**2 - 1/3*k**4 + 2/3*k**3 - 2/3*k = 0.
-1, 1
Let g = 2 - 2. Let h be -1*1/2*g. Suppose -2/9*d**3 - 2/9*d**2 + h + 2/9*d + 2/9*d**4 = 0. What is d?
-1, 0, 1
Let x(p) = -6*p**3 - 13*p**2 - 9*p. Let z(g) = g**4 - g**2 - g. Let q(c) = c**3 - 6*c**2 + 4*c + 6. Let n be q(5). Let v(o) = n*z(o) - x(o). Factor v(i).
i*(i + 2)**3
Determine m so that 3/4*m**5 + 0 + 15/4*m**3 + 3/2*m**2 + 3*m**4 + 0*m = 0.
-2, -1, 0
Suppose 5*v = 2*v + 6. Factor 4*m**3 + 11*m**4 - 10*m**3 - m**2 - 2*m**4 - v*m**2.
3*m**2*(m - 1)*(3*m + 1)
Let q(s) be the third derivative of 1/480*s**6 + 0*s - 1/3*s**3 + 5*s**2 + 1/8*s**4 + 0 - 1/40*s**5. Factor q(r).
(r - 2)**3/4
Determine t, given that 0 + 0*t - 1/5*t**2 = 0.
0
Suppose 3*x - 8 = 2*r, x - 25 + 13 = 3*r. Let 0*a + 1/2*a**5 + 0*a**3 + x*a**2 + 0 + 1/2*a**4 = 0. Calculate a.
-1, 0
Let v(m) = 13*m**2 + 18*m - 24. Let b(n) = -4*n**2 - 6*n + 8. Let l(r) = -7*b(r) - 2*v(r). Factor l(a).
2*(a - 1)*(a + 4)
Suppose 0 = 3*n + 5*r - 2 - 1, 5*r + 4 = 4*n. Let w(i) = 3*i**3 - i + 1. Let b be w(n). Find o such that -5*o**3 + 4*o + o**3 + b*o**2 - 3*o + 0*o**3 = 0.
-1/4, 0, 1
Let x be 3 - ((-342)/14)/(-9). Determine y, given that 0 + 4/7*y**2 + 0*y - 2/7*y**3 - x*y**4 = 0.
-2, 0, 1
Suppose -2*c = -5*c. Let s be (-2 - (-1 + 0))*c. Factor s*z - 1/2*z**4 + 0 + 1/4*z**5 + 1/4*z**3 + 0*z**2.
z**3*(z - 1)**2/4
Suppose 9 = 4*x - l, l - 3*l - 6 = -2*x. Find q such that -2/5*q**x + 4/5 - 2/5*q = 0.
-2, 1
Factor 14*b**2 + 16*b**2 + 4*b**3 - 6*b**2.
4*b**2*(b + 6)
Let u(h) be the second derivative of -h**4/48 - h**3/3 - 7*h**2/8 - 6*h - 4. Find v such that u(v) = 0.
-7, -1
Let i(z) be the third derivative of -z**4/24 + z**3/3 - z**2. Let n be i(2). Factor 0*u + 5*u**2 - 2*u + n*u.
u*(5*u - 2)
Suppose 0 = -4*j - 4*t - 140, 2*t = j + 6*t + 23. Let p = -37 - j. Solve 0 + 1/4*r + 1/4*r**p = 0.
-1, 0
Let l be (-3 - 44/(-14))*2. Let d(v) be the first derivative of -l*v**2 - 2/21*v**3 - 2/7*v - 1. Let d(y) = 0. What is y?
-1
Let x(p) be the first derivative of p**6/27 - 4*p**5/45 + 4*p**3/27 - p**2/9 + 25. Determine l, given that x(l) = 0.
-1, 0, 1
Let w = -16 - -43. Factor 32*b**3 + 147*b**4 + 14*b + w - 78*b**2 + 87*b**3 - 86*b + 49*b**3.
3*(b + 1)**2*(7*b - 3)**2
Let r(y) be the third derivative of y**8/560 - 2*y**7/175 + y**6/100 + y**5/25 - 3*y**4/40 + 19*y**2. Find c, given that r(c) = 0.
-1, 0, 1, 3
Let s(x) = x**2 + x. Let g(m) = m + 2*m + m**2 + 2*m + 5*m**2. Let z(r) = -2*g(r) + 11*s(r). Factor z(i).
-i*(i - 1)
Let c(o) = 8*o**4 - 10*o**3 + 8*o**2 - 6. Let y(j) = -9*j**3 + 3*j**4 + 4*j**4 + 7*j**2 - 5 + 0*j**3. Let m(n) = -5*c(n) + 6*y(n). Factor m(i).
2*i**2*(i - 1)**2
Let y(h) be the second derivative of -h**7/630 + h**6/360 + h**5/360 - h**3/6 + 4*h. Let k(z) be the second derivative of y(z). Suppose k(x) = 0. What is x?
