(b) be the third derivative of b**5/60 + 2*b**2. Determine u so that z(u) = 0.
0
Let u be 1/((-2)/8) - -4. Let a(o) be the first derivative of 1 + u*o - 1/6*o**3 - 1/4*o**2. Factor a(w).
-w*(w + 1)/2
Let n(k) be the third derivative of 0*k - 21/20*k**5 - 1/14*k**7 - 17/40*k**6 - 11/8*k**4 + k**2 - k**3 + 0. Suppose n(x) = 0. Calculate x.
-1, -2/5
Let y(v) be the first derivative of 3*v**4/4 - 5*v**3 + 12*v**2 - 12*v + 7. Factor y(m).
3*(m - 2)**2*(m - 1)
Suppose 125 = 19*f + 68. Factor 0*b**2 + 1/5*b**f - 4/5*b + 0.
b*(b - 2)*(b + 2)/5
Find g, given that 2/5*g**5 - 2*g**4 + 0 + 18/5*g**2 + 0*g + 6/5*g**3 = 0.
-1, 0, 3
Let v(m) = m**2 - 1. Let u(l) = 4*l**2 + l - 5. Suppose -5*h + 4*i = 2*i - 5, 11 = -3*h + 4*i. Let q(w) = h*u(w) - 15*v(w). Factor q(f).
-3*f*(f - 1)
Let f(d) be the first derivative of -d**4/24 - d**3/18 + d**2/12 + d/6 + 56. Determine m, given that f(m) = 0.
-1, 1
Let m(r) be the third derivative of 0*r**3 + 0*r - 1/525*r**7 + 0*r**4 + 1/150*r**5 + r**2 + 0 - 1/300*r**6 + 1/840*r**8. Determine b so that m(b) = 0.
-1, 0, 1
Let t = 20 - 18. Suppose 0 = 3*x + x + 20, 0 = t*n + x + 1. Solve -8/9*q - 2/3*q**n + 8/9 = 0.
-2, 2/3
Suppose -2*h = -v, 0 = -v + 6*v. Let x = h + 3. Suppose -3*m**2 + x*m + 0*m**3 + 2*m**3 - m**3 - 1 = 0. What is m?
1
Factor 120*u**3 + 114*u**3 - 229*u**3 + 35*u**2.
5*u**2*(u + 7)
Let 26*t**2 + 65*t**3 + 21*t + 56*t**2 + 5*t**5 - 22*t**2 - t + 30*t**4 = 0. Calculate t.
-2, -1, 0
Suppose 4/5*q**3 + 0 + 8/5*q**2 + 4/5*q = 0. What is q?
-1, 0
Let r(d) = -d**3 - 13*d**2 - 10*d + 15. Let g be r(-12). Let l be g/15 + (-21)/(-10). Factor -l*z - 3/2*z**2 + 3/2*z**4 + 3/2*z**3 + 0.
3*z*(z - 1)*(z + 1)**2/2
Let n(m) be the second derivative of 5*m**3 + 0 - 4*m**4 - 2*m**2 - 8/5*m**5 - 7*m. Factor n(o).
-2*(o + 2)*(4*o - 1)**2
Let n(u) be the first derivative of 1/6*u**3 + 1/24*u**4 + 0*u + 1 + 1/240*u**5 - 1/2*u**2. Let h(r) be the second derivative of n(r). Solve h(x) = 0.
-2
Let s = -1 + 5. Factor -8 + 3*i**2 - 14*i**3 + s + 13*i**3.
-(i - 2)**2*(i + 1)
Factor -2*g**3 - 6*g + 3*g + g**3 + 4*g.
-g*(g - 1)*(g + 1)
Let h(d) = -10*d**4 - 6*d**3 - 2*d**2 - 2*d. Let t(o) = -o**5 + 51*o**4 + 29*o**3 + 11*o**2 + 11*o. Let i(x) = 22*h(x) + 4*t(x). Determine u so that i(u) = 0.
-2, 0
Suppose -2*u - g - 8 = -24, -4*g = -u - 10. Let h be 9/u - 1/(-2). Suppose -8 - 2*j**2 + 3*j**h - 8*j - j**2 - 2*j**2 = 0. What is j?
-2
Suppose -3*a = -8*a - 25. Let k = a - -9. Suppose -5*d**3 - 2 + k*d**3 - 2 - 5*d**2 - 2*d - 6*d = 0. What is d?
-2, -1
Let s = 1 - -1. Let j(n) = -n**2 + 3*n + 4*n**2 - s*n - 4*n. Let h(o) = 12*o**2 - 13*o + 1. Let l(y) = 4*h(y) - 18*j(y). Find w, given that l(w) = 0.
