 6*q**2 + 5*q + 1. Let k(a) = h(a) + 6*s(a). Let m be k(-6). What is g in m - 2*g**2 + 8*g - 2 - 7 = 0?
2
Let b = 37948/1215 - 8/243. Factor b*x**2 - 32*x + 48/5 - 36/5*x**3.
-4*(x - 3)*(3*x - 2)**2/5
Find h such that 1/4*h**5 - 1/4*h**4 - 1/4*h**3 + 0 + 1/4*h**2 + 0*h = 0.
-1, 0, 1
Suppose -8 = -2*k - 2. Suppose -5*s**3 + 0*s**4 + 2*s**5 - k*s**5 + 4*s**4 + 2*s**2 = 0. What is s?
0, 1, 2
Suppose -4*j + 8*j = 0. Find v such that j*v**2 - 8*v + 0*v**4 + 6*v**3 + 0*v**2 + 2*v**4 = 0.
-2, 0, 1
Let t(y) be the second derivative of y**6/300 - 2*y**5/75 + y**4/15 - y**3/3 + 4*y. Let x(k) be the second derivative of t(k). Suppose x(n) = 0. What is n?
2/3, 2
Factor 9/4*w + 3/4*w**4 - 9/4*w**3 - 3/2 + 3/4*w**2.
3*(w - 2)*(w - 1)**2*(w + 1)/4
Let v(x) = -x**3 - 6*x**2 - 5*x - 8. Let t(w) = w**3 + 6*w**2 + 6*w + 7. Let k(n) = 4*t(n) + 3*v(n). Suppose k(h) = 0. What is h?
-4, -1
Let j(u) be the second derivative of -u**4/18 - 16*u**3/9 - 5*u**2 - 47*u. Find v such that j(v) = 0.
-15, -1
Suppose -79 = -4*i + 89. Let l = i - 125/3. Factor 0*f - f**4 + 0 + 1/3*f**5 - l*f**2 + f**3.
f**2*(f - 1)**3/3
Let j be (1/(-2))/(4/(-32)). Determine i, given that 2*i**2 - 2 - i**2 + j - 2*i**3 - 6*i + 5*i**2 = 0.
1
Let h be ((-6)/(-4))/3 - 20/(-56). Let w = -76 + 534/7. Factor -w*k**2 - h*k - 4/7.
-2*(k + 1)*(k + 2)/7
Let k be (22/(-4) + 5)/(10/(-8)). Factor -k*p + 0 - 2/5*p**2.
-2*p*(p + 1)/5
Let v = 2 - -1. Let 4*s**4 - s**v + 3*s**3 + s**2 + 2*s**5 - s**2 = 0. What is s?
-1, 0
Let f = 31 - 13. Let n be (6/7)/(f/28). Factor 0 + 2*u**2 + 2/3*u + n*u**3.
2*u*(u + 1)*(2*u + 1)/3
Let l(n) = n**2 + n. Let s = 10 + -12. Let a(g) = -2*g**3 - 4*g**2 - 2*g. Let y(v) = s*l(v) - a(v). Factor y(f).
2*f**2*(f + 1)
Let u(y) be the second derivative of 9/25*y**5 + 54/5*y**3 - 243/10*y**2 + 0 - 4*y - 1/50*y**6 - 27/10*y**4. Factor u(o).
-3*(o - 3)**4/5
Let c(d) be the first derivative of 4*d**3/3 - 4*d**2 - 12*d + 46. Factor c(j).
4*(j - 3)*(j + 1)
Let i(r) be the first derivative of 1/30*r**4 + 1/50*r**5 - 1/5*r**2 - 2*r - 1/15*r**3 - 1. Let v(h) be the first derivative of i(h). Factor v(l).
2*(l - 1)*(l + 1)**2/5
Let r(f) be the second derivative of f**7/168 + 3*f**6/40 + 3*f**5/8 + 23*f**4/24 + 11*f**3/8 + 9*f**2/8 + f. Factor r(o).
(o + 1)**3*(o + 3)**2/4
Let i = 22 + -20. Suppose 0 = -7*f + i*f + 10. Suppose -24/7*p + 16/7 - 2/7*p**3 + 12/7*p**f = 0. Calculate p.
2
Let n be 70/45*(-4 + (-166)/(-7)). Factor -130/3*g**4 - 2/3 - 14/3*g + n*g**3 + 4/3*g**2 + 50/3*g**5.
2*(g - 1)**3*(5*g + 1)**2/3
Solve 0 + 6*p**4 - 2/3*p - 7/3*p**2 + p**3 = 0 for p.
-1/2, -1/3, 0, 2/3
Let f(i) = -105*i**4 - 145*i**3 + 20*i**2 + 40*i - 20. Let a(l) = l**4 - l**3 + l - 1. Let o(s) = 20*a(s) - f(s). Solve o(w) = 0.