-1/4, 0, 1
Let g(q) be the first derivative of -q**4/8 + q**3/6 + q**2/2 + 5. Let g(m) = 0. What is m?
-1, 0, 2
Let n(m) be the first derivative of 0*m**2 + 0*m**4 + 0*m + 1 + 0*m**3 - 2/5*m**5 - 1/3*m**6. Determine k so that n(k) = 0.
-1, 0
Suppose 0 = 2*x + 5*t - 12, -4*x - 5*t + 13 = -x. Find n, given that -9*n**2 - 21*n - x - 5 + 2 - 2 = 0.
-2, -1/3
Solve -3*p**2 - p - p**3 + p**2 + 0*p + 0*p**2 = 0 for p.
-1, 0
Factor 30 + 5*v**3 - 5*v**2 - 42*v - 11*v + 13*v + 30.
5*(v - 2)**2*(v + 3)
Solve 0 + 2/3*x - 2/3*x**2 = 0 for x.
0, 1
Suppose -5*i - 6 = 4*a, 4*a = 3*i - 0*a - 22. Let -8*l**i - 5*l**5 - 10*l - 4*l**5 + 4*l**4 + 4 - l**5 + 20*l**3 = 0. Calculate l.
-1, 2/5, 1
Let o(c) be the second derivative of -c**4/48 + c**2/8 - 21*c. Factor o(p).
-(p - 1)*(p + 1)/4
Let h = -1/10 + 3/5. Factor 0*t + 0*t**3 + h*t**4 + 1/2*t**5 + 0 + 0*t**2.
t**4*(t + 1)/2
Let p(d) = 3*d + 9. Let v be p(-3). Suppose -1/4*i**2 + v*i + 0 = 0. What is i?
0
Let r be 60/9*12/15. Factor -7*v**3 + 1/3*v**2 + 4/3 + r*v.
-(v - 1)*(3*v + 2)*(7*v + 2)/3
Let j(h) be the third derivative of -1/840*h**7 - 1/96*h**4 + 0 - 3*h**2 + 0*h + 0*h**3 + 1/480*h**6 + 1/240*h**5. Factor j(r).
-r*(r - 1)**2*(r + 1)/4
Let m(t) be the third derivative of -t**7/42 + t**6/8 - t**5/4 + 5*t**4/24 - 7*t**2. Factor m(l).
-5*l*(l - 1)**3
Let s = 589 + -587. Let -1/2*z**s + 1/2*z + 1 = 0. Calculate z.
-1, 2
Let y be 4/6*(-3 + 6). Suppose 5*p = -2*b + 19, 8*b = -3*p + 3*b + 19. Factor -27*i**4 - 9*i**2 + 18*i**p - 2*i**y + 12*i**5 + 8*i**2.
3*i**2*(i - 1)**2*(4*i - 1)
Factor 0 - 3/8*f**2 + 3/2*f.
-3*f*(f - 4)/8
Let d(a) be the third derivative of 1/20*a**5 - 2*a**2 + 0 + 0*a**4 + 1/120*a**6 - 2/3*a**3 + 0*a. Let k(u) be the first derivative of d(u). Factor k(j).
3*j*(j + 2)
Let g(i) be the third derivative of i**8/112 - i**7/5 + 49*i**6/40 - i**2 + 11*i. Solve g(q) = 0.
0, 7
Suppose -2*u + 35 = 5*q, 0 = 4*q - 5*u + 5. Suppose 3*l + l = -4*b + 16, q*l = -5. Find m such that -b + 6 - 2*m**5 - 4*m**2 - m**4 + 4*m**4 + 2*m**3 = 0.
-1, -1/2, 1
Factor 0 - 8*c + 2 + 10 - 15*c**2 + 65*c.
-3*(c - 4)*(5*c + 1)
Let i(g) = -8*g + 34. Let a be i(4). Factor 12/5*x**a - 4/5*x**3 - 8/5*x + 0.
-4*x*(x - 2)*(x - 1)/5
Let v be 1 - (1/18 + 4/(-8)). Let n(k) be the second derivative of 4/3*k**4 + 0 + v*k**3 - k + 3/10*k**5 + 2/3*k**2. Determine m, given that n(m) = 0.
-2, -1/3
Suppose 17*n + 11*n - 84 = 0. Factor 4*d - 1 - 15/4*d**2 + 5/4*d**4 - 1/2*d**n.
(d - 1)**2*(d + 2)*(5*d - 2)/4
Let g = -7 + 16. Let k be (6/g*-3)/(-1). Factor 4*x**2 - 4*x**2 + 2*x**k.
2*x**2
Let w(z) be the first derivative of 2/5*z**2 + 8/5*z**4 + 0*z - 14/25*z**5 + 1 - 22/15*z**3. Factor w(o).
-2*o*(o - 1)**2*(7*o - 2)/5
Let u(a) be the third derivative of a**7/70 + a**6/4 - a**2. Factor u(z).
