ose 3*d - 13 = -5*g, g = 3*d - 0*g + 17. Let o be (-1)/(d - (-21)/6). What is b in 4/5*b**o + 3/5*b**5 - 6/5*b**3 + 3/5*b - 2/5 - 2/5*b**4 = 0?
-1, 2/3, 1
Factor -308*s**2 + s + 302*s**2 + 3*s - 10*s**3.
-2*s*(s + 1)*(5*s - 2)
Let c(p) be the second derivative of 2*p**6/75 - p**5/10 + p**4/30 + 2*p**3/15 + 3*p. Find u such that c(u) = 0.
-1/2, 0, 1, 2
Let q(s) be the first derivative of 0*s**3 + 1/20*s**5 - 2 - 1/12*s**6 + 0*s + 0*s**2 + 1/16*s**4. Determine w, given that q(w) = 0.
-1/2, 0, 1
Let s = -1 + 4. Let n = s + 0. Suppose -1/3*u**n - 1/3*u**2 + 0*u + 0 = 0. What is u?
-1, 0
Suppose -2*j - 20 = -2*p, 2*p = 5*j - 13 + 33. Factor 0*x**4 + x**4 - 2*x + 2*x**3 + p - 10 - x**2.
x*(x - 1)*(x + 1)*(x + 2)
Factor -3*b**2 + 5*b - b**3 - 3*b + 4*b**2.
-b*(b - 2)*(b + 1)
Let -26/5*n**2 - 2/5*n**4 - 24/5*n - 8/5 - 12/5*n**3 = 0. What is n?
-2, -1
Let u(g) be the second derivative of -3*g**5/20 - 3*g**4/4 - g**3 + 13*g. Factor u(x).
-3*x*(x + 1)*(x + 2)
Let v(u) = -4*u**2 - 5. Suppose 0*l + 8 = -2*l + 4*b, -l = -b. Let n(d) = l - 8 - 2*d**2 - d**2. Let c(h) = -5*n(h) + 4*v(h). Let c(m) = 0. What is m?
0
Let s(w) = -3*w**2 + 4*w - 5. Let v be s(3). Let x be 2/v - (-18)/30. Factor -1/2*h + x*h**3 + 1/2*h**2 - 1/2.
(h - 1)*(h + 1)**2/2
Let j(u) = -u**2 + 5*u - 2. Let l be j(4). Let 0*a**l - a**2 + 3*a**2 - 2*a + 2*a**3 - 2*a**4 = 0. Calculate a.
-1, 0, 1
Let n(l) be the third derivative of l**3 + 0*l + l**2 + 0 + 1/20*l**5 + 3/8*l**4. Factor n(o).
3*(o + 1)*(o + 2)
Let p(b) = -b**2 + 3*b + 6. Suppose 4*r + 40 = 4*h + h, -5*h - 4*r = 0. Let u be p(h). Find f, given that 2/3 + 2*f + u*f**2 + 2/3*f**3 = 0.
-1
Suppose 5*r + 4*c = 35, 2*r + 0*c + 9 = 3*c. Suppose -r*b = -7*b. Determine z so that -2/5*z**2 + b*z + 0 - 2/5*z**3 = 0.
-1, 0
Let y = 20 - 13. Factor 5*s**2 - y*s**2 - 2*s**2 + 4*s.
-4*s*(s - 1)
Let m(r) be the third derivative of 0*r**5 - 1/180*r**6 + 3*r**2 + 0 + 0*r**4 + 1/315*r**7 + 0*r**3 + 0*r. Factor m(i).
2*i**3*(i - 1)/3
Let a be 1/(-3*(-2)/(-48)). Let k be 7/((-420)/a)*5. Suppose 0*r + k*r**2 + 0 + 2/3*r**3 = 0. What is r?
-1, 0
Factor -6/5 + 2/5*l + 6/5*l**2 - 2/5*l**3.
-2*(l - 3)*(l - 1)*(l + 1)/5
Find p, given that 16/9*p + 0 - 14/9*p**4 - 40/9*p**2 - 52/9*p**3 = 0.
-2, 0, 2/7
Let b be 6/18*(-4 - -4). Determine v so that 0*v**3 + b*v - 2/5 - 2/5*v**4 + 4/5*v**2 = 0.
-1, 1
Let a(z) be the second derivative of -z**7/70 - z**6/40 + z**5/20 + z**4/8 + 2*z**2 - 2*z. Let q(v) be the first derivative of a(v). Factor q(w).
-3*w*(w - 1)*(w + 1)**2
Factor 6*j**3 - 3*j**3 - 10 + 10 + 9*j**2 + 6*j.
3*j*(j + 1)*(j + 2)
Let v(h) = -h**3 + h - 1. Let u(w) = -2*w**3 + 12*w**2 - 10*w + 2. Let x(z) = -u(z) - 2*v(z). Let x(n) = 0. What is n?
