 + 403. Factor -2/3*d**2 - 1/3*d + 0 - w*d**3.
-d*(d + 1)**2/3
Suppose -1 = 3*l - 2*l. Let i be -1*(14/(-10) - l). Let 8/5*c**3 + 0 - i*c**2 + 0*c - 8/5*c**5 + 2/5*c**4 = 0. What is c?
-1, 0, 1/4, 1
Let 1/8*z**5 + z + 0 + 5/2*z**2 + 7/8*z**4 + 9/4*z**3 = 0. Calculate z.
-2, -1, 0
Suppose 43 = 6*s - 7*s. Let v = s + 131/3. Factor -2/3*c + 0 + v*c**2.
2*c*(c - 1)/3
Find q, given that 9/8*q**3 + 0 - 3/8*q**5 + 0*q**4 + 0*q - 3/4*q**2 = 0.
-2, 0, 1
Let a be -2*5/20*0. Let d(c) be the first derivative of a*c - 3*c**2 - c**3 + 3/4*c**4 - 3. Find k, given that d(k) = 0.
-1, 0, 2
Let m(d) = 2*d - 6. Let u be m(6). Let o(p) = -8*p**3 + 2*p**2 + 6*p. Let s(b) = -15*b**3 + 4*b**2 + 11*b. Let x(i) = u*s(i) - 11*o(i). Factor x(z).
-2*z**2*(z - 1)
Let h(d) = 5*d + 1. Let s(n) = 6*n + 2. Let b(w) = 5*h(w) - 4*s(w). Let k be b(5). Suppose -1/3*t**k + t - 2/3 = 0. Calculate t.
1, 2
Suppose 0*a = -4*a + 24. Suppose a = 2*w - 2*l, -4*w + l = 4*l - 19. Let 3 - 4*p**3 - 7 + 2 + 0*p + 2*p**4 + w*p = 0. Calculate p.
-1, 1
Determine u so that -14 - u**3 + 9 + u + 5 = 0.
-1, 0, 1
Let p = 1 + 1. Factor -4*m**4 + 2*m**2 + 2*m**2 + 0*m**p + 0*m**4.
-4*m**2*(m - 1)*(m + 1)
Let c be 0/((-1)/((-3)/(-6))). Let h(r) be the third derivative of 7/360*r**6 + 0 + c*r - r**2 - 1/9*r**3 - 7/72*r**4 + 1/90*r**5. What is n in h(n) = 0?
-1, -2/7, 1
Suppose 3*c = -2*c + 10. Find y, given that -3*y**3 - y**5 + 4*y**3 + y**c + 0*y**2 - y**4 = 0.
-1, 0, 1
Factor 0*n + 2/3*n**5 - 1/3*n**3 + 0*n**2 - 1/3*n**4 + 0.
n**3*(n - 1)*(2*n + 1)/3
Let n(f) be the second derivative of f**4/36 - f**3/3 + 3*f**2/2 + 20*f. Suppose n(a) = 0. Calculate a.
3
Suppose -5*g = -2*g - 15. Suppose -20 = -0*a - g*a. Factor 11*y**2 - 11*y**2 + 2*y**3 + 2*y**a.
2*y**3*(y + 1)
Let g(f) = 2*f - 2. Let z be g(4). Factor -z + 6 - h**2 + 2*h**3 - h**4.
-h**2*(h - 1)**2
Let d(s) be the second derivative of -2/15*s**4 + 4*s + 1/105*s**7 + 0 + 4/75*s**6 + 3/50*s**5 + 0*s**2 - 4/15*s**3. Solve d(n) = 0 for n.
-2, -1, 0, 1
Let k(x) be the second derivative of x**4/3 + 4*x**3 + 18*x**2 - 3*x. Find l, given that k(l) = 0.
-3
Let c(l) be the first derivative of 2*l**7/21 - l**6/6 - 3*l**5/20 + 5*l**4/12 - l**3/6 - 5*l - 4. Let k(o) be the first derivative of c(o). Factor k(p).
p*(p - 1)**2*(p + 1)*(4*p - 1)
Let f(d) = d - 2*d + 5*d**2 - 6*d**2. Let u(l) = -6*l**2 - l - 4. Let s(j) = -15*f(j) + 3*u(j). Suppose s(y) = 0. Calculate y.
2
Let y(x) be the second derivative of -1/24*x**4 - 1/24*x**7 + 1/60*x**6 + 0*x**3 + 0*x**2 - 2*x + 0 + 7/80*x**5. Let y(i) = 0. Calculate i.
-1, 0, 2/7, 1
Factor -2*l - 3 - 2 - l + 11 - 3*l**2.
-3*(l - 1)*(l + 2)
Solve 3/4*f + 1/4*f**2 + 1/2 = 0 for f.