-1, -2/5, 0, 2/5
Let q(u) be the first derivative of 0*u + 1/4*u**4 + 2 + 0*u**2 + 2/3*u**3. Factor q(a).
a**2*(a + 2)
Let h(n) be the third derivative of n**7/60 + 5*n**6/96 + 13*n**5/240 + n**4/48 + 12*n**2. Find q, given that h(q) = 0.
-1, -1/2, -2/7, 0
Let s(x) be the first derivative of x**5/15 + x**4/2 + 4*x**3/3 + 2*x**2 - 2. Let p(l) be the second derivative of s(l). Determine j so that p(j) = 0.
-2, -1
Let n(k) be the second derivative of -7*k**5/5 - 13*k**4/3 - 10*k**3/3 + 2*k**2 - 12*k. Determine s, given that n(s) = 0.
-1, 1/7
Let u(h) be the first derivative of -5*h**3/3 - 35*h**2/2 - 50*h + 27. Solve u(c) = 0 for c.
-5, -2
Let p(s) be the first derivative of 9*s**6/2 + 6*s**5 - 17*s**4/4 - 16*s**3/3 + 2*s**2 - 33. Find d such that p(d) = 0.
-1, 0, 2/9, 2/3
Factor 2/7*j**4 - 2*j - 6/7*j**2 + 12/7 + 6/7*j**3.
2*(j - 1)**2*(j + 2)*(j + 3)/7
Let o = 2 + 2. Suppose -4*b**2 + 7*b - b**5 - 5*b - b**5 + o*b**4 = 0. Calculate b.
-1, 0, 1
Let c be 2/4*66/11. Factor 11*g + 0*g**3 + g + 12*g**2 + 2*g**c + g**3.
3*g*(g + 2)**2
Let c(w) be the second derivative of w**5/80 + 5*w**4/24 - 11*w**3/24 + 15*w. Suppose c(h) = 0. What is h?
-11, 0, 1
Let u(o) be the first derivative of -o**6/480 - o**5/80 - o**4/32 - o**3/24 + 5*o**2/2 - 2. Let v(w) be the second derivative of u(w). Factor v(r).
-(r + 1)**3/4
Suppose -9 + 1 = -4*q. Suppose 3*s - 2*s + 0*s - s**q = 0. What is s?
0, 1
Let l(a) be the second derivative of 5*a + 0 + 2/21*a**3 - 1/7*a**2 - 1/42*a**4. Factor l(z).
-2*(z - 1)**2/7
Let r = -63 + 66. Determine j, given that -4/3*j - 8/3*j**4 - 10/3*j**2 + 22/3*j**r + 0 = 0.
-1/4, 0, 1, 2
Suppose -4*v + 4*h + 3 + 1 = 0, -h = 5*v - 29. Suppose -s + 15 = 3*o, -28 = -2*s - v*o - 2. Determine w, given that 2*w**3 - 2*w + 5*w**s - 2*w**5 - 3*w**3 = 0.
-1, 0, 1
Find p, given that -1/6*p**2 - 2 + 7/6*p = 0.
3, 4
Let t(n) be the second derivative of 0*n**2 + 0 + 1/2*n**4 + 1/15*n**6 + 1/3*n**3 + 2*n + 3/10*n**5. Factor t(b).
2*b*(b + 1)**3
Suppose 4*x**3 - 59*x**4 + 61*x**4 + 2*x**2 + 0*x**3 = 0. Calculate x.
-1, 0
Let p be 4/2*6/4. Let j(r) = -2*r + 0*r + r**2 + 5*r**3 - 3*r + 4*r. Let v(g) = -4*g**3 - 2*g**2. Let z(o) = p*v(o) + 2*j(o). Determine i so that z(i) = 0.
-1, 0
Factor s - 83 + 83 + 2*s**2.
s*(2*s + 1)
Let f(q) be the first derivative of -4/9*q**3 - 16/3*q + 5/3*q**4 - 6 - 16/3*q**2 + 4/15*q**5 - 2/9*q**6. Factor f(o).
-4*(o - 2)**2*(o + 1)**3/3
Let z(a) be the second derivative of a**4/12 + 5*a**3/6 + 2*a**2 + 27*a. Factor z(x).
(x + 1)*(x + 4)
Let q(l) be the second derivative of 5*l**7/168 + l**6/12 + l**5/10 - l**4/4 + l. Let s(g) be the third derivative of q(g). Determine d, given that s(d) = 0.
-2/5
Suppose -8*i + 4*i + 12 = 0. Let u = i - 1. Factor -6/7*w**u + 10/7*w - 4/7.
-2*(w - 1)*(3*w - 2)/7
Suppose 2*b = -0*b + 6. Let m = b - 1. Factor -9*y**2 + 2*y**2 + 2*y + 5*y**m.