0, 1, 2
Let t(w) = -w - 1. Let s be t(-4). Suppose -2*x + s = -9. Factor 0*u + x*u**3 - 3*u**2 - 5*u**3 + 3*u - 1.
(u - 1)**3
Let o be (3/2 - -1) + -2. Let m(t) = -3*t**3 - t. Let p be m(-1). Solve -o - 2*c**5 + c**2 + p*c**3 - 2*c - 1/2*c**4 = 0.
-1, -1/4, 1
Suppose 0*f = -4*f + 4, 3*f - 3 = 4*o. Factor 2/11*p**2 + o + 6/11*p**3 + 6/11*p**4 + 2/11*p**5 + 0*p.
2*p**2*(p + 1)**3/11
Let i(n) be the first derivative of 4*n**5/5 - n**4 - 4*n**3/3 + 2*n**2 + 3. Let i(d) = 0. What is d?
-1, 0, 1
Let q(u) = u**3 + 10*u**2 - 7*u - 11. Let n(d) be the second derivative of -d**5/20 - 3*d**4/4 + d**3 + 5*d**2 - 4*d. Let w(c) = -7*n(c) - 6*q(c). Factor w(s).
(s - 1)*(s + 2)**2
Suppose -2*z + 3*k = -5*z + 24, -k + 11 = 2*z. Let 3/5*w**z + 3/5*w - 6/5*w**2 + 0 = 0. Calculate w.
0, 1
Let z(m) = -6*m**3 + 4*m**2 + 2*m - 2. Let r(n) = -n**5 + n**4 - 31*n**3 + 20*n**2 + 10*n - 10. Let i = 16 + -12. Let p(d) = i*r(d) - 22*z(d). Factor p(u).
-4*(u - 1)**3*(u + 1)**2
Let v be -1 - -1 - (-5)/5. Factor 2*k**3 + 2*k - v + 2*k**2 - 4*k**3 - 2 + 1.
-2*(k - 1)**2*(k + 1)
Let t(x) = x - 4. Let f be t(9). Let b(o) be the third derivative of -1/24*o**4 + 0 + 0*o + 2*o**2 + 0*o**3 + 1/60*o**f. Factor b(c).
c*(c - 1)
Suppose 4*x = -2*i - 16, -x + 6*x - 1 = i. Let m be (-9)/i*(3 + -1). Determine l so that 3/2 + 3/2*l**2 + m*l = 0.
-1
Let g(u) be the first derivative of u**5/20 - 3*u**4/8 + u**3/3 + 3*u**2/4 - 5*u/4 - 72. Suppose g(j) = 0. Calculate j.
-1, 1, 5
Let b(z) = -7*z - 3. Let v(u) = 10*u + 5. Let x(q) = -7*b(q) - 5*v(q). Let g be x(-4). Factor 1/2*n + 1/2*n**3 + n**2 + g.
n*(n + 1)**2/2
Factor -95/3*g + 4 + 16/3*g**3 + 184/3*g**2.
(g + 12)*(4*g - 1)**2/3
Let a = -4/271 - -4348/813. Let a*i**2 + 0 + 10/3*i**3 + 8/3*i + 2/3*i**4 = 0. What is i?
-2, -1, 0
Let j be 65/3 - (-10)/(-15). Let 6*z**2 + 0*z**3 + 21*z**5 - 6*z**4 + z**5 - j*z**3 - z**5 = 0. Calculate z.
-1, 0, 2/7, 1
Let t(g) be the second derivative of 7*g**5/20 + g**4 - 2*g**3/3 + 9*g. Solve t(v) = 0.
-2, 0, 2/7
Factor 0 - 2/5*z**2 - 4/5*z + 2/5*z**3.
2*z*(z - 2)*(z + 1)/5
Let f(u) be the first derivative of 2*u**5/45 + 2*u**4/9 + 10*u**3/27 + 2*u**2/9 + 32. Factor f(n).
2*n*(n + 1)**2*(n + 2)/9
Let f be (0/(-4 - 1))/1. Let z(t) be the third derivative of -1/60*t**5 - 3*t**2 + 0*t**3 + 1/210*t**7 + 0 + 0*t + f*t**4 + 0*t**6. Factor z(i).
i**2*(i - 1)*(i + 1)
Let d(t) = 2*t - 2. Let a be d(3). Let k(g) be the second derivative of a*g**3 + 0 + 4/3*g**2 + 9/2*g**4 + 2*g. Factor k(l).
2*(9*l + 2)**2/3
Let u(x) = 18*x**3 + 16*x**4 + 9 - 59*x**3 + 4 + 4*x**4 + 8*x**2. Let s(a) = -10*a**4 + 20*a**3 - 4*a**2 - 6. Let f(t) = -13*s(t) - 6*u(t). Factor f(g).
2*g**2*(g - 1)*(5*g - 2)
Let p be ((-6)/9)/(6/(-27)). Let i be (0/(4 - p))/(-2). Factor -5/2*n**3 - n**2 + i + 0*n.
