f**5/300 + f**4/30 - 2*f**3/15 - f**2/2 - 2. Let j(d) be the second derivative of y(d). Determine k so that j(k) = 0.
2
Let k(w) be the second derivative of 0*w**2 + 6*w - 3/10*w**6 + 0 - 3/4*w**4 - w**3 + 6/5*w**5. Let k(a) = 0. What is a?
-1/3, 0, 1, 2
Suppose -w - 2*w = 0. Factor -3*d - d**4 + 3*d**3 + w + d**2 + 2*d**4 - 2.
(d - 1)*(d + 1)**2*(d + 2)
Let w = 169/18 + -80/9. Let a(f) be the first derivative of 2*f - 1/3*f**3 + 1 + w*f**2. Solve a(b) = 0 for b.
-1, 2
Let h(u) = -4*u**5 - 19*u**4 - 15*u**3 + 3. Let l(o) = 36*o**5 + 172*o**4 + 136*o**3 - 28. Let i(q) = -28*h(q) - 3*l(q). Factor i(y).
4*y**3*(y + 1)*(y + 3)
Let q(j) be the first derivative of 1/12*j**2 + 1/9*j**3 - 1/12*j**4 - 5 + 1/36*j**6 - 1/6*j - 1/30*j**5. Determine z so that q(z) = 0.
-1, 1
Factor -23*l**2 + 48*l**2 - 11*l + l + 35*l**3.
5*l*(l + 1)*(7*l - 2)
Suppose 12 = -18*n + 12. What is c in 1/3*c**2 + 0*c + n = 0?
0
Let o(g) be the first derivative of -3*g**5/40 + g**4/8 + 10*g + 6. Let f(u) be the first derivative of o(u). Find k such that f(k) = 0.
0, 1
Let d(t) = -10*t - 7. Let b be d(-1). Let i(o) be the second derivative of 1/12*o**b + 1/40*o**5 + 0 - 3*o + 1/12*o**4 + 0*o**2. Factor i(k).
k*(k + 1)**2/2
Find s such that 0 + 2/9*s**5 + 0*s**3 + 4/9*s**4 - 2/9*s - 4/9*s**2 = 0.
-1, 0, 1
Let y be -2*((-1)/2 - 1). Factor -4*c - 2*c**2 - 2*c**3 - c**y + 5*c**3.
2*c*(c - 2)*(c + 1)
Suppose -1/3*n**4 - 1/3*n**3 + 1/3*n**5 + 1/3*n**2 + 0*n + 0 = 0. Calculate n.
-1, 0, 1
Let t be 2/(-3) + (-16)/(-24). Let a(z) be the first derivative of 0*z**2 + 2 + t*z + 4/5*z**5 + 5/4*z**4 + 1/3*z**3. Find o such that a(o) = 0.
-1, -1/4, 0
Let p(f) be the second derivative of 1/11*f**3 + 1/33*f**4 - 1/231*f**7 + 1/11*f**2 - 2*f + 0 - 1/55*f**5 - 1/55*f**6. Factor p(z).
-2*(z - 1)*(z + 1)**4/11
Suppose 2*z + 2 = -4, 0 = -t - z. Let x = -11/20 + 53/60. Factor 0*i + 0*i**t - x*i**4 + 1/3*i**2 + 0.
-i**2*(i - 1)*(i + 1)/3
Let p(m) be the second derivative of 1/36*m**4 - 1/18*m**3 + 0 + 1/60*m**5 - 4*m - 1/6*m**2. Suppose p(c) = 0. What is c?
-1, 1
Let y be ((-3)/9)/((-3)/36). Factor 5*t**4 + 0*t**4 - 2*t**3 - 3*t**4 - y*t**2.
2*t**2*(t - 2)*(t + 1)
Let r(k) be the first derivative of 2*k**6/3 + 18*k**5/5 + 5*k**4 - 10*k**3/3 - 12*k**2 - 8*k - 6. Solve r(g) = 0 for g.
-2, -1, -1/2, 1
Let v(k) be the third derivative of 1/30*k**5 + 1/504*k**8 + 0*k**3 - 1/18*k**4 + 1/180*k**6 + 0*k - 1/105*k**7 + 0 - 3*k**2. Suppose v(r) = 0. Calculate r.
-1, 0, 1, 2
Suppose -5*k - c = -25, -2*k + 1 = 5*c - 32. Let g(w) be the second derivative of 1/16*w**k + 0 - 1/8*w**2 - w - 1/12*w**3. Determine v, given that g(v) = 0.
-1/3, 1
Let s(x) be the second derivative of 1/30*x**4 - 8*x - 1/75*x**6 + 0*x**2 + 0 - 1/15*x**3 + 1/50*x**5. Find k such that s(k) = 0.
