0. What is r?
-2, 0
Find c, given that -5/4*c**4 - 1 + 9/4*c**2 - 2*c**3 + 2*c = 0.
-2, -1, 2/5, 1
Let y(h) be the third derivative of -1/60*h**6 + 0*h + 4/75*h**5 + 3*h**2 + 0 - 2/15*h**3 - 1/60*h**4. Determine s so that y(s) = 0.
-2/5, 1
Suppose -20 = -2*t + 3*i, 4*i = -2*t - 9 + 1. Solve 2/3*u**2 - 2/3*u**t - 2/3*u + 2/3*u**3 + 0 = 0 for u.
-1, 0, 1
Let w(b) be the second derivative of 1/2*b**2 + 1/3*b**4 + 0 + b + 5/6*b**3. Factor w(d).
(d + 1)*(4*d + 1)
Let m(x) be the third derivative of -x**7/2940 + x**6/1260 + x**5/420 - x**4/84 + x**3/2 + 3*x**2. Let d(p) be the first derivative of m(p). Factor d(a).
-2*(a - 1)**2*(a + 1)/7
Let f be 364/105 - 6/9. Let j = f - 23/10. Find i, given that 1 + 2*i**2 + j*i**3 + 5/2*i = 0.
-2, -1
Let l(q) = 4*q**5 - 8*q**4 + 7*q**3 + 4*q**2 - 11*q + 7. Let d(s) = 3*s**5 - 7*s**4 + 7*s**3 + 3*s**2 - 10*s + 6. Let y(f) = 3*d(f) - 2*l(f). Factor y(p).
(p - 2)**2*(p - 1)**2*(p + 1)
Let n = -193/5 + 39. Factor -4/5*l - n - 2/5*l**2.
-2*(l + 1)**2/5
Let r(o) = -o**2 + 5*o. Let j be r(7). Let c = -10 - j. Let -2/11 - 4/11*z**5 - 8/11*z**2 - 4/11*z**3 + 8/11*z + 10/11*z**c = 0. What is z?
-1, 1/2, 1
Let s be (1 - (-35)/(-36)) + (-18)/(-81). Let p(l) be the first derivative of 1 + 0*l + 1/6*l**3 + s*l**2 - 1/8*l**4 - 1/10*l**5. Factor p(o).
-o*(o - 1)*(o + 1)**2/2
Let a be (24/10)/(4/(-60)). Let t be (-8)/a + (-1)/(-9). Factor -t*i**3 + 0 + 0*i**2 + 0*i - 1/3*i**4.
-i**3*(i + 1)/3
Let a be -2*(9/(-10))/((-72)/(-420)). Solve -6 + 24*v - a*v**2 = 0 for v.
2/7, 2
Let g(t) be the third derivative of t**6/900 + t**5/150 + t**4/60 - t**3/6 + 4*t**2. Let j(i) be the first derivative of g(i). Find y, given that j(y) = 0.
-1
Let t(a) be the first derivative of 1/6*a**6 + 0*a**5 + 0*a**2 + 0*a + 0*a**3 - 1/4*a**4 + 3. Factor t(o).
o**3*(o - 1)*(o + 1)
Let m(c) be the second derivative of -c**7/294 - 2*c**6/105 - c**5/28 - c**4/42 + 21*c. Factor m(u).
-u**2*(u + 1)**2*(u + 2)/7
Let l(s) be the first derivative of s**6/1620 + s**5/270 - s**4/36 + 2*s**3 - 5. Let n(p) be the third derivative of l(p). Factor n(g).
2*(g - 1)*(g + 3)/9
Let y(x) be the second derivative of -x**4/108 - x**3/18 - x**2/9 - 4*x. Factor y(w).
-(w + 1)*(w + 2)/9
Suppose f = 2*f. Let s be f + 0/(-3) + 2. Factor 1/3*g + 0 - 1/3*g**s.
-g*(g - 1)/3
Let x(f) = -10*f**2 + 10*f - 12. Let b(l) = -l**2 + l - 8. Let p(q) = 3*q**2 - 3*q + 15. Let y(h) = 5*b(h) + 3*p(h). Let u(n) = 5*x(n) + 12*y(n). Factor u(r).
-2*r*(r - 1)
Let t(c) = 2*c**2 + 4*c - 8. Let q(l) = 3*l**2 + 3*l - 8. Let y(i) = -4*q(i) + 5*t(i). Determine h so that y(h) = 0.
2
Let n(s) = -s. Let u = -1 - 5. Let z be n(u). Factor -z*w**4 - 9*w**5 - 6*w**4 + 12*w**5 + 12*w**3.