3*z**3*(z + 10)
Let w = -5 - 5. Let q be (-9 + 8)*4/w. Find f, given that 3/5*f**4 + 0 + f**3 - q*f**2 + 0*f = 0.
-2, 0, 1/3
Let -1/3*r**2 + 0 + 0*r + 1/3*r**4 - 1/6*r**5 + 1/6*r**3 = 0. What is r?
-1, 0, 1, 2
Let i(y) be the second derivative of 0 + 0*y**5 + 0*y**3 + 1/24*y**4 + 0*y**2 - 1/60*y**6 - y. What is l in i(l) = 0?
-1, 0, 1
Let l be 6/((-1)/1 + 3). Suppose 0 = l*m + 1 - 7. Factor -5*n + 4*n**2 + 0 - n**3 + m + 0*n.
-(n - 2)*(n - 1)**2
Factor -38*d**3 - 2 - 22*d**4 - 18*d**2 - 2*d**2 - 12*d**2 - 5*d**5 - 13*d.
-(d + 1)**4*(5*d + 2)
Let p(w) = 7*w**5 + 9*w**4 + 3*w**3 - 5*w**2 + 6*w. Let o(d) = -6*d**5 - 8*d**4 - 3*d**3 + 4*d**2 - 5*d. Let a(u) = -6*o(u) - 5*p(u). What is q in a(q) = 0?
-1, 0
Factor -2/9*f**2 - 2/3*f**3 - 2/3*f**4 + 0 - 2/9*f**5 + 0*f.
-2*f**2*(f + 1)**3/9
Let i(f) be the third derivative of -4/33*f**3 - 1/330*f**5 - 7*f**2 + 1/33*f**4 + 0*f + 0. Solve i(l) = 0 for l.
2
Let r(d) be the third derivative of d**6/40 + d**5/5 + d**4/2 - 7*d**2. Let r(i) = 0. Calculate i.
-2, 0
Let -15/2*c**4 - 5/2*c**5 + 0 + 0*c - 5/2*c**2 - 15/2*c**3 = 0. What is c?
-1, 0
Suppose -13*k + 7*k = 8*k. Determine r, given that 0*r + 2/3 + k*r**3 - 4/3*r**2 + 2/3*r**4 = 0.
-1, 1
Let a(j) be the second derivative of -j**4/66 - 10*j**3/33 - 25*j**2/11 + 5*j. Suppose a(g) = 0. What is g?
-5
Let v(h) be the first derivative of 0*h**3 - 2/25*h**5 - 1/10*h**2 + 3/20*h**4 - 1 + 0*h. Factor v(o).
-o*(o - 1)**2*(2*o + 1)/5
Let 23*d**5 - 4*d**3 + 6*d**5 - 16*d**4 - 41*d**5 = 0. What is d?
-1, -1/3, 0
Let o(a) = 2*a**2 + 2*a - 2. Let f be o(3). Suppose -4*z = -f - 18. Factor 4*j + 2*j**4 - 6*j**2 - z*j**3 + 10*j**3.
2*j*(j - 1)**2*(j + 2)
Let x(w) be the first derivative of w**5 - 5*w**4/2 - 35*w**3/3 - 10*w**2 - 47. Let x(r) = 0. Calculate r.
-1, 0, 4
Suppose 0 = -x - 0*x + 3, -3*f + 3 = -x. Let h(j) = 2 - 3*j**2 - 2. Let g(u) = 16*u**2 - u. Let q(r) = f*g(r) + 11*h(r). Factor q(s).
-s*(s + 2)
Let d(l) be the second derivative of -3/10*l**2 + 0 - 1/5*l**3 - 4*l + 3/20*l**4. Factor d(f).
3*(f - 1)*(3*f + 1)/5
Solve -3/7*h**2 + 3/7 + 0*h = 0.
-1, 1
Let o(g) = -5*g**5 - 11*g**4 + 14*g**3 + 2*g**2. Let a(q) = 9*q**5 + 21*q**4 - 27*q**3 - 3*q**2. Let k(v) = -6*a(v) - 11*o(v). Factor k(y).
y**2*(y - 2)**2*(y - 1)
Let x(s) = -s + 1. Let w(f) = -9*f**2 + 15*f + 24. Let b(h) = -w(h) + 6*x(h). Factor b(k).
3*(k - 3)*(3*k + 2)
Let s = -4 + 2. Let w = s + 4. Factor 3/2 - 6*f - 15/2*f**w.
-3*(f + 1)*(5*f - 1)/2
Let i(r) be the first derivative of r**6/2 - 18*r**5/5 + 33*r**4/4 - 2*r**3 - 18*r**2 + 24*r + 24. Solve i(q) = 0 for q.
-1, 1, 2
Let w = 1/11 + 39/55. Factor 2/5*y - 2/5*y**4 + 2/5*y**5 - 2/5 - w*y**3 + 4/5*y**2.
2*(y - 1)**3*(y + 1)**2/5
Let r(d