o) be the second derivative of 0*o**2 + 0*o**3 + u - 1/12*o**4 + 3*o. Suppose d(n) = 0. Calculate n.
0
Let k = -5 + 8. Let g(a) = a**2 + 2*a - 1. Let r be g(-3). Determine b so that 3*b**3 - 2*b**4 - b**5 - 2*b**k + 3*b**4 - b**r = 0.
-1, 0, 1
Let l be 0/4 + (1 - 35). Let i = 34 + l. Factor 2/7*u**2 - 2/7*u**3 + 4/7*u + i.
-2*u*(u - 2)*(u + 1)/7
Let i(q) = 2*q**3 - 3*q**2 + 2*q - 6. Let g be i(2). Factor -5/3*j**g + 0 - 1/3*j**4 + 4/3*j**3 + 2/3*j.
-j*(j - 2)*(j - 1)**2/3
Let i(d) = 8*d**3 + 13*d**2 - 45*d + 24. Let x(h) = 20*h**3 + 32*h**2 - 112*h + 60. Let u(b) = -12*i(b) + 5*x(b). Find a, given that u(a) = 0.
-3, 1
Suppose 0 = -2*y - 135 + 139. Let a(i) be the second derivative of 1/2*i**y - 3*i + 1/12*i**4 + 0 + 1/3*i**3. Suppose a(l) = 0. Calculate l.
-1
Factor 8/5*t + 4/5*t**4 - 4/5*t**5 + 12/5*t**3 + 0 - 4*t**2.
-4*t*(t - 1)**3*(t + 2)/5
Let b = -42 + 41. Let z be (0/b)/(11 - 10). Suppose -2/7*n**2 + 0*n + z = 0. Calculate n.
0
Solve 0 - 4/5*d - 1/5*d**3 + 4/5*d**2 = 0.
0, 2
Let m(t) = -t**2 - 1. Let b(f) = 2*f**2 + 5*f - 1. Let w(v) = b(v) + 3*m(v). Find d such that w(d) = 0.
1, 4
Let g be (1 + 3/(-2))/(90/(-240)). Find j such that 8/3*j**2 - g*j**3 + 0*j + 4/3*j**5 - 8/3*j**4 + 0 = 0.
-1, 0, 1, 2
Solve 4*x + 4*x - 3*x + x**2 - 3*x = 0.
-2, 0
Suppose -3*f + 3*h + 114 = 0, -2*f = -h + 20 - 98. Let z be 16/f + (-36)/(-10). Factor 0 - 2/9*u**z + 2/9*u**3 + 2/9*u**2 - 2/9*u.
-2*u*(u - 1)**2*(u + 1)/9
Let u(d) be the third derivative of d**7/14 + 11*d**6/30 + 23*d**5/30 + 5*d**4/6 + d**3/2 + 15*d**2. Find k such that u(k) = 0.
-1, -3/5, -1/3
Let l(t) be the first derivative of -t**6/4 + 9*t**5/10 + 9*t**4/4 - 5*t**3 - 63*t**2/4 - 27*t/2 + 5. Factor l(b).
-3*(b - 3)**2*(b + 1)**3/2
Factor 120*i + 401*i**3 + 304*i**3 - 12 - 22*i**5 - 525*i**4 - 557*i**2 + 122*i**2 + 169*i**5.
3*(i - 1)**3*(7*i - 2)**2
Let p(d) be the first derivative of -2*d**6/7 + 8*d**5/35 + d**4/7 + 12. What is z in p(z) = 0?
-1/3, 0, 1
Factor -s**2 - 178*s**3 + 183*s**3 + 80 + s**2 - 60*s.
5*(s - 2)**2*(s + 4)
Factor 30*n**2 + 3*n**4 - 30*n**2 - 3*n**3.
3*n**3*(n - 1)
Let j be (-3 - -3)/(-2)*1/(-2). Suppose 5*f + 4*h - 9 = 5, -h = -1. Factor 0 + j*s + 0*s**f + 1/2*s**3 + 1/2*s**4.
s**3*(s + 1)/2
Factor 1/4*u**2 + 49/4 - 7/2*u.
(u - 7)**2/4
Let o = -747/2 - -374. Suppose -g + o*g**2 + 1/2 = 0. Calculate g.
1
Let s(q) be the third derivative of -q**6/24 - 5*q**5/12 - 5*q**4/8 + 15*q**3/2 - 14*q**2 + 3. Factor s(p).
-5*(p - 1)*(p + 3)**2
Let r be (-1)/(-6) + (-207)/(-54). Factor -r*k**3 - k - 2*k + 7*k**3.