-1, 0, 1
Suppose 0 = -5*n + 2*n - 15. Let u = n - -8. Factor -5*y - 12*y**3 + 5*y**4 + 3*y + 12*y**2 - u*y**2.
y*(y - 1)**2*(5*y - 2)
Let p(c) be the second derivative of -25*c**4/54 + 40*c**3/27 - 16*c**2/9 + 7*c. Factor p(a).
-2*(5*a - 4)**2/9
Let l(h) = -8*h**4 - 152*h**3 + 36*h**2 + 152*h. Let k(t) = -t**4 - 17*t**3 + 4*t**2 + 17*t. Let s(n) = -28*k(n) + 3*l(n). Find r, given that s(r) = 0.
-5, -1, 0, 1
Let g(c) be the third derivative of -c**7/140 + c**6/40 - c**5/40 - 15*c**2. Factor g(x).
-3*x**2*(x - 1)**2/2
Let v(s) be the first derivative of -1 + 1/4*s**4 - s**3 + 3*s - 1/2*s**2. Suppose v(o) = 0. What is o?
-1, 1, 3
Factor 0*o**2 - 12*o**2 - 11*o - o**3 + 4 - o**4 + 21*o**2.
-(o - 1)**3*(o + 4)
Let r(h) = -13*h**3 + 8*h**2 + 5*h + 5. Let b(f) = 84*f**3 - 52*f**2 - 32*f - 32. Let l(g) = -5*b(g) - 32*r(g). Factor l(q).
-4*q**2*(q - 1)
Find c such that 61 + 739 + 1037*c - 1117*c + 2*c**2 = 0.
20
Let w(z) be the first derivative of z**4/54 - z**3/9 - 4*z - 2. Let r(g) be the first derivative of w(g). Factor r(b).
2*b*(b - 3)/9
Let n(f) be the third derivative of f**7/70 + 7*f**6/40 + 9*f**5/10 + 5*f**4/2 + 4*f**3 - 5*f**2. Factor n(r).
3*(r + 1)*(r + 2)**3
Suppose 4*k = -0*k - 2*r + 2, -k - 4*r = -4. Let i(t) = t + 1. Let f be i(3). Factor -2/5*g**f + k + 4/5*g**3 + 0*g - 2/5*g**2.
-2*g**2*(g - 1)**2/5
Factor -8 - 12*j**3 - 30*j**2 - 37*j + 9*j - 2*j**2.
-4*(j + 1)**2*(3*j + 2)
Let o(k) be the first derivative of k**8/560 + k**7/280 - k**6/120 - k**5/40 + k**3 - 7. Let z(r) be the third derivative of o(r). Factor z(f).
3*f*(f - 1)*(f + 1)**2
Let f(x) be the third derivative of -x**6/540 - x**5/270 + x**4/54 - 8*x**2. Find s, given that f(s) = 0.
-2, 0, 1
Let h = -31281/7 - -1596290/357. Let d = h + 11/17. Find o such that d*o + 4/3 + 2*o**2 = 0.
-1, -2/3
Suppose a = -n + 1, 3*a - 1 = -0*n - 2*n. Let i - i**n + 9 - 9 - 2*i = 0. Calculate i.
-1, 0
Let t(r) be the first derivative of -r**6/90 - r**5/30 + r**4/3 + 7*r**3/3 + 2. Let h(a) be the third derivative of t(a). Factor h(c).
-4*(c - 1)*(c + 2)
Let f(s) be the first derivative of -3*s**4/4 + 2*s**3/3 + 7*s**2/2 + 2*s + 3. Determine a so that f(a) = 0.
-1, -1/3, 2
Let c = 25 + -22. Find x such that -4*x**c - 9*x**2 - 27*x**2 - 86 - 58*x - 22 - 50*x = 0.
-3
Let d(g) = -6*g**5 - 4*g**4 + 13*g**3 + 9*g**2 - 2*g. Let b(t) = 3*t**5 + 2*t**4 - 7*t**3 - 5*t**2 + t. Let u(q) = -5*b(q) - 3*d(q). Find j such that u(j) = 0.
-1, 0, 1/3, 1
Let u be (-30)/(-22) - 4/4. Let c = u + -1/33. Solve c*l**2 - 2/3 - 1/3*l = 0.
-1, 2
Suppose 19*r = 17*r. Solve 0*d - 2/9*d**3 - 2/9*d**2 + r = 0.
-1, 0
Let s be (-20)/(16/(-4)) + (-1 - 2). Factor 0 + 0*c**s - 2/5*c**5 - 4/5*c**4 + 0*c - 2/5*c**3.
-2*c**3*(c + 1)**2/5
Let f = 30 - 26. Suppose f*p = 5*p. Factor p + 0*z + 2/9*z**4 - 2/9*z**2 + 0*z**3.
