- 6 = 5*j, 3*w + 9 = 4*j. Let k(m) = -m**2 + m. Let h be k(j). Solve h + 2/3*s**2 - 7/3*s**3 + 4/3*s**4 + 1/3*s = 0.
-1/4, 0, 1
Let g be 2 + (16 - -2)/3. Let j = g - 5. Find v, given that -2*v + 0 + 2*v**j + 0 = 0.
-1, 0, 1
Determine z so that -11/5*z**5 - 24/5*z + z**2 - 9/5*z**4 + 7*z**3 + 4/5 = 0.
-2, -1, 2/11, 1
Let f(b) = 48*b**2 + 20*b + 3. Let d(c) = 96*c**2 + 39*c + 6. Let h(m) = -4*d(m) + 9*f(m). Factor h(s).
3*(4*s + 1)**2
Factor -55*a**2 + 2*a**5 - a + 51*a**2 - a + 4*a**4.
2*a*(a - 1)*(a + 1)**3
Let n(o) be the first derivative of 2*o**5/5 - 2*o**3/3 + 5. Factor n(q).
2*q**2*(q - 1)*(q + 1)
Suppose 5*h = 60 + 30. Factor 10*p**3 - 3 + h*p**2 + 7 - 9*p**4 + 11*p**4 + 14*p.
2*(p + 1)**3*(p + 2)
Let c(y) be the first derivative of -y**3/18 - y**2/12 - 9. Factor c(p).
-p*(p + 1)/6
Factor 211*g**4 + 36*g**5 - 65*g + 290*g**2 - 530*g**3 + 214*g**4 + 5 - 161*g**5.
-5*(g - 1)**3*(5*g - 1)**2
Let i(w) be the second derivative of -w**4/8 - 5*w**3/4 + 50*w. Find a such that i(a) = 0.
-5, 0
Let a(f) be the first derivative of -2*f**5/45 - 11*f**4/18 - 2*f**3/3 + 11*f**2/9 + 20*f/9 - 35. Determine z so that a(z) = 0.
-10, -1, 1
Let o(c) = -2*c**3 + c**2 + c - 1. Let q(y) = y**3. Let d(r) = -3*o(r) - 3*q(r). Factor d(u).
3*(u - 1)**2*(u + 1)
Let h = 7 + -4. Let k be ((-8)/h)/((-6)/9). Solve 5*q**3 - k*q**2 + 0*q - 2*q + q**3 + 0*q**3 = 0.
-1/3, 0, 1
Let o(c) = -19*c + 2. Let b be o(-1). Suppose -b + 1 = -5*a. Determine m, given that 2/9*m + 4/9 + 8/9*m**3 - 10/9*m**5 - 20/9*m**2 + 16/9*m**a = 0.
-1, -2/5, 1
Find d such that 8*d**2 - 3*d**2 - d**2 = 0.
0
Let a(p) be the second derivative of -p**4/114 + 2*p**3/57 + 43*p. Factor a(d).
-2*d*(d - 2)/19
Let q(k) be the second derivative of k**4/9 - 16*k**3/9 + 14*k**2/3 - 13*k. Determine t, given that q(t) = 0.
1, 7
Suppose -2*p + 7 = 1. Suppose k = -3*i - i + p, 2*i + 5*k = -21. Factor i*c**4 + 36/7*c**3 + 16/7*c + 40/7*c**2 + 2/7*c**5 + 0.
2*c*(c + 1)*(c + 2)**3/7
Let s be ((-2)/((-20)/(-6)))/(21/(-28)). Factor -s*n**3 - 2/5*n**2 + 0*n + 6/5*n**4 + 0.
2*n**2*(n - 1)*(3*n + 1)/5
Let q(w) be the second derivative of -2*w + 0*w**5 + 0 + 0*w**3 + 0*w**6 + 0*w**2 + 1/42*w**7 + 0*w**4. Solve q(o) = 0 for o.
0
Suppose 3*t = 8*t. Let q(u) be the first derivative of t*u**3 + 4/35*u**5 + 0*u - 1/21*u**6 + 1 + 0*u**2 - 1/14*u**4. Factor q(z).
-2*z**3*(z - 1)**2/7
Let s(d) = -3*d**3 + 2*d**2 - 9*d + 5. Suppose 3*u - 15 = -0*u. Let v(o) = -2*o**3 + 2*o**2 - 8*o + 4. Let x(z) = u*v(z) - 4*s(z). Factor x(a).
2*a*(a - 1)*(a + 2)
Let w(a) be the first derivative of -a**5/5 + a**4/2 + 3. Factor w(x).
-x**3*(x - 2)
Solve 7*p**4 + p**4 + 21*p**5 + 4*p**3 - 17*p**5 = 0.