3*k*(k - 1)*(k + 1)
Suppose 0 = c + 3*s - 5, 3*c - 4*s + 2*s - 4 = 0. Factor 2/7*z**4 + 6/7*z**3 - 6/7*z - 4/7 + 2/7*z**c.
2*(z - 1)*(z + 1)**2*(z + 2)/7
Let c(j) be the third derivative of j**6/180 - 29*j**5/90 + 56*j**4/9 - 196*j**3/9 + 9*j**2 - j. Factor c(h).
2*(h - 14)**2*(h - 1)/3
Let j(t) = t**3 + t**2 - t - 1. Let m(i) = -9*i**3 - 6*i**2 + 6*i + 6. Let c(x) = -6*j(x) - m(x). Find q, given that c(q) = 0.
0
Let c(m) = -m**2 + 1. Let h(y) = 34*y**2 - 34*y. Let f(p) = 4*c(p) + h(p). What is o in f(o) = 0?
2/15, 1
Let o(c) be the third derivative of c**8/1344 - c**7/420 - c**6/160 + c**5/60 + c**4/24 - 2*c**2 - 1. Factor o(q).
q*(q - 2)**2*(q + 1)**2/4
Let r(o) be the first derivative of 16/3*o**3 + 8 + 2*o**2 + 0*o. Factor r(h).
4*h*(4*h + 1)
Let y(g) be the second derivative of -g**5/60 - g**4/6 - 2*g**3/3 - g**2/2 - 4*g. Let d(z) be the first derivative of y(z). What is h in d(h) = 0?
-2
Suppose -3/8*d**5 - 27/8*d**3 - 9/4*d**4 - 3/2*d**2 + 0 + 0*d = 0. Calculate d.
-4, -1, 0
Let n = 51 - 151/3. Factor -n*w + 1/3*w**2 + 1/3.
(w - 1)**2/3
Let b(t) = -t**2 + 5*t - 2. Let n be b(3). Let w = 6 - n. Suppose -w*r**3 + 2*r**4 + 4*r**4 - 4*r**4 = 0. What is r?
0, 1
Suppose -6 = -z - 2. Suppose 0 = y + 3*k - 2, -z*y - y - 4*k + 32 = 0. What is h in 28*h**2 - 16*h**3 - 24*h - 1/2*h**5 + 9/2*h**4 + y = 0?
1, 2
Let z(h) be the first derivative of -1/9*h**3 + 0*h**2 + 1/3*h + 7. Find r such that z(r) = 0.
-1, 1
Let p = 788/301 - 2/43. Find v such that 4/7 - p*v + 24/7*v**3 + 2/7*v**2 = 0.
-1, 1/4, 2/3
Let l(r) = r**3 - 6*r**2 - 4 + 7*r - r**2 + 1 + 0. Let n be l(6). Factor -4*o**n - 2/5 - 2*o - 2*o**4 - 2/5*o**5 - 4*o**2.
-2*(o + 1)**5/5
Factor 3 + 5/2*n**2 - 23/4*n + 1/4*n**3.
(n - 1)**2*(n + 12)/4
Let r(w) be the second derivative of w**8/1680 - w**7/1260 + w**4/6 + 3*w. Let p(n) be the third derivative of r(n). Find f, given that p(f) = 0.
0, 1/2
Suppose -3*d + 11 = 4*z, d = -2*d - 3*z + 9. Let o(f) be the first derivative of 0*f**2 + 0*f - d - 2/9*f**3. Factor o(q).
-2*q**2/3
Suppose 19*a**2 - 36*a**4 - 16*a**5 + 6 - 2 + 24*a - 8*a**3 + 13*a**2 = 0. What is a?
-1, -1/4, 1
Suppose 4*d = -n + 33, 5*d - 4*n + n - 54 = 0. Suppose f = -2*f + d. Factor -2*s**f - 4*s**2 + 2*s**4 + 4*s**2.
2*s**3*(s - 1)
Suppose 25 = 15*x - 10*x. Solve 8*k**2 - 9*k**x - 26*k**2 + 2*k**5 + 21*k**4 - 2*k**5 - 6*k**3 - 3 + 15*k = 0.
-1, 1/3, 1
Let d(w) be the third derivative of w**7/420 - w**6/90 - w**5/20 - 2*w**3/3 - 7*w**2. Let v(s) be the first derivative of d(s). Determine y so that v(y) = 0.
