*o(n). Determine f so that j(f) = 0.
0
Factor 0 + 1/4*h**2 + 1/4*h**3 - 1/4*h**4 - 1/4*h.
-h*(h - 1)**2*(h + 1)/4
Let t(p) be the third derivative of -p**6/40 + 3*p**5/10 + 7*p**4/8 - 38*p**2. Factor t(u).
-3*u*(u - 7)*(u + 1)
Determine o, given that 2/11*o**3 + 8/11 - 2/11*o**2 - 8/11*o = 0.
-2, 1, 2
Let x(i) = i**2 - 5*i + 1. Let a be x(5). Find o, given that 0*o + o**2 + 0*o - a = 0.
-1, 1
Let r(k) be the second derivative of -k**6/480 - k**5/240 - 4*k**2 - 3*k. Let w(a) be the first derivative of r(a). What is n in w(n) = 0?
-1, 0
Let j(n) be the first derivative of -n**6/540 - n**5/54 - 7*n**4/108 - n**3/9 + n**2 - 10. Let v(m) be the second derivative of j(m). Factor v(o).
-2*(o + 1)**2*(o + 3)/9
Find h, given that 6/5*h**4 + 2/5*h**5 + 2/5*h - 4/5*h**3 + 6/5 - 12/5*h**2 = 0.
-3, -1, 1
Let l(r) be the second derivative of r**2 + 0 + 0*r**3 + 4*r + 1/15*r**6 - 1/3*r**4 + 0*r**5. Suppose l(n) = 0. Calculate n.
-1, 1
Let n(u) = 14*u**2 + 6*u + 6. Let t(x) = -x**2 - 1. Let y(c) = n(c) + 10*t(c). Factor y(v).
2*(v + 2)*(2*v - 1)
Let d(s) be the third derivative of -s**11/997920 + s**9/90720 - s**7/15120 - s**5/12 + 2*s**2. Let w(c) be the third derivative of d(c). Factor w(n).
-n*(n - 1)**2*(n + 1)**2/3
Suppose -3*n**3 + 9*n**2 + 12*n - 9*n - n**2 = 0. Calculate n.
-1/3, 0, 3
Solve -2/5*g + 0*g**3 + 0 + 4/5*g**4 - 4/5*g**2 + 2/5*g**5 = 0.
-1, 0, 1
Let l be 8/2 - (-30)/(-12). Factor 0 + 1/2*x**3 + x - l*x**2.
x*(x - 2)*(x - 1)/2
Let y(k) = -k**3 + 2*k**2 + 3*k + 2. Let s be y(-1). Suppose 2/7*a**s - 2/7*a**4 - 2/7*a**3 + 2/7*a**5 + 0*a + 0 = 0. Calculate a.
-1, 0, 1
Let a(g) be the first derivative of 7/3*g**6 + 1 + 46/5*g**5 + 27/2*g**4 + 26/3*g**3 + 2*g**2 + 0*g. Factor a(r).
2*r*(r + 1)**3*(7*r + 2)
Suppose o - 2 - 2 = 0. Factor -c**4 - c**o + 3*c**3 + c**3 - 4*c + 4*c**4 - 2.
2*(c - 1)*(c + 1)**3
Let o(r) be the third derivative of 0*r**4 + 2*r**2 + 0 + 0*r + 0*r**6 + 0*r**5 + 1/840*r**7 + 0*r**3. Determine y, given that o(y) = 0.
0
Let r = -8 + 13. Suppose -r*i - 3*x + 27 = -0*i, -4*x = -4*i - 4. Suppose 2/3*g + 0*g**2 - 2/9*g**i + 4/9 = 0. What is g?
-1, 2
Factor 0 + 2/9*x**3 + 0*x - 2/9*x**2.
2*x**2*(x - 1)/9
Suppose -2*i - 4 = 5*v, 2*i + 0 = 3*v + 12. Factor -g**2 - 2*g - 5 + 0*g + 2*g**3 + i + 3*g**2.
2*(g - 1)*(g + 1)**2
Let f = 3 + -1. Let i = -5/3 + f. Factor 1/3*u**3 + 2/3*u**2 + 0 + i*u.
u*(u + 1)**2/3
Let x be -9 - -11 - (-1 - 1/(-3)). Suppose -7*h**3 - 1/3*h - 22/3*h**4 + 0 - 8/3*h**2 - x*h**5 = 0. Calculate h.
-1, -1/2, -1/4, 0
Factor -42*r**4 + 30*r**4 + 4*r**2 - 3*r**3 + 7*r**5 - r**3 - 2 - 3*r + 10*r**2.
(r - 1)**3*(r + 1)*(7*r + 2)
Let c(x) = -x**2 + 5*x - 4. Let i be c(3). Factor -4*u - 2*u**i - 5 + 13 - 10.
