y(t).
2*t*(t + 1)*(11*t + 2)/9
Factor 16/3*m**2 - 32/3*m**3 - 2/3*m + 0.
-2*m*(4*m - 1)**2/3
Let x(z) be the first derivative of z**8/448 - z**6/160 + 3*z**2/2 - 6. Let a(h) be the second derivative of x(h). Find g such that a(g) = 0.
-1, 0, 1
Let j(t) = -6*t**5 + 6*t**4 - 30*t**3 + 70*t**2 - 66*t + 15. Let x(y) = y**5 - y**4 + 6*y**3 - 14*y**2 + 13*y - 3. Let i(w) = 2*j(w) + 11*x(w). Factor i(s).
-(s - 1)**4*(s + 3)
Let u be 52/(-90) + (-12)/(-15). Solve 0*a**3 + 4/9*a**4 - 2/9*a + 0 + u*a**5 - 4/9*a**2 = 0 for a.
-1, 0, 1
Let c(l) be the third derivative of l**7/63 + l**6/30 - 2*l**5/45 - l**4/6 - l**3/9 - 32*l**2. What is w in c(w) = 0?
-1, -1/5, 1
Let n(p) = -p**2 - p + 6. Let a be n(-4). Let g = a + 9. Let -4/5*u**4 + 0*u - 2/5*u**g + 0*u**2 + 6/5*u**5 + 0 = 0. What is u?
-1/3, 0, 1
Let r(o) be the first derivative of 1/6*o**3 - 1/2*o**2 + 0*o + 1. Determine c so that r(c) = 0.
0, 2
Suppose 2/5*t - 14/5*t**2 + 8/5*t**5 - 26/5*t**4 + 6*t**3 + 0 = 0. Calculate t.
0, 1/4, 1
Suppose -3*o = -5*o + 78. Factor -k**5 + o*k**4 + 4 - 7*k + 30*k**3 + 31*k + 57*k**2 + 10*k**5 + 37*k**3.
(k + 1)**3*(3*k + 2)**2
Let y be 3 - 96/28 - -1. Let l be 6/70 + 1/(7 + -2). Let -2/7*r**2 + y*r - l = 0. Calculate r.
1
Factor 18*m - 8*m + 4*m**2 - 43*m + 52 - 23*m.
4*(m - 13)*(m - 1)
Let k(y) = -7*y**4 - 6*y**3 - 5*y**2 + 6*y. Let l(x) = 2*x - 11*x**4 + 5*x**4 - 4*x**2 - 5*x**3 + 3*x. Let s(c) = -5*k(c) + 6*l(c). Let s(w) = 0. What is w?
-1, 0, 1
Let s(l) be the third derivative of -l**6/780 + l**5/65 - l**4/13 + 8*l**3/39 + 32*l**2. Factor s(n).
-2*(n - 2)**3/13
Solve -215*x**3 + 236*x**3 + 9*x - 3*x + 33*x**2 - 60*x**4 = 0 for x.
-2/5, -1/4, 0, 1
Let i(j) = -j**3 - j**2 - 9*j - 9. Let f(y) be the second derivative of y**5/10 + y**4/6 + 7*y**3/3 + 7*y**2 - 3*y. Let r(q) = 5*f(q) + 8*i(q). Factor r(x).
2*(x - 1)*(x + 1)**2
Suppose 2*i + 3*f - 13 = 2, 25 = 3*i + 5*f. Let b(y) be the second derivative of -y + 1/3*y**2 + 2/9*y**3 + i + 1/18*y**4. What is r in b(r) = 0?
-1
Suppose -16 = -2*k - h - 5, -5*k = -5*h - 5. Let a(u) be the first derivative of 7/10*u**2 + 2/5*u - 2 + 3/20*u**k + 8/15*u**3. Factor a(c).
(c + 1)**2*(3*c + 2)/5
Let z(d) be the first derivative of -2*d**5/55 + 7*d**4/22 - 10*d**3/11 + 9*d**2/11 - 45. Factor z(x).
-2*x*(x - 3)**2*(x - 1)/11
Let z(s) = s - 12. Let n be z(12). Suppose n*k = -2*k. What is c in k*c - c**5 + c**3 + 0 - 1/4*c**2 + 1/4*c**4 = 0?
-1, 0, 1/4, 1
Let k(c) = c - 3*c**2 + 2*c**2 + c**3 - c**2. Let u be k(2). Find b, given that 4 - 2 + b**5 - u - b**3 = 0.
-1, 0, 1
Let u(k) be the third derivative of 0*k - 1/20*k**5 + 1/8*k**4 + 2*k**2 + k**3 + 0. Determine y, given that u(y) = 0.
-1, 2
Let o(h) = h**3 + 6*h**2 - h - 5. Let k(a) = -a**2. Let u(p) = -k(p) - o(p). Find l such that u(l) = 0.
-5, -1, 1
Determine c so that 0 - 1/2*c**4 + 0*c - 1/2*c**3 + 0*c**2 = 0.