-2/3, 1
Suppose -16 = 4*s - 40. Let h(l) be the second derivative of 0*l**4 + 1/120*l**s + 2*l + 0*l**3 - 1/80*l**5 + 0 + 0*l**2. Factor h(u).
u**3*(u - 1)/4
Let g(j) be the first derivative of j**8/672 - j**6/120 + j**4/48 - j**2 + 3. Let t(a) be the second derivative of g(a). Solve t(l) = 0 for l.
-1, 0, 1
Let h(s) be the third derivative of -2*s**7/735 - s**6/210 - 24*s**2. Factor h(f).
-4*f**3*(f + 1)/7
Suppose 0 = -4*k + 3*k + 4. Suppose -k*j = j - 10. Let 1/3*p + 1/3*p**j - 1/3*p**3 - 1/3 = 0. Calculate p.
-1, 1
Let i be 25/10 - 2/4. Let c(f) be the first derivative of 0*f + 0*f**i - 1/15*f**6 + 0*f**5 + 0*f**3 + 1 + 1/10*f**4. Factor c(b).
-2*b**3*(b - 1)*(b + 1)/5
Let j(i) = -10*i**2 + 13*i - 7. Let s(t) = -19*t**2 + 27*t - 13. Let q(l) = -5*j(l) + 3*s(l). Let q(z) = 0. Calculate z.
2/7, 2
Let g(l) be the second derivative of 1/15*l**5 + 0 - 1/60*l**6 - l - 3/2*l**2 - 1/12*l**4 + 0*l**3. Let n(c) be the first derivative of g(c). Factor n(p).
-2*p*(p - 1)**2
Let l = -144/7 + 1324/63. Let i(k) be the third derivative of 0*k - 1/9*k**4 + 0 + 1/90*k**5 + l*k**3 - 3*k**2. Factor i(b).
2*(b - 2)**2/3
Let b(t) be the third derivative of t**6/40 - t**5/15 + t**4/24 + 3*t**2. Determine m so that b(m) = 0.
0, 1/3, 1
Let h(r) be the second derivative of r**5/90 - r**4/18 + 2*r**3/27 + 3*r + 1. What is s in h(s) = 0?
0, 1, 2
Let p(j) = j**3 + j. Let o be p(1). What is b in 0*b - 4 + o*b**3 + 3*b - 26*b**2 - 10*b**3 - 25*b = 0?
-2, -1, -1/4
Let s(j) = -7*j**4 - 21*j**3 - 54*j**2 - 60*j - 24. Let b(a) = a**4. Let k(n) = 4*b(n) + s(n). Solve k(d) = 0 for d.
-2, -1
Let y(b) = -b + 17. Let l be y(14). Factor -3*m**4 - 13*m - 9*m**l + 10*m + 1 - 9*m**2 - 1.
-3*m*(m + 1)**3
Suppose 22/3*i**3 - 2/3*i**4 - 70/3*i**2 + 50/3*i + 0 = 0. What is i?
0, 1, 5
Let c(p) be the second derivative of -p**6/30 + 3*p**5/4 - 4*p**4 - 32*p**3/3 + p. Find g such that c(g) = 0.
-1, 0, 8
Let h(b) = -3*b**2 + b - 2. Let s(n) = 2*n**2 - n + 2. Let a(o) = 3*h(o) + 4*s(o). Factor a(z).
-(z - 1)*(z + 2)
Let s(b) = -b**3 + 4*b**2 + 6*b - 5. Let x be s(5). Suppose -4*o = -23 + 3. Suppose 0*z**4 + x*z**2 + 0 - 1/2*z + z**3 - 1/2*z**o = 0. Calculate z.
-1, 0, 1
Let l(i) be the first derivative of -i**4/26 - 2*i**3/13 + 8*i/13 + 2. Solve l(a) = 0.
-2, 1
Suppose -2*s - 12 = -5*s. Let l be (-30)/((-1)/s*6). Let -l*z**2 + 4*z - z + z**3 + 2 - 22*z**3 = 0. Calculate z.
-1, -2/7, 1/3
Let n(y) be the third derivative of -y**6/24 - y**5/4 - 5*y**4/12 - 13*y**2. Factor n(c).
-5*c*(c + 1)*(c + 2)
Let o(x) be the second derivative of -x**5/25 + x**4/30 + 4*x**3/15 - 3*x**2/2 - 3*x. Let f(u) be the first derivative of o(u). Solve f(q) = 0.
-2/3, 1
Let y(o) be the first derivative of -o**4/20 - 8*o**3/5 - 96*o**2/5 - 512*o/5 - 18. Factor y(t).
-(t + 8)**3/5
Let u(t) = 2*t + 4*t + t**2 + 0*t**2 + 5*t**2 - 11. Let m(w) = w**2 + w - 2. Let b(h) = 22*m(h) - 4*u(h). Factor b(s).