-2, -1
Let i(u) = u - 1. Let l be i(4). Let z(n) be the second derivative of 2*n + 0*n**2 - 1/5*n**5 + 0 - 1/3*n**l - 1/2*n**4. Factor z(t).
-2*t*(t + 1)*(2*t + 1)
Let z(u) be the second derivative of -u**6/135 + 4*u**5/45 - 4*u**4/9 + 32*u**3/27 - 16*u**2/9 + 15*u. Factor z(v).
-2*(v - 2)**4/9
Let a(o) = o - 7. Let u be a(6). Let d(p) = p**5 - p**3 - p**2 - p. Let k(t) = -26*t**4 - 28*t**3 - 8*t**2 - 6*t. Let b(x) = u*k(x) + 10*d(x). Factor b(f).
2*f*(f + 1)**3*(5*f - 2)
Let v be (10/4)/(-5)*2. Let o(r) = -4*r**3 - 4*r**2 + 4. Let u(n) = n**2 + n + 1. Let t(g) = v*o(g) + 4*u(g). Determine h so that t(h) = 0.
-1, 0
Suppose -19 = -4*f - v, -2*v + 4 = 3*f - 4. Let h be f/(-4)*12/(-9). Determine u, given that 0*u - 3*u**2 - 7 + 3 - 7*u + h = 0.
-2, -1/3
Suppose 0 = -v - 0*v + 2. Suppose 4 = -3*d - 4*x + 17, 0 = -3*d + v*x + 7. Determine k, given that 140*k**4 + k - 14*k**4 + 4 - 90*k**d - 50*k**2 + 9*k = 0.
-1/3, -2/7, 1/3, 1
Let x = -12 + 16. Factor -5*n**2 + 6*n + x*n**2 - 3*n**2 + n**2.
-3*n*(n - 2)
Suppose i - 3*a + 2 + 10 = 0, 12 = 3*a. Let v(z) be the second derivative of i*z**2 - 1/3*z**4 + 0 - 1/10*z**5 - 1/3*z**3 - 3*z. Factor v(c).
-2*c*(c + 1)**2
Let r(p) be the second derivative of -p + 0 + 1/15*p**3 + 0*p**4 + 1/105*p**7 + 0*p**6 + 0*p**2 - 1/25*p**5. Find b, given that r(b) = 0.
-1, 0, 1
Let h be (-3 + 0/3)/(-1). Let d(f) be the first derivative of 1/18*f**4 + 0*f - 4/27*f**h - 1 + 1/9*f**2. Factor d(m).
2*m*(m - 1)**2/9
Let c(i) be the second derivative of 5*i**7/21 + i**6/2 - i**5/2 - 5*i**4/4 - 18*i. Determine k, given that c(k) = 0.
-3/2, -1, 0, 1
Factor 3/2*g**2 - 33/2*g + 0.
3*g*(g - 11)/2
Let i be (1 - 1)/(3 + -2). Suppose -2*z = -i*z - 8. Find s, given that 2/3*s**2 + 0*s**3 + 0 - 2/3*s**z + 0*s = 0.
-1, 0, 1
Let w = 134 + -94. Suppose h + 0*h = 3*i + 18, 5*h - w = 5*i. Factor -2*v**h + 2*v**3 - 3*v**2 + v**2 + 1 + v**4.
(v - 1)**2*(v + 1)**2
Let r(j) = 3*j**2 + 48*j - 33. Let m(u) = -u - 1. Let v(z) = 9*m(z) + r(z). Factor v(d).
3*(d - 1)*(d + 14)
Let g(x) be the third derivative of x**6/1020 + x**5/510 - x**4/204 - x**3/51 - 17*x**2. Let g(n) = 0. Calculate n.
-1, 1
Let l(f) be the first derivative of -3 + 4/9*f**3 - 1/6*f**4 - 4/3*f + 1/3*f**2. Suppose l(q) = 0. What is q?
-1, 1, 2
Let q = -30 - -34. Let x(y) be the first derivative of 4/3*y**3 - 1/3*y**6 + 1 + y**2 - 4/5*y**5 + 0*y**q + 0*y. Suppose x(n) = 0. Calculate n.
-1, 0, 1
Suppose -20 = -4*d - 8. Let -18 - 3*q**3 + 18 + 2*q**2 + q**d = 0. What is q?
0, 1
Let q be (-9)/(-4) - 3/12. Let f(l) be the second derivative of 1/10*l**6 + 9/4*l**4 + 3*l + 7/2*l**3 + 0 + 3/4*l**5 + 3*l**q. Factor f(p).
3*(p + 1)**3*(p + 2)
Let x(g) be the third derivative of g**5/160 - 3*g**4/32 - 28*g**2. Solve x(l) = 0.
0, 6
Factor -1/2*y**2 - 1/6*y**3 - 1/2*y - 1/6.