-1, 0
Let q(k) = k**4 - k**2 - 1. Let v(m) = 5*m**5 - 6*m**4 - 80*m**3 - 184*m**2 - 165*m - 44. Let h(w) = -6*q(w) - v(w). Let h(a) = 0. Calculate a.
-2, -1, 5
Let d(i) be the first derivative of i**9/756 - i**8/84 + i**7/30 - i**6/30 + i**3 - 8. Let m(g) be the third derivative of d(g). Factor m(q).
4*q**2*(q - 3)*(q - 1)**2
Let s(j) be the second derivative of j**4/54 + j**3/9 + 2*j**2/9 + 11*j. What is m in s(m) = 0?
-2, -1
Let h = 9575/3 - 3150. Let i = h - 41. Determine n so that -4/3 - i*n**2 - 2*n = 0.
-2, -1
Let i be 39/30 + 0 + 2/(-4). Let i*t**3 + 0 + 2/5*t**2 + 0*t + 2/5*t**4 = 0. Calculate t.
-1, 0
Let n(m) be the second derivative of m**6/120 + m**5/40 + m**4/48 + 19*m. Determine h, given that n(h) = 0.
-1, 0
Let z(m) be the second derivative of -m**5/10 + m**4/3 + m**3 + 6*m. Factor z(x).
-2*x*(x - 3)*(x + 1)
Let i be (0/1)/(8 - (8 - 1)). Determine v, given that 0 - 3/4*v**2 + i*v - 1/4*v**3 = 0.
-3, 0
Suppose -4*y + 5*f = 24, 5*y - 5*f = -4*f - 30. Let c(v) = v + 9. Let z be c(y). Factor -r**2 + z*r**2 - r**3 + 0*r**3 - r**2.
-r**2*(r - 1)
Let g(w) be the second derivative of -w**6/6 + 5*w**5/4 - w - 6. Factor g(o).
-5*o**3*(o - 5)
Determine o, given that o - 5*o**5 + 0*o**4 - 3*o**4 + 0*o**3 - 3*o + 3*o**2 + 7*o**3 = 0.
-1, 0, 2/5, 1
Let c(l) be the third derivative of l**6/900 + l**5/450 - 4*l**2. Factor c(n).
2*n**2*(n + 1)/15
Let u be (-4)/(-18) - 70/(-9). Let j be (2/2)/(u/80). Factor 8*p**2 + p**4 - 5*p**2 - j*p**4 - 6*p**5.
-3*p**2*(p + 1)**2*(2*p - 1)
Let s = 56 - 137. Let k = 259/3 + s. Let 8/3*b - 1/3 - k*b**2 = 0. Calculate b.
1/4
Let k(m) be the first derivative of m**9/5040 + 3*m**8/2800 + 3*m**7/1400 + m**6/600 - m**3/3 - 2. Let r(x) be the third derivative of k(x). Factor r(q).
3*q**2*(q + 1)**3/5
Let -2/7*s**2 + 0 + 2/7*s = 0. What is s?
0, 1
Let b = 92321452/195 + -473442. Let x = -2/195 + b. Factor 2/3*n**2 + 2/3*n**4 + 0*n - x*n**3 + 0.
2*n**2*(n - 1)**2/3
Let n = -431 - -3883/9. Let k = -17 - -17. Factor k - 2/9*b**2 - n*b.
-2*b*(b + 2)/9
Let r = 81 - 77. Factor -3/2*j + 3/4*j**r - 3/4*j**2 + 0 + 3/2*j**3.
3*j*(j - 1)*(j + 1)*(j + 2)/4
Let v(u) = -u**2 + 6*u + 10. Let i be v(7). Suppose 0 = -i*w - 0*w. Factor 1/2*g**2 + 0 + 1/4*g**3 + w*g.
g**2*(g + 2)/4
Suppose -4*u + 19 = p, 2*u = -4*p + 2*p + 14. Suppose -2*i - 5*b + 31 = 0, b + 4 = -i + u*i. Factor -2*k**2 + 2*k**i - 4 - 4*k**2 - 2*k**2 + 10*k.
2*(k - 2)*(k - 1)**2
Let t(i) = -8*i**4 - i**3 + 21*i**2 - 7*i - 5. Let s(r) = 39*r**4 + 6*r**3 - 105*r**2 + 36*r + 24. Let f(q) = -5*s(q) - 24*t(q). Factor f(j).
-3*j*(j - 1)**2*(j + 4)
Let o(k) be the second derivative of 5*k**7/14 + 7*k**6/6 - 7*k**5/4 - 25*k**4/4 + 20*k**3/3 + 10*k**2 - k. Let o(y) = 0. Calculate y.
-2, -1/3, 1
Let y = -22 - -24. Let a(d) be the second derivative of 0*d**4 + 3*d + 1/4*d**3 + 0*d**y - 3/40*d**5 + 0. Determine c, given that a(c) = 0.