2*z**2*(z - 1)*(z + 1)/9
Let b(s) be the first derivative of -3*s + 1/18*s**4 - 2 + 0*s**2 + 3/20*s**5 + 7/90*s**6 + 0*s**3. Let x(f) be the first derivative of b(f). Factor x(t).
t**2*(t + 1)*(7*t + 2)/3
Let p(m) be the first derivative of m**4/4 - 2*m**3/3 + m**2/2 + 9. What is z in p(z) = 0?
0, 1
Suppose 0 = 2*t + 6*t - 24. Factor 0*l + 2/7*l**2 + 0 + 2/7*l**4 - 4/7*l**t.
2*l**2*(l - 1)**2/7
Let t be (1/(-2) - 3/(-6))/(-1). Suppose -2/3*p**3 + t - 2/3*p**2 + 2/3*p**4 + 2/3*p = 0. Calculate p.
-1, 0, 1
Let q(y) be the third derivative of y**5/30 + y**4/12 - 2*y**3/3 - 4*y**2. Let c(o) = -o**2 - o + 1. Let m(u) = -4*c(u) - q(u). Determine i so that m(i) = 0.
-1, 0
Let a(q) be the second derivative of q**7/126 - 7*q**6/90 + 17*q**5/60 - 17*q**4/36 + q**3/3 + 8*q. Factor a(d).
d*(d - 3)*(d - 2)*(d - 1)**2/3
Let c(v) be the first derivative of -v**7/840 + v**5/120 + v**3 + 1. Let o(i) be the third derivative of c(i). Factor o(p).
-p*(p - 1)*(p + 1)
Suppose -3*z + 3 - 15 = 0, -33 = -x + 5*z. Factor -4 - x + 12*k - 2*k**2 - 1.
-2*(k - 3)**2
Let w = -1 - -1. Let v = -104/7 - -340/21. Factor 4/3*u**2 + 11/3*u**3 - 3*u**5 - 2*u**4 - v*u + w.
-u*(u + 1)**2*(3*u - 2)**2/3
Let l(z) be the second derivative of -z**8/20160 - z**7/7560 - z**4/6 - 8*z. Let q(p) be the third derivative of l(p). Factor q(k).
-k**2*(k + 1)/3
Let i be (162/(-504))/((-6)/32). Factor 18/7*x**2 - i*x + 2/7.
2*(3*x - 1)**2/7
Let g(m) be the second derivative of -2*m**7/3 + 36*m**6/5 - 68*m**5/5 - 8*m**4 - 2*m + 10. Determine k, given that g(k) = 0.
-2/7, 0, 2, 6
Suppose -31 = -2*q + 5*d, 3*q + d - 25 = -4. Factor -1 + y + q*y**3 - 8*y**3 + y**2 - y**3 + 0*y**2.
-(y - 1)**2*(y + 1)
Let f = 22/7 + -169/56. Let x(m) be the second derivative of -m + 1/48*m**4 - f*m**2 + 0 + 0*m**3. Factor x(w).
(w - 1)*(w + 1)/4
Let y be -2 + 2 + 2 + 1. What is j in 2*j - 2*j**y + 2/3*j**4 - 4/3 + 2/3*j**2 = 0?
-1, 1, 2
Let s = 8/33 + -7/165. Find z, given that -s*z**3 + 0 + 0*z**2 + 0*z = 0.
0
Let -3/2*k**4 + 0 + 0*k + 0*k**3 + 0*k**2 + 1/2*k**5 = 0. Calculate k.
0, 3
Let m(o) = -4*o**2 - 6*o - 4*o + 4*o**2 - 4*o**3. Let c(l) = -l**3 - 3*l. Let f(j) = 14*c(j) - 4*m(j). Factor f(v).
2*v*(v - 1)*(v + 1)
Let c(k) be the second derivative of 2*k + 0*k**4 + 0*k**2 - 1/24*k**3 + 1/80*k**5 + 0. What is p in c(p) = 0?
-1, 0, 1
Suppose 5*p - 5*d - 20 = 0, 0 = 3*p + 5*d + 12 + 8. Suppose 5*c = h, 4*h - 5*c = -p*h. Find u, given that -2/7*u**4 + 4/7*u**3 + h*u**2 - 4/7*u + 2/7 = 0.
-1, 1
Factor 0*o + 1/6*o**3 + 0 - 1/2*o**2.
o**2*(o - 3)/6
Let p(s) be the second derivative of -s**4/16 + s**3/8 + 3*s**2/4 + 6*s. What is j in p(j) = 0?
-1, 2
Factor -9 + 14 - 25*c**2 + 2*c + 15*c**3 + 3*c.
5*(c