-2*(u + 1)**2
Let p(j) = j**3 - 9*j**2 + j - 9. Suppose -3*u - 1 + 28 = 0. Let r be p(u). Solve -2 + 3*q + 2*q**3 + r*q**2 - 6*q**2 + 3*q = 0.
1
Let j(m) be the first derivative of -3/2*m**2 - 3/2*m**3 + 2 - 1/2*m. What is v in j(v) = 0?
-1/3
Let w(f) be the second derivative of 0 + f**2 + f - 1/120*f**5 - 1/24*f**4 + 0*f**3. Let o(q) be the first derivative of w(q). What is s in o(s) = 0?
-2, 0
Let t(p) be the third derivative of -p**5/45 + 11*p**4/18 - 20*p**3/9 - 13*p**2. Factor t(r).
-4*(r - 10)*(r - 1)/3
Let b(s) be the first derivative of 2*s**5/85 + 3*s**4/17 + 26*s**3/51 + 12*s**2/17 + 8*s/17 - 38. Factor b(h).
2*(h + 1)**2*(h + 2)**2/17
Let k(m) = -m - 1. Let h(v) = -v**2 - 5*v - 4. Let l(z) = 4*h(z) - 20*k(z). Factor l(c).
-4*(c - 1)*(c + 1)
Let y be -1*(2 + -3 + 2). Let q(j) = j**3 + j**2 - j - 1. Let r(l) = 5*l**3 + l**2 - 5*l - 1. Let b(c) = y*r(c) + q(c). What is o in b(o) = 0?
-1, 0, 1
Suppose 0 = -7*s - 4*s + 13*s. Let l(v) be the third derivative of 0 + 4*v**2 - 1/660*v**6 + 0*v**4 - 1/330*v**5 + 0*v + s*v**3. Let l(z) = 0. What is z?
-1, 0
Let g(o) be the third derivative of -3*o**5/8 + 13*o**4/16 - o**3/2 - o**2. Factor g(w).
-3*(3*w - 2)*(5*w - 1)/2
Let d(r) = -r**2 + 2*r**2 + 0*r**2. Let m(q) = -q**2 - q. Let u(z) = 6*d(z) + 3*m(z). Find x such that u(x) = 0.
0, 1
Factor -2 + 14*b + 3*b**2 - 6*b - 7*b.
(b + 1)*(3*b - 2)
Suppose -4 = -3*j + 5. Let c(m) be the first derivative of 2/21*m**3 - j + 8/7*m - 4/7*m**2. Factor c(v).
2*(v - 2)**2/7
Let h(p) be the second derivative of 9*p**7/14 - 12*p**6/5 + 12*p**5/5 - 38*p. Find v such that h(v) = 0.
0, 4/3
Let s(a) = 94*a**5 + 180*a**4 + 34*a**3 - 41*a**2 + 11*a. Let q(v) = 19*v**5 + 36*v**4 + 7*v**3 - 8*v**2 + 2*v. Let u(d) = 11*q(d) - 2*s(d). Factor u(t).
3*t**2*(t + 1)**2*(7*t - 2)
Let b = 41/351 - -1/27. Find n, given that -b*n + 0 - 2/13*n**2 = 0.
-1, 0
Let n(c) be the first derivative of -c**6/10 + 16*c**5/25 - 8*c**4/5 + 2*c**3 - 13*c**2/10 + 2*c/5 + 7. Find q, given that n(q) = 0.
1/3, 1, 2
Let u = 163 - 649/4. Let 0 + u*y**2 - 1/2*y**3 - 1/4*y = 0. What is y?
0, 1/2, 1
Let k be -2 + (1 - -1) + 2. Factor -4/7 + 2/7*x**k + 2/7*x.
2*(x - 1)*(x + 2)/7
Suppose -3*g = -6*g. Let j be (-1 + (g - 0))*-4. Determine i so that 4/7 + 2/7*i**j + 18/7*i**2 + 2*i + 10/7*i**3 = 0.
-2, -1
Let f(m) be the first derivative of m**4/20 + 2*m**3/15 + m**2/10 - 3. Suppose f(j) = 0. Calculate j.
-1, 0
Let j(f) = -6*f**2 + 46*f - 116. Let n(t) = t**2 - 9*t + 23. Let b(a) = 3*j(a) + 16*n(a). Solve b(l) = 0.
-5, 2
Let y(s) = -s**3 + 20*s**2 + 42*s + 47. Let i be y(22). Factor -4/7*h - 6/7*h**2 + 0 - 2/7*h**i.
-2*h*(h + 1)*(h + 2)/7
Suppose 1 - 3 = -m. Factor 2*x**3 - 8*x**2 - x**3 + 2*x**2 + 5*x**m.
x**2*(x - 1)
Let x(o) be the first derivative of 2*o**5/65 - 2*o**3/13 - 2*o**2/13 + 60. Factor x(a).