-1, 0, 1
Suppose -2/3 + 2/3*x**2 + 0*x = 0. Calculate x.
-1, 1
Let a(g) = -3*g - 10. Let q be a(-5). Let b(i) be the third derivative of -1/6*i**4 + 0*i + 1/30*i**q + 1/3*i**3 + 3*i**2 + 0. Factor b(r).
2*(r - 1)**2
Determine f so that -4/7*f**2 - 12/7*f**4 - 4/7*f**5 - 12/7*f**3 + 0*f + 0 = 0.
-1, 0
Factor -5*y**4 - 1 - 5*y + 2*y**3 + 3*y**3 - 8 + 15*y**2 - 1.
-5*(y - 2)*(y - 1)*(y + 1)**2
Suppose -3*q - 2*q = -15. Factor 3*x + q*x**2 - 3*x**3 - 3*x**2.
-3*x*(x - 1)*(x + 1)
Let m(h) be the first derivative of h**5/2 + 15*h**4/16 - 5*h**3/4 - 5*h**2/4 + 8. Determine q, given that m(q) = 0.
-2, -1/2, 0, 1
Let y(s) = s. Let j be y(-5). Let m be (3 - 0) + j/4. Find k, given that 0 - 3/4*k**2 + 5/4*k**5 - m*k**3 + 3/4*k**4 + 1/2*k = 0.
-1, 0, 2/5, 1
Suppose 4*l + 4*l = 3*l. Let g(j) be the second derivative of -j - 1/15*j**3 + l - 1/30*j**4 + 0*j**2. Factor g(z).
-2*z*(z + 1)/5
Let f(g) = 10*g**2 + 60*g + 175. Let r(z) = z**2 - 1. Let c(p) = -f(p) + 5*r(p). Suppose c(j) = 0. What is j?
-6
Let r(n) = 9*n**3 - 21*n**2 + 20*n - 13. Let v(m) = 4*m**3 - 10*m**2 + 10*m - 6. Let z(f) = 4*r(f) - 10*v(f). Factor z(x).
-4*(x - 2)*(x - 1)**2
Let a(w) = 3*w**2 - 15*w + 3. Let v(h) = h**2 - 4*h + 1. Let j(b) = 2*a(b) - 9*v(b). Suppose j(u) = 0. What is u?
1
Let r(i) = i**2 - 6*i - 15. Let d be r(8). Let b(x) be the first derivative of -2/5*x**5 + x**4 - 2*x**2 - d + 2*x + 0*x**3. Find s, given that b(s) = 0.
-1, 1
Let w = 4 - 5. Let n = 4 + w. Factor 1/4*a**4 - 1/4*a + 1/4*a**n + 0 - 1/4*a**2.
a*(a - 1)*(a + 1)**2/4
Let n(f) be the second derivative of f**5/30 - f**3/9 + 6*f. Factor n(a).
2*a*(a - 1)*(a + 1)/3
Let p(n) be the first derivative of n**4/24 + n**3/18 - n**2/12 - n/6 + 10. Factor p(m).
(m - 1)*(m + 1)**2/6
Suppose 0*t = -3*t + 9. Let m = -198 + 596/3. What is i in 0 - m*i + 0*i**2 + 2/3*i**t = 0?
-1, 0, 1
Let g(t) = -2*t - 5. Let v be g(-4). Let a be 0 + (-1)/(v/(-9)). Factor 2*h**2 + 2*h + h**a + 2*h - 3*h.
h*(h + 1)**2
Let r(c) be the first derivative of -c**4 + 52*c**3/3 - 46*c**2 + 44*c + 60. Factor r(z).
-4*(z - 11)*(z - 1)**2
Factor -79*k**3 - 9*k**2 - 2*k + 3*k**4 + 82*k**3 + 6 - k.
3*(k - 1)**2*(k + 1)*(k + 2)
Let p(t) be the second derivative of -2*t**3 + 5/12*t**5 + 0 + 7*t + 4/3*t**2 + 5/6*t**4. Factor p(z).
(z + 2)*(5*z - 2)**2/3
Let j(z) be the second derivative of -1/56*z**7 - z - 1/8*z**4 + 1/40*z**6 - 1/8*z**3 + 3/8*z**2 + 0 + 3/40*z**5. Factor j(w).
-3*(w - 1)**3*(w + 1)**2/4
Let l(f) be the second derivative of -f + 0 + 1/4*f**4 + 0*f**2 + 0*f**3. Factor l(r).
3*r**2
Suppose -46 = -5*h + 4. Let m be (-1)/h*60/(-8). Solve 0 - m*r**5 + 2*r**4 + 0*r + 1/2*r**2 - 7/4*r**3 = 0.
0, 2/3, 1
Factor 14*o**2 + 10*o**2 - 45*o - 5*o**3 + 6*o**2.
-5*o*(o - 3