-n**2*(5*n + 2)/2
Suppose -2*v + 160 = -82. Let t = v - 355/3. Factor 7/3*l**3 + 12*l - t - 10*l**2.
(l - 2)**2*(7*l - 2)/3
Let y(k) = 80*k**3 - 98*k**2 - 125*k + 53. Let d(f) = -27*f**3 + 33*f**2 + 42*f - 18. Let z(v) = -17*d(v) - 6*y(v). Factor z(b).
-3*(b - 2)*(b + 1)*(7*b - 2)
Find b, given that 0 - 63/2*b**3 - 27/2*b**4 - 24*b**2 - 6*b = 0.
-1, -2/3, 0
Let u = -28 + 42. Suppose 0 = 5*b + 4 - u. Determine l so that 0*l - 4/3*l**3 + 0 - 2/3*l**b - 2/3*l**4 = 0.
-1, 0
Factor 4/3 - 32/3*x**2 - 10/3*x - 6*x**3.
-2*(x + 1)**2*(9*x - 2)/3
Suppose -4 = -f + 2*i, i - 3 = 2*f - 5. Factor 4/3*m**3 - 10/3*m**5 + 0*m**2 - 2*m**4 + f*m + 0.
-2*m**3*(m + 1)*(5*m - 2)/3
Let j = -31/118 - -4085/17346. Let l = j + 46/147. Factor -4/7*y**2 - 2/7*y + 0 - l*y**3.
-2*y*(y + 1)**2/7
Suppose -4*x = -4*o + 12, 0*x + 4*o - 26 = -3*x. Let u be ((-9)/(-12))/(x/8). Factor 0*c**2 + u*c**2 + 2*c + 6*c - 2*c.
3*c*(c + 2)
Factor 2/5*s**2 - 4/5*s**3 + 0*s + 2/5*s**4 + 0.
2*s**2*(s - 1)**2/5
Let w = 20 + -20. Suppose 2*t - 3*t - 5*o = 15, t - o - 3 = w. Determine j, given that t - 1/3*j - 1/3*j**3 - 2/3*j**2 = 0.
-1, 0
Solve 3 + 2*p**2 - 3 + 6*p - 1 + 5 = 0 for p.
-2, -1
Let t(i) be the first derivative of -i**5/45 - i**4/12 - i**3/9 - i**2/18 - 6. Find n, given that t(n) = 0.
-1, 0
Let g(n) = 6*n + 3. Let d(h) = h**3 + 9*h**2 - h - 12. Let p be d(-9). Let s(r) = -r**2. Let y(m) = p*s(m) + g(m). Determine f so that y(f) = 0.
-1
Let o = 5 - -2. Suppose -k = -o + 5. Factor 1/4*f**5 + 0*f**3 + 1/4*f**4 + 0*f**k + 0 + 0*f.
f**4*(f + 1)/4
Solve -20/3*g**3 - 80/3*g - 32/3 - 22*g**2 - 2/3*g**4 = 0 for g.
-4, -1
Let l be ((-1)/((-6)/8))/((-8)/(-12)). Factor 0 + 0*d + l*d**3 - 2/3*d**2.
2*d**2*(3*d - 1)/3
Let f(r) be the second derivative of -r**7/14 + 3*r**5/10 - r**3/2 - 4*r. Factor f(b).
-3*b*(b - 1)**2*(b + 1)**2
Let x(s) be the second derivative of -s**4/3 + 80*s**3/3 - 800*s**2 - 47*s. Factor x(f).
-4*(f - 20)**2
Let l(r) be the first derivative of 3 + 0*r - 1/12*r**3 + 1/8*r**2. Factor l(a).
-a*(a - 1)/4
Factor 0*z - 1/2*z**2 - 1/2*z**3 + 0.
-z**2*(z + 1)/2
Factor -q**2 + 3*q**5 + 3*q**4 - 5*q**3 + 2*q**3 + 0*q**2 - 2*q**2.
3*q**2*(q - 1)*(q + 1)**2
Let i(z) be the third derivative of z**8/336 - z**6/40 + z**5/30 - 24*z**2. Determine s so that i(s) = 0.
-2, 0, 1
Factor 7*x**3 - 40*x**2 + 5*x**3 - 60*x + 5*x**4 - 9*x**3 + 2*x**3.
5*x*(x - 3)*(x + 2)**2
Suppose 0 = 6*l + 3*l - 18. Let b(p) be the first derivative of 0*p - 4 - 1/2*p**l - 29/4*p**4 - 19/6*p**3 - 28/5*p**5. Suppose b(u) = 0. What is u?
-1/2, -2/7, -1/4, 0
Let w(i) be the second derivative of -i**6/5 - 79*i**5/50 - 8*i**4/15 + 4*i**3/3 - 39*i. Let w(c) = 0. Calculate c.
-5, -2/3, 0, 2/5
Let n be 1130/36*24/80. Let f = n + -35/4. Factor f*d**2 + 8/3 + 8/3*d.
2*(d + 2)**2/3
Let s be 1 + 0 + 1