3*w**3*(w - 2)**2
Let -18/13 - 14/13*v**2 - 2/13*v**3 - 30/13*v = 0. What is v?
-3, -1
Suppose 5*b + 15 = 40. Let y(d) = -7*d**4 + 9*d**2 - 7. Let c(h) = -4*h**4 + 5*h**2 - 4. Let n(u) = b*c(u) - 3*y(u). Find s such that n(s) = 0.
-1, 1
Let k(s) be the third derivative of -s**6/600 + s**5/75 - s**4/24 + s**3/15 + 15*s**2. Suppose k(n) = 0. What is n?
1, 2
Let j be (-50)/(-6) - 4/(-6). Let a be (-7)/j - 2/(-2). Let 2/9*l**3 - a*l + 2/9*l**2 - 2/9 = 0. What is l?
-1, 1
Let d(a) be the third derivative of a**7/315 - a**6/108 - a**5/270 + 5*a**4/108 - 2*a**3/27 + 5*a**2. Find o such that d(o) = 0.
-1, 2/3, 1
Let a(l) = 2*l**2 + 4*l + 2. Let u be a(-2). Suppose y = 5 + u. Let 6 - j - j - y*j - 3*j**2 + 6*j**2 = 0. Calculate j.
1, 2
Suppose -5*z - 4*k = -37, 4*k - 8*k = -2*z + 26. Suppose 4*a + 1 - z = 0. Let -n**4 + 1/2*n - 1/2*n**5 + n**a + 0*n**3 + 0 = 0. What is n?
-1, 0, 1
Let c(g) be the second derivative of -g**4/108 - g**3/27 - 5*g. Determine k, given that c(k) = 0.
-2, 0
Let l(g) = g**2 - g - 4. Let p be l(3). Factor p*t**5 - 4*t**2 - 2*t**4 + 4*t**2.
2*t**4*(t - 1)
Suppose -14/9*y + 2/9*y**4 + 2*y**2 - 10/9*y**3 + 4/9 = 0. Calculate y.
1, 2
Let k(q) be the second derivative of -1/12*q**4 + 0 + 1/6*q**3 - 2*q + 0*q**2. Factor k(r).
-r*(r - 1)
Let h(d) be the first derivative of -75*d**5/4 + 275*d**4/8 - 15*d**3 - 27*d**2/4 + 27*d/4 + 21. Suppose h(t) = 0. What is t?
-1/3, 3/5
Let n(u) be the first derivative of 5*u**4/4 + 5*u**3/3 - 5*u**2/2 - 5*u + 19. Factor n(k).
5*(k - 1)*(k + 1)**2
Let j(t) be the second derivative of -1/24*t**4 + 1/6*t**3 - t + 0 + 0*t**2. Factor j(l).
-l*(l - 2)/2
Let g(s) = 2*s**5 - 2*s**4 + 4*s**2 - 10*s + 2. Let k(h) = h**4 - h**3 - h. Let c(v) = -g(v) + 4*k(v). What is r in c(r) = 0?
-1, 1
Let y(i) be the third derivative of 0 + 0*i**3 + 1/66*i**4 + i**2 + 0*i - 1/330*i**5. Factor y(q).
-2*q*(q - 2)/11
Let w(c) be the first derivative of -c**6/72 - c**5/30 + 7*c**4/48 - c**3/9 + 14. Determine t so that w(t) = 0.
-4, 0, 1
Let z(r) = -7*r**4 + 9*r**3 - 4*r**2 - 9*r + 8. Let v(j) = -8*j**4 + 8*j**3 - 4*j**2 - 8*j + 8. Let l(n) = 3*v(n) - 4*z(n). Factor l(y).
4*(y - 2)*(y - 1)**2*(y + 1)
Let n(q) be the first derivative of -5*q**4/16 - 5*q**3/2 - 15*q**2/2 - 10*q + 33. Factor n(l).
-5*(l + 2)**3/4
Let l(w) = -w**4 + w**3 - w**2 - w + 1. Let a(r) = 5*r**5 + 8*r**4 - 28*r**3 + 18*r**2 + 3*r - 3. Let v(c) = -a(c) - 3*l(c). Let v(t) = 0. What is t?
-3, 0, 1
Let v(w) be the second derivative of -w**7/5040 - w**6/720 + w**4/12 - 5*w. Let o(u) be the third derivative of v(u). Solve o(p) = 0.
-2, 0
Let t(v) be the third derivative of v**7/420 + v**6/120 + 23*v**2. Suppose t(y) = 0. What is y?
-2, 0
Let j(f) be the first derivative of 1/6*f**3 - 10 + 3/2*f + f**2. Determine n, given that j(n) = 0.