-1, 0
Suppose 5*d - 2*l - 1 + 11 = 0, 5*d + l - 5 = 0. Solve d + 2/11*b + 0*b**2 - 2/11*b**3 = 0.
-1, 0, 1
Let w be (3/420)/(9/24). Let c(b) be the third derivative of -1/15*b**5 + w*b**7 + b**2 + 1/12*b**4 + 0*b + 0 - 1/168*b**8 + 0*b**6 + 0*b**3. Factor c(l).
-2*l*(l - 1)**3*(l + 1)
Let i be 1/2 - (-45)/(-330). Factor 2/11*u - 4/11 - 2/11*u**3 + i*u**2.
-2*(u - 2)*(u - 1)*(u + 1)/11
Determine m, given that -3*m**2 + 67 - 67 = 0.
0
Suppose -4*g = 2*b, 0 = -2*g + g - 4*b. Let -4*x**2 + g + 5*x**2 + 0 = 0. Calculate x.
0
Let c(h) = 10*h**4 + 35*h**3 - 5*h**2. Let o(a) = 5*a**4 + 17*a**3 - 2*a**2. Let j(k) = 2*c(k) - 5*o(k). Let j(s) = 0. Calculate s.
-3, 0
Let a(t) be the third derivative of 0*t + 0 + 0*t**4 + 1/80*t**5 - 1/8*t**3 + 4*t**2. Factor a(d).
3*(d - 1)*(d + 1)/4
Suppose -4*g + 5*g = 2. Let i(q) be the second derivative of q + 1/63*q**7 + 1/45*q**6 + 0 + 0*q**g - 1/30*q**5 + 0*q**3 - 1/18*q**4. Solve i(s) = 0.
-1, 0, 1
Let l(f) = -f**2 - f. Let u(r) = 3*r**2 - 6*r + 7. Let v(q) = 2*l(q) + u(q). Find h such that v(h) = 0.
1, 7
What is d in -1/4*d**4 + 1/2*d**2 + 0*d**3 - 1/4 + 0*d = 0?
-1, 1
Suppose -4*m - u = -2 - 9, -3*m - 5*u + 4 = 0. Factor -4*w - w**3 - 5*w**m + 8*w - 6*w**2 - 4*w**3.
-2*w*(w + 1)*(5*w - 2)
Factor 2/7*z**2 - 2/7 - 1/7*z + 1/7*z**3.
(z - 1)*(z + 1)*(z + 2)/7
Factor -3/2*s**2 - 3/2*s**3 + 0 + 3*s.
-3*s*(s - 1)*(s + 2)/2
Let u(x) = -x**2 - 5*x + 2. Suppose 2*z - 2*q + 10 = 0, q = -z + 3*q - 5. Let o be u(z). Suppose -n**o - 1 - n + 2*n + n = 0. What is n?
1
Factor -2*p**3 + 8*p**4 - 8*p + p**5 + 8*p**3 - 8*p**2 + 3*p**5 - 2*p**5.
2*p*(p - 1)*(p + 1)*(p + 2)**2
Solve -8/17 - 16/17*g + 14/17*g**3 + 2/17*g**5 - 2/17*g**2 + 10/17*g**4 = 0.
-2, -1, 1
Let y(x) be the second derivative of 1/18*x**4 + 0 - 1/135*x**6 + 0*x**2 - 7/180*x**5 + 2*x + 1/6*x**3. Let b(r) be the second derivative of y(r). Factor b(a).
-2*(a + 2)*(4*a - 1)/3
Let x(j) be the first derivative of 4*j**5/5 - 4*j**3 - 4*j**2 + 16. Factor x(z).
4*z*(z - 2)*(z + 1)**2
Let n(w) = w**5 + 4*w**4 + 3*w**3 + 2*w - 2. Let u(k) = -k**5 - 5*k**4 - 4*k**3 - 3*k + 3. Let o(r) = -3*n(r) - 2*u(r). Let o(d) = 0. Calculate d.
-1, 0
Suppose 4*q + 7 = 5*q - 4*i, 2*i = 2*q - 8. Factor 4/5*m**q + 0*m**4 - 2/5*m + 0 - 2/5*m**5 + 0*m**2.
-2*m*(m - 1)**2*(m + 1)**2/5
Let w(j) be the second derivative of 1/10*j**5 - 1/30*j**6 + 1/6*j**4 + 0 - 1/2*j**2 - 1/6*j**3 - 9*j - 1/42*j**7. Factor w(k).
-(k - 1)**2*(k + 1)**3
Let s = -3/130 - -287/1170. Factor 0*v + 2/3*v**2 - 8/9 - s*v**3.
-2*(v - 2)**2*(v + 1)/9
Suppose 3*s + 2*b - 6 = 0, 9 = 3*b - 0. Let m(f) be the second derivative of s + 1/30*f**4 - f + 2/5*f**2 + 1/5*f**3. Factor m(i).