-1, 0, 3
Let y(p) = -8*p**3 - 6*p**2 + 6. Let i(m) = 17*m**3 + 13*m**2 + m - 13. Let l be (8 + 2)*1 + -1. Let u = l + -5. Let r(a) = u*i(a) + 9*y(a). Factor r(z).
-2*(z - 1)*(z + 1)*(2*z + 1)
Let q(p) be the first derivative of -p**5/15 + p**4/3 - 5*p**3/9 + p**2/3 + 7. Suppose q(c) = 0. What is c?
0, 1, 2
Find p such that 2*p**2 - 22*p**3 + 5*p**5 + 12*p**3 - 2*p**4 + 8 - 3*p**5 + 16*p = 0.
-1, 2
Let h(n) = -5*n**3 + 3*n**2 + 3*n - 3. Let o(s) = 4*s**3 - 2*s**2 - 2*s + 2. Let l(p) = 2*h(p) + 3*o(p). Factor l(a).
2*a**3
Let x(f) = -2*f**3 - 3*f**2 + f + 2. Let v be x(-2). Suppose 3*d**5 - 4*d**4 + d**3 - d**3 + d**v = 0. Calculate d.
0, 1
Let z(b) be the third derivative of b**7/105 - b**6/30 + b**5/30 + 2*b**2. Factor z(r).
2*r**2*(r - 1)**2
Let t(x) be the second derivative of -21*x**6/20 - 33*x**5/20 + x**4/8 + x**3/2 + x - 5. Find m, given that t(m) = 0.
-1, -1/3, 0, 2/7
Let r(f) = -5*f + f**2 + 4*f + 2*f - 1. Let g(j) = 2*j**2 + 2*j + 4*j - 5*j - 1. Let x(z) = -g(z) + r(z). Find w, given that x(w) = 0.
0
Let b(i) be the third derivative of 0 - 1/6*i**4 - 4/3*i**3 + i**2 + 1/30*i**6 + 0*i + 2/15*i**5. Let b(u) = 0. What is u?
-2, -1, 1
Let p(i) be the first derivative of -4*i**3/3 + 112*i**2/9 - 16*i/3 + 43. Suppose p(n) = 0. What is n?
2/9, 6
Factor 4*u**2 + 4*u**2 + 2*u**4 - 4*u + 4*u**5 - 10*u**4.
4*u*(u - 1)**3*(u + 1)
Let r = -1344 - -1347. Let 0 + 0*w - 28/3*w**r + 5*w**5 - 14/3*w**4 - 8/3*w**2 = 0. Calculate w.
-2/3, -2/5, 0, 2
Suppose -2*k**4 - 3*k - 4*k**5 - 7*k**4 + 6*k**2 + 7*k**5 + 3*k**4 = 0. What is k?
-1, 0, 1
Let s(t) = -3*t**3 + 7*t**2 - 11*t + 1. Let b(g) = -12*g**3 + 27*g**2 - 45*g + 3. Let r(u) = 2*b(u) - 9*s(u). Solve r(j) = 0 for j.
1
Suppose -1024/5 - 128*z**2 - 256*z - 4*z**4 - 32*z**3 - 1/5*z**5 = 0. What is z?
-4
Suppose -8*f + 12 + 28 = 0. Factor 2/3*h**4 + 0*h - 2/3*h**3 - 2/3*h**2 + 2/3*h**f + 0.
2*h**2*(h - 1)*(h + 1)**2/3
Let b(c) = -3*c**3 + 4*c**2 - 3*c. Let q be b(2). Let k be 2/q + (-68)/(-84). Factor -k*d**2 + 0*d + 2/3.
-2*(d - 1)*(d + 1)/3
Let p(x) be the second derivative of -x**8/2688 - x**7/1680 + x**6/720 - 5*x**4/12 - 3*x. Let k(m) be the third derivative of p(m). Factor k(j).
-j*(j + 1)*(5*j - 2)/2
Let u = -61 - -296/5. Let g = u - -41/20. Factor -1/4 - 1/4*m**3 + g*m + 1/4*m**2.
-(m - 1)**2*(m + 1)/4
Let o(k) be the second derivative of 0 - 3*k**2 - 3/20*k**5 - k**4 - 5/2*k**3 + 6*k. Solve o(s) = 0.
-2, -1
Let v(y) = -22*y + 1. Let z be v(1). Let a be 6/z + 32/14. Determine l, given that -2*l**4 + l**a + 43*l**3 - 3*l**2 - 47*l**3 = 0.
-1, 0
Let t(d) = 2*d**3 + d**2 + 7*d - 29. Let q(w) = -12*