2*a*(a - 2)*(a + 1)**2/13
Let m = -3 - -12. Factor 24*y**2 + m*y**4 + 3*y**3 - 6*y**3 - 3*y - 18*y**3 - 9*y**2.
3*y*(y - 1)**2*(3*y - 1)
Let m be (-2 + 40)/(4 - -4) + -4. Factor -m*s**3 + 3/4*s + 3/4*s**2 - 3/4.
-3*(s - 1)**2*(s + 1)/4
Let z(c) = -c + 24. Suppose 0 = m - 4*y + 20, -5*y - 2 + 27 = 2*m. Let b be z(m). Solve 45*n**3 + 41*n**4 - 33*n**2 + 6*n + n**4 - 18*n**3 - b*n**5 = 0 for n.
-1, 0, 1/4, 1/2, 2
Let j(l) = -2*l**3 - 2*l**2 - l + 4. Let g(v) = -v**3 - 3*v**2 - v + 5. Let t(n) = 3*g(n) - 4*j(n). Let b be t(1). Factor 0*r**2 + 0 + 2/3*r**b + 0*r + 0*r**3.
2*r**4/3
Let 2*w - 4/3*w**2 + 2/9*w**3 + 0 = 0. What is w?
0, 3
Factor 0 + 1/6*a**3 + 0*a + 1/6*a**2.
a**2*(a + 1)/6
Let o(x) be the second derivative of x**7/35 + x**6/60 - x**5/10 - x**4/12 - x**2/2 - 5*x. Let a(q) be the first derivative of o(q). Let a(n) = 0. Calculate n.
-1, -1/3, 0, 1
Let o(w) be the third derivative of w**7/2940 - w**3/3 + 3*w**2. Let q(u) be the first derivative of o(u). Factor q(z).
2*z**3/7
Let i(r) be the third derivative of r**5/30 + r**4/4 + 5*r**2. Let c be i(-3). Factor c*p + 0 - 2/5*p**2.
-2*p**2/5
Let c be (2/(-28) + 0)*84/(-42). Let v(b) be the second derivative of -1/70*b**5 + c*b**3 + 0*b**4 + 0 - 2/7*b**2 - 2*b. Let v(i) = 0. Calculate i.
-2, 1
Let y be 4/6*((-30)/(-8) - 3). Factor y*b + 1/2*b**2 + 0.
b*(b + 1)/2
Suppose 5*a - 4*b = 23, 0 = a + 3*a + 5*b - 2. Suppose -7/2*g**4 + 0 + 0*g - g**a + 0*g**2 = 0. Calculate g.
-2/7, 0
Factor -3/2*l**4 - l**5 + 1/2*l**2 + 0 + 0*l + 0*l**3.
-l**2*(l + 1)**2*(2*l - 1)/2
Let r(d) = -1. Let s(v) = 3*v**2 - 3*v + 6. Let y(w) = -6*r(w) - s(w). Determine g, given that y(g) = 0.
0, 1
Let v(x) be the first derivative of -x**4 + 0*x**3 + 0*x**5 + 0*x + 3 + x**2 + 1/3*x**6. Factor v(o).
2*o*(o - 1)**2*(o + 1)**2
Let c(n) be the first derivative of -n**9/10584 - n**8/5880 + 4*n**3/3 + 2. Let u(s) be the third derivative of c(s). Find d such that u(d) = 0.
-1, 0
Factor -3/8*x**3 + 0 + 3/4*x**2 - 3/8*x**4 + 0*x.
-3*x**2*(x - 1)*(x + 2)/8
Let q(s) be the third derivative of s**5/40 + s**4/16 + s**2. Factor q(j).
3*j*(j + 1)/2
Let f(k) be the third derivative of 2*k**7/105 + k**6/15 - k**4/3 - 2*k**3/3 - 3*k**2. Determine q, given that f(q) = 0.
-1, 1
Find q such that -5*q + 3*q - q**3 + q**2 + 0*q**4 - q**4 + 3*q = 0.
-1, 0, 1
Find i, given that -413 - i**2 + 413 = 0.
0
Find b, given that 0 + 2/19*b**5 - 6/19*b**2 + 2/19*b**3 - 4/19*b + 6/19*b**4 = 0.
-2, -1, 0, 1
Let q(w) be the third derivative of -w**8/504 + w**6/30 - 4*w**5/45 + w**4/12 + 14*w**2. Let q(t) = 0. Calculate t.
-3, 0, 1
Let a be (4 - 4)*(1 + -2). Determine i, given that a - 2/5*i - 2/5*i**2 = 0.
-1, 0
Let l(c) be the first derivative of -5 + 1/14*c**4 + 0*c**2 + 0*c**3 + 0*c. Fa