2*(i + 1)*(i + 2)/5
Let w(m) = 6*m + 3*m**3 - 8*m**3 + 17 - m**3 - 12*m**2. Let j(r) = 9*r**3 + 18*r**2 - 9*r - 25. Let u(x) = 5*j(x) + 7*w(x). Factor u(y).
3*(y - 1)*(y + 1)*(y + 2)
Let h(d) be the first derivative of -1/3*d**3 + 1/5*d**5 - 3 + d - 1/21*d**7 + 0*d**4 + 0*d**2 + 0*d**6. Let v(t) be the first derivative of h(t). Factor v(l).
-2*l*(l - 1)**2*(l + 1)**2
Suppose 0 = -q - 2*u + 16 - 4, 3*q - 31 = -5*u. Solve k**3 - k + 0*k**2 - k**2 + q - 1 = 0 for k.
-1, 1
Factor 34*t**3 + 4*t**2 - 2*t - 3 - 17*t**3 - t**4 - 15*t**3.
-(t - 3)*(t - 1)*(t + 1)**2
Let u(b) = -b**3 + 6*b**2 - b + 8. Let n be u(6). Solve 6*g + 18*g**2 - 15*g**n + 9 + 6*g = 0 for g.
-3, -1
Let c(v) be the second derivative of -v**5/5 - v**4/3 - 6*v. Solve c(g) = 0 for g.
-1, 0
Let b = -472 - -947/2. Find a such that -b*a**2 + 1/2*a**3 + 3/2*a - 1/2 = 0.
1
Let x(y) be the third derivative of 1/60*y**5 + 1/8*y**4 + 0 + 0*y + 2*y**2 + 1/3*y**3. Solve x(w) = 0 for w.
-2, -1
Factor -2*b**4 - 23 - 2*b**5 - 2*b + 8 + 13 - 2*b**3 + 4*b**2 + 6*b**3.
-2*(b - 1)**2*(b + 1)**3
Let o(p) be the second derivative of -p**6/75 + p**5/25 + p**4/30 - 2*p**3/15 + 6*p. Find s, given that o(s) = 0.
-1, 0, 1, 2
Let d(y) be the third derivative of 0*y + 1/80*y**5 - 1/32*y**4 + 0 + 1/24*y**3 + 8*y**2 - 1/480*y**6. Determine n, given that d(n) = 0.
1
Let p(t) be the third derivative of 0 + 1/72*t**4 - 2*t**2 + 0*t - 1/180*t**5 + 0*t**3. Factor p(n).
-n*(n - 1)/3
Let p(q) = 5*q - 82. Let g be p(17). Factor -1/5*u**g + 0 - 1/5*u - 2/5*u**2.
-u*(u + 1)**2/5
Find h such that -h + 5*h**4 + 38*h**3 - h**2 - 25*h**3 - 2 + 10*h**2 = 0.
-1, 2/5
Let d(h) = h**3 + 7*h**2 + 6*h + 4. Let x be d(-6). Factor -5*i**3 + 3*i**2 + 0*i**2 - i + i**x + 5*i**3 - 3*i**3.
i*(i - 1)**3
Let b be (-23)/(-7) - 2/7. Factor m**4 + 2*m**3 + 0*m - b*m**3 - m**2 + m.
m*(m - 1)**2*(m + 1)
Let a(z) be the second derivative of 0 + 1/6*z**4 - z - 2*z**2 + 1/3*z**3. Find u such that a(u) = 0.
-2, 1
Suppose -i + 1 = 3. Let f be (-2)/i - (2 - 2). Determine o, given that -f + 0*o**2 + 2*o**2 - o**4 + 0 = 0.
-1, 1
Let h(f) = 10*f - 4. Let v be h(3). Suppose -68 = -5*b + 2*g, -2*g = -5*b - g + 64. Determine a, given that -b*a**4 - 3*a**4 + 4*a - 2*a - 13*a**2 + v*a**3 = 0.
0, 1/3, 2/5, 1
Factor 0 - 3/4*v**5 - 3/8*v**4 + 3/2*v**3 + 9/8*v**2 + 0*v.
-3*v**2*(v + 1)**2*(2*v - 3)/8
Let s(g) = -2*g - 15. Let j be s(-10). Solve -h**5 + 0*h**j + 5*h**3 - 2*h**5 + 4*h**3 + 6*h**2 = 0 for h.
-1, 0, 2
Let a(k) be the second derivative of 0*k**4 + 0 - 1/60*k**5 + 2/9*k**3 + 0*k**2 + 2*k. Factor a(b).
-b*(b - 2)*(b + 2)/3
Let z(x) = x**2 + 4*x + 2. Let i be z(-4). Factor -8*b + 3 - 3 - 2*b**i - 8.
-2*(b + 2)**2
Suppose 3/4*h**3 + 0 - 3/4*h + 3/4*h**4 - 3/4*h**2 = 0. Calculate h.