-2*y*(y - 1)
Let c be 0/(6 - 4)*-1. Let w(k) be the first derivative of -k**4 + 0*k**5 + 0*k + 1/3*k**6 + c*k**3 + 1 + k**2. Suppose w(m) = 0. Calculate m.
-1, 0, 1
Let k be ((-4)/(-2) - 3)*-2. Suppose 0 = -6*p + k*p. Factor 0 + p*c + 1/4*c**4 + 0*c**2 - 1/4*c**3.
c**3*(c - 1)/4
Let r(u) be the third derivative of u**10/252000 - u**8/16800 + u**6/1200 + u**5/10 + 4*u**2. Let h(m) be the third derivative of r(m). Factor h(l).
3*(l - 1)**2*(l + 1)**2/5
Let m be (1 + -2)*1 + 3. Let k = m + 0. Factor 5*f**k - 2*f**3 + 7*f + 4 + f + 3*f**3.
(f + 1)*(f + 2)**2
Let h(q) be the first derivative of -q**6/3 - 2*q**5/5 + q**4 + 4*q**3/3 - q**2 - 2*q - 17. Determine z so that h(z) = 0.
-1, 1
Let -58*s**3 + 4*s**2 - s**2 - 27*s**5 + 45*s**4 + 37*s**3 = 0. What is s?
0, 1/3, 1
Let x(v) be the first derivative of 3*v**5/5 - 3*v**3 + 3*v**2 + 1. Factor x(y).
3*y*(y - 1)**2*(y + 2)
Let j(s) be the first derivative of 0*s + 3/2*s**2 - 4*s**3 - 2. Let j(x) = 0. What is x?
0, 1/4
Let y(f) be the second derivative of 1/15*f**4 + 0 - f - 2/75*f**6 - 1/105*f**7 + 1/15*f**3 + 0*f**5 + 0*f**2. Factor y(z).
-2*z*(z - 1)*(z + 1)**3/5
Let b(p) = -12*p**4 - 32*p**3 + 100*p**2 + 12*p + 34. Let r(m) = -m**4 - 3*m**3 + 9*m**2 + m + 3. Let l(h) = 6*b(h) - 68*r(h). Let l(g) = 0. What is g?
0, 1
Suppose -6*a + 11*a - 30 = 0. Factor -9*s**3 + 5*s**3 + 12*s**2 + 18*s + a*s**3.
2*s*(s + 3)**2
Suppose 5 = 3*o + g, 4*o + g - 3 = 4. Let a(c) be the second derivative of 2/9*c**3 - 3*c + 0*c**o + 1/18*c**4 + 0 - 1/30*c**5. Factor a(i).
-2*i*(i - 2)*(i + 1)/3
Let i(q) = -7*q**4 - 3*q**3 - 5*q + 5. Let m(g) = 6*g**4 + 2*g**3 + 3*g - 3*g**4 + g**4 - 4 + 1. Let j(l) = 6*i(l) + 10*m(l). Let j(c) = 0. Calculate c.
0, 1
Let o = -23 + 26. Let 0*l - 1/3*l**4 - 1/3*l**2 - 2/3*l**o + 0 = 0. Calculate l.
-1, 0
Let d be 0 - (-6 + (-4)/(-4)). Suppose 0 = -d*b + 10*b. Factor b*a + 0 - 3/2*a**3 + 0*a**2.
-3*a**3/2
Let i(o) = -40*o**2 - 135*o - 135. Let t(v) = -v**3 + 39*v**2 + 135*v + 135. Let h(a) = -6*i(a) - 5*t(a). Factor h(u).
5*(u + 3)**3
Let r(w) be the first derivative of -3*w**5/35 + 3*w**4/14 - 3*w**2/7 + 3*w/7 - 10. Factor r(y).
-3*(y - 1)**3*(y + 1)/7
Let k(m) be the third derivative of 0 + 1/9*m**3 + m**2 + 0*m + 1/12*m**4 + 1/180*m**6 + 1/30*m**5. Factor k(n).
2*(n + 1)**3/3
Let b be (3/10)/(9/12). Let z(h) be the first derivative of -2/5*h - 1/10*h**4 - 3/5*h**2 - b*h**3 - 1. Factor z(f).
-2*(f + 1)**3/5
Let y(a) = 14*a**3 + 17*a**2 + 20*a - 17. Let l(o) = 5*o**3 + 6*o**2 + 7*o - 6. Let m = -53 + 36. Let r be 56/9 - 2/9. Let b(u) = m*l(u) + r*y(u). Factor b(z).
-z*(z - 1)*(z + 1)
Let m(b) be the first derivative of b**8/5040 - b**6/540 + b**4/72 + 5*b