-2*s*(s + 1)
Let a = -4 - -7. Suppose -z = a*z - 16. Factor u**5 + u - u**4 - 3*u**z + 6*u**3 + 0*u**4 - 4*u**2.
u*(u - 1)**4
Let y be 2/(-5 - -1)*-2. Factor 0*d**3 - y + 3*d - 2*d**3 + d**4 - d.
(d - 1)**3*(d + 1)
Let a = 13 - 7. Let r be a - (1 - (-1 - 0)). Factor -r + 5 - 3 - 2*o**2 + 6*o - 2.
-2*(o - 2)*(o - 1)
Let d(t) be the third derivative of t**6/480 + t**5/240 - t**4/48 + 6*t**2. Factor d(a).
a*(a - 1)*(a + 2)/4
Let u(k) be the second derivative of -k**4/6 + k**3/3 + 12*k. What is h in u(h) = 0?
0, 1
Suppose -2/13 + 16/13*p - 14/13*p**2 = 0. What is p?
1/7, 1
Let h(y) = 6*y**2 - 12*y - 4. Let g(u) = -5*u**2 + 11*u + 4. Let j(v) = 2*g(v) + 3*h(v). Suppose j(p) = 0. What is p?
-1/4, 2
Suppose 0 = 2*p - 23 + 7. Suppose -24*r + 20*r + p = 0. Suppose 1 + 1/2*y**r - 3/2*y = 0. What is y?
1, 2
Let v = -1 - -1. Find n such that 2/5*n**3 - 2/5*n**5 + 0 + 0*n**2 + v*n**4 + 0*n = 0.
-1, 0, 1
Factor -4 + 4 + c**3 - 3*c**3 - 2*c**4.
-2*c**3*(c + 1)
Suppose -2*a - 5*t = -a - 55, 3*a - 2*t - 114 = 0. Factor v**4 - 40 + v**3 + a.
v**3*(v + 1)
Let g(l) be the first derivative of l**6/540 + l**5/60 + 4*l**3/3 + 10. Let q(o) be the third derivative of g(o). Factor q(j).
2*j*(j + 3)/3
Let f = 667 + -658. Factor -f*l - 3/2*l**2 - 27/2.
-3*(l + 3)**2/2
Let b(c) be the first derivative of 0*c**2 - 8/15*c**5 + 3 + 5/6*c**4 - 4/9*c**3 + 1/9*c**6 + 0*c. Factor b(k).
2*k**2*(k - 2)*(k - 1)**2/3
Let b(r) be the third derivative of -1/1440*r**6 + 1/6*r**3 + r**2 - 1/120*r**5 + 0 + 0*r - 1/24*r**4. Let s(q) be the first derivative of b(q). Factor s(o).
-(o + 2)**2/4
Suppose 2*t = -s + 2, 0 = -s - 5*t - 2 + 7. Suppose 2/3*h**4 + 2/3*h**5 - 2/3*h**3 + 0 - 2/3*h**2 + s*h = 0. Calculate h.
-1, 0, 1
Let k(m) be the third derivative of -m**5/12 + 15*m**4/8 - 20*m**3/3 - 8*m**2. Factor k(y).
-5*(y - 8)*(y - 1)
Factor 5*j**3 + 64*j + 13 + 32*j**2 - 13 - j**3.
4*j*(j + 4)**2
Let c be (-8)/(0 + -3 - -1). Factor -q**5 + 4*q**2 + 2*q**3 - q + 0*q - c*q**2.
-q*(q - 1)**2*(q + 1)**2
Suppose -6*q + 4*q = 4*q. Let y(z) be the first derivative of -1/2*z**6 + 0*z**3 - 3/5*z**5 + 0*z + 2 + q*z**2 + 0*z**4. Find h, given that y(h) = 0.
-1, 0
Let x(l) = -2*l**3 - 4*l**2 + 4*l - 4. Let f(q) = 2*q**3 + 5*q**2 - 5*q + 5. Let w(m) = 4*f(m) + 5*x(m). Factor w(p).
-2*p**3
Let b(t) be the second derivative of -t**5/10 - t**4/3 + t**3/3 + 2*t**2 - 4*t. Factor b(s).
-2*(s - 1)*(s + 1)*(s + 2)
Let s(g) = -g**3 + 5*g**2 + g + 2. Let h be s(5). Suppose h*y - 2*y = 40. Factor 0*w + 2*w + 2*w**2 - 10*w + y.
2*(w - 2)**2
Suppose -3*c - 5 + 11 = 0. Let s(g) be the first derivative of 3 - 4/15*g**3 + 0*g + 0*g**4 + 1/5*g**c - 1/15*g**6 + 4/25*g**5. Factor s(n).
-2*n*(n - 1)**3*(n + 1