-(y + 1)**3/6
Factor 1/3 - 1/2*l**3 - 1/6*l**2 - 1/6*l**4 + 1/2*l.
-(l - 1)*(l + 1)**2*(l + 2)/6
Let z(t) be the first derivative of -t**3/2 - 9*t**2/4 - 3*t + 9. Determine y so that z(y) = 0.
-2, -1
Let h(z) = -z**3 + 2*z**2 - 2. Let g(a) = 3*a**3 - 5*a**2 + 5. Let j = 4 - 9. Suppose 3*t + 0 = -6. Let m(d) = j*h(d) + t*g(d). Suppose m(s) = 0. Calculate s.
0
Find t, given that 10/13 - 2/13*t**2 + 8/13*t = 0.
-1, 5
Let q(i) be the first derivative of i**6/4 - 6*i**5/5 + 9*i**4/4 - 2*i**3 + 3*i**2/4 + 23. Factor q(r).
3*r*(r - 1)**4/2
Let b = -4 + 8. Suppose b*u = u + 6. Solve -u*m**3 - 12*m**3 + 6*m**4 + 10*m**5 - 5*m**2 - m**2 + 4*m = 0 for m.
-1, 0, 2/5, 1
Let n(i) be the second derivative of 1/33*i**3 + 1/33*i**4 + i + 0*i**2 + 1/110*i**5 + 0. Determine s, given that n(s) = 0.
-1, 0
Let g = 343 - 683/2. Find y, given that 1/2*y**2 + 0 - g*y = 0.
0, 3
Factor 3/5*y**2 + 0 + 6/5*y.
3*y*(y + 2)/5
Factor 2*v - 4/3 + 0*v**2 - 2/3*v**3.
-2*(v - 1)**2*(v + 2)/3
Let v(u) = 13*u**2 + 64*u + 123. Let j(d) = -20*d**2 - 96*d - 184. Let a(p) = 5*j(p) + 8*v(p). Determine x, given that a(x) = 0.
-4
Let n be (1 - 0)*(-8 - -8). Suppose 5*h - 6 - 4 = n. Factor -2 + h*v**2 - 2*v**2 + 4*v**2 - 2*v**4.
-2*(v - 1)**2*(v + 1)**2
Let r(v) = -6*v**2 - 38*v - 10. Let k(o) = -2*o**2 - 13*o - 3. Suppose 40 = -3*d - 2*s, d + 3 = -4*s - 7. Let g(y) = d*k(y) + 5*r(y). Let g(l) = 0. Calculate l.
-2
Let a(o) be the first derivative of 1/5*o**4 + 2/5*o - 2/5*o**2 + 0*o**3 - 2 - 2/25*o**5. Factor a(j).
-2*(j - 1)**3*(j + 1)/5
Let x(t) be the third derivative of t**7/525 - 7*t**6/300 - 17*t**5/150 - 3*t**4/20 + 27*t**2. What is s in x(s) = 0?
-1, 0, 9
Let q(m) be the first derivative of -m**7/42 + m**6/30 + m**5/10 - m**4/6 - m**3/6 + m**2/2 + m + 2. Let w(x) be the first derivative of q(x). Factor w(c).
-(c - 1)**3*(c + 1)**2
Let c(d) be the first derivative of -1/8*d**2 + 1 - 1/4*d + 1/16*d**4 + 1/12*d**3. Factor c(a).
(a - 1)*(a + 1)**2/4
Let 4*v**3 - 4*v**2 - 1 - 10*v - 1 - 10*v**2 - 10*v**3 = 0. Calculate v.
-1, -1/3
Let i(t) be the third derivative of t**10/151200 + t**5/10 - 6*t**2. Let a(k) be the third derivative of i(k). Let a(m) = 0. Calculate m.
0
Let z(b) = 5*b**4 - 5*b**3 - b**2 + 9*b - 9. Let j(y) = -y**4 + y**3 - 2*y + 2. Let i(a) = -18*j(a) - 4*z(a). Factor i(m).
-2*m**2*(m - 2)*(m + 1)
Suppose n + 112 = -6*n. Let c = n - -18. Factor 0 - 1/2*z - 1/2*z**5 + z**3 + 0*z**4 + 0*z**c.
-z*(z - 1)**2*(z + 1)**2/2
Let u be -3*(93/(-90) - -1). Let v(o) be the first derivative of -4 - 2/25*o**5 - u*o**4 + 2/15*o**3 + 0*o + 1/5*o**2. Factor v(j).
-2*j*(j - 1)*(j + 1)**2/5
Suppose -4*l + 8 = -12. Factor -3*w**3 - 1 - 2*w + 1 + 0*w**4 + w**5 + w**4 - l*w**2.
w*(w - 2)*(w + 1)**3
Let j(s) be the second derivative of 3*s**6/2 - 15*s**5/2 + 185*s**4/12 - 50*s**3