-3, -1
Let g(f) be the second derivative of f**5/70 + f**4/14 + 2*f**3/21 + 33*f. Determine p so that g(p) = 0.
-2, -1, 0
Let z(l) be the first derivative of -2*l**3/15 - 24*l**2/5 - 288*l/5 + 9. Factor z(i).
-2*(i + 12)**2/5
Let b(k) be the first derivative of k**6/6 - 3*k**5/5 + k**4/2 + 2*k**3/3 - 3*k**2/2 + k + 7. Factor b(s).
(s - 1)**4*(s + 1)
Let r(f) be the second derivative of -f**7/56 + f**6/40 + 3*f**5/80 - f**4/16 - 27*f. Factor r(m).
-3*m**2*(m - 1)**2*(m + 1)/4
Let o = 35 - 174/5. Factor 1/5*v + o*v**2 + 0.
v*(v + 1)/5
Factor 2 + 3*o**2 + 42*o**3 - 39*o**3 - 2 - 6*o.
3*o*(o - 1)*(o + 2)
Let s(a) be the second derivative of 1/2*a**2 + 1/24*a**4 - 2*a + 0 - 1/4*a**3. Determine i so that s(i) = 0.
1, 2
Let a(p) be the second derivative of p**6/1080 + p**5/360 - 2*p**3/3 - 2*p. Let k(q) be the second derivative of a(q). Factor k(i).
i*(i + 1)/3
Let h(s) be the first derivative of -3*s**7/70 - s**6/10 - s**5/15 + 4*s**2 + 4. Let j(k) be the second derivative of h(k). Let j(r) = 0. What is r?
-2/3, 0
Let g be -2 - (1 - 28/9). Let p(i) be the second derivative of -2/27*i**3 + g*i**2 + 1/54*i**4 + 2*i + 0. Solve p(f) = 0 for f.
1
Factor 29*z + 3*z**3 - z**3 - 6*z**3 + 32 - 77*z + 24*z**2.
-4*(z - 2)**3
Let c(r) be the third derivative of -3*r**5/70 + 5*r**4/21 - 4*r**3/21 + 2*r**2. Factor c(m).
-2*(m - 2)*(9*m - 2)/7
Suppose 4*s - 3*s + o = 11, 2*s - 4*o = 52. Suppose 0 = -3*g, -3*w - 3*g + s - 4 = 0. Factor 2*l + 12 - 12 - w*l**2 + 2*l**3.
2*l*(l - 1)**2
Let g(j) be the second derivative of j**7/21 + 7*j**6/30 - j**5/5 - 18*j. Find x such that g(x) = 0.
-4, 0, 1/2
Factor 1/2*n**2 - 1/2*n + 0.
n*(n - 1)/2
Let w(h) = -h + 14. Let q be w(11). Factor -3*g**4 + g**4 + 2*g**q + g**4.
-g**3*(g - 2)
Determine c so that 0*c - 2/3*c**2 + 0 + 1/3*c**3 = 0.
0, 2
Let q(f) be the first derivative of -1/12*f**4 + f**2 + 1/60*f**6 + 1 + 0*f + 0*f**5 + 0*f**3. Let k(w) be the second derivative of q(w). Solve k(d) = 0 for d.
-1, 0, 1
Let s(k) be the second derivative of 0*k**2 + 1/3*k**3 + 1/6*k**4 + 0 - k. Factor s(u).
2*u*(u + 1)
Let l be (-9)/(-3) - (2 + 0). Let u = -1 + l. What is c in 0*c**2 + u + 0*c + 2/3*c**3 = 0?
0
Let w(p) be the first derivative of -p**8/112 - p**7/14 - 3*p**6/40 + 9*p**5/20 - 7*p**2/2 + 3. Let x(c) be the second derivative of w(c). Factor x(l).
-3*l**2*(l - 1)*(l + 3)**2
Let t(y) = -27*y**5 + 12*y**4 + 12*y**3 - 12*y**2 - 15*y + 15. Let p(g) = 7*g**5 - 3*g**4 - 3*g**3 + 3*g**2 + 4*g - 4. Let r(k) = 15*p(k) + 4*t(k). Factor r(b).
-3*b**2*(b - 1)**2*(b + 1)
Let i(s) = s**3 + s**2. Let u(j) = -j**3 - 16*j**2 - 27*j - 12. Let a(y) = -2*i(y) + u(y). Factor a(b).
-3*(b + 1)**2*(b + 4)
Factor -b + 6*b**2 + 2*b**2 - 2 - 4*b**2 + 3*b.
2*(b + 1)*(2*b - 1)
Let m(u) be the second derivative of 2/9*u**4 + 3*u +