first derivative of p(r). Factor q(u).
(u - 1)**2*(u + 1)
Let r(u) be the second derivative of u**4/96 + u**3/48 - u**2/8 + 4*u. Solve r(q) = 0.
-2, 1
Let b(t) = t**3 + 4*t**2 - 4*t + 7. Let s be b(-5). Factor -a**2 + a**2 + 2*a - 4*a - s*a**2.
-2*a*(a + 1)
Let j be (-102)/(-27) + 2/9. What is y in y**4 + y**j + 7*y**5 - 9*y**5 = 0?
0, 1
Let h(b) = -2*b**5 + 10*b**4 - 13*b**3 - 33*b**2 - 7*b. Let a(q) = q**5 - 10*q**4 + 14*q**3 + 34*q**2 + 6*q. Let w(j) = 7*a(j) + 6*h(j). Factor w(d).
-5*d**2*(d - 2)*(d + 2)**2
Suppose 0 - 3/2*f + 3/2*f**2 = 0. What is f?
0, 1
Let h(u) be the third derivative of -u**6/30 - 4*u**5/15 - 2*u**4/3 + 12*u**2. Factor h(f).
-4*f*(f + 2)**2
Let b = 4 - 2. Factor -9*d**b - 2*d - 18*d**4 - 7*d**2 - 10*d**2 - 40*d**3 - 2*d.
-2*d*(d + 1)**2*(9*d + 2)
Let t be ((-5)/3)/((-20)/24). Let n(r) be the second derivative of 0*r**4 - 1/20*r**5 + 0 + 1/6*r**3 + 0*r**t - 3*r. Factor n(x).
-x*(x - 1)*(x + 1)
Factor -1/6*z**5 + 0*z**2 + 0*z**4 + 1/6*z**3 + 0*z + 0.
-z**3*(z - 1)*(z + 1)/6
Let n(z) = 4*z**3 - 4*z**2 + 4*z. Let t(g) = -g**3 + g + 0*g**3 - 2*g. Let w(s) = n(s) + 6*t(s). Determine m so that w(m) = 0.
-1, 0
Suppose 5*r = -0*r. Let g(l) be the third derivative of 0*l + r - 1/180*l**6 - l**2 + 0*l**3 - 1/36*l**4 + 1/45*l**5. Factor g(b).
-2*b*(b - 1)**2/3
Let k(y) be the first derivative of -y**4 - 4*y**3/3 - 10. Factor k(a).
-4*a**2*(a + 1)
Let g(w) be the third derivative of w**7/2940 + w**6/630 + w**3/6 - 2*w**2. Let c(y) be the first derivative of g(y). Suppose c(v) = 0. Calculate v.
-2, 0
Let i(b) be the first derivative of b**5/180 + 2*b**2 + 4. Let g(m) be the second derivative of i(m). Suppose g(h) = 0. What is h?
0
Let c(l) be the second derivative of -40*l**7/21 + 26*l**6/15 - 2*l**5/5 + 10*l. Solve c(t) = 0.
0, 1/4, 2/5
Suppose 0 = -5*d + 9*d - 52. Let b be (0/d)/(1 + -6). Solve t**3 + 7/2*t**4 - 7/2*t**2 - t + b = 0 for t.
-1, -2/7, 0, 1
Factor -3/5 + 0*o + 3/5*o**2.
3*(o - 1)*(o + 1)/5
Let d(v) be the third derivative of -v**6/30 - 16*v**5/105 - 11*v**4/42 - 4*v**3/21 - 16*v**2. Factor d(q).
-4*(q + 1)**2*(7*q + 2)/7
Let h = 3 - 1. Let d(f) be the first derivative of -1/18*f**4 + 0*f**h + 0*f**3 - 1 - 2/45*f**5 + 0*f. Factor d(z).
-2*z**3*(z + 1)/9
Suppose -10 = 2*d - i - 32, -d = -5*i - 20. Suppose w - 2 + 3 = -2*z, -d = 5*z. Solve 0*t + 1/3*t**4 - 1/3*t**5 + 1/3*t**w - 1/3*t**2 + 0 = 0 for t.
-1, 0, 1
Suppose -7*g = -2*g - 20. Let x(o) be the first derivative of -1/8*o**g + 0*o**2 + 1 + 0*o + 3/20*o**5 + 0*o**3. Factor x(c).
c**3*(3*c - 2)/4
Let o(c) = -c**5 - c**4 + c + 1. Let u(k) = 12*k**5 - 4*k**4 + 4*k**3 + 12*k**2 - 16*k - 8. Let d(f) = -8*o(f) - u(f). Suppose d(r) = 0. What is r?
-1, 0, 1, 2
Let n = 89/42 + -11/6. Let h = 4 + -2. Find w, given that -2/7*w**h - n*w + 0 = 0.
-1, 0
Let h(l) = -3*l**4 + 9*l**3 + 27*l**2 + 15*l. Let m(a) = a**5 + 4*a**4 - 9*a**3 - 26*a**2 - 14*a. Let q(r) = 2*h(r) + 3*m(r). Factor q(k).
3*k*(k - 2)*(k + 1)**2*(k + 2)
Let x(w) be the third derivative of -w**5/60 + w**4/12 - w**3/6 - 10*w**2. Factor x(f).
-(f - 1)**2
Let y = 37/8 + -33/8. Factor 1/2*g**2 - y*g - 1/2 + 1/2*g**3.
(g - 1)*(g + 1)**2/2
Let r(o) be the second derivative of -o**10/10080 + o**8/2240 - o**4/12 + 3*o. Let a(m) be the third derivative of r(m). Factor a(t).
-3*t**3*(t - 1)*(t + 1)
Let o(r) be the third derivative of -r**6/180 + r**5/45 + r**4/36 - 2*r**3/9 - 5*r**2. Factor o(x).
-2*(x - 2)*(x - 1)*(x + 1)/3
Let h(j) be the second derivative of j**6/60 - j**5/10 - 3*j**2/2 + 4*j. Let o(t) be the first derivative of h(t). Suppose o(c) = 0. What is c?
0, 3
Let x(p) = -4*p**2 - 7*p + 5. Let v(i) = -2*i**2 - 4*i + 2. Let y(s) = 10*v(s) - 4*x(s). Let y(b) = 0. Calculate b.
-3, 0
Suppose 0 = -5*f - 4*f. Let n(b) be the third derivative of -1/120*b**6 + 1/210*b**7 + 0 + 0*b**4 + 0*b + 0*b**5 + 4*b**2 + f*b**3. Suppose n(g) = 0. What is g?
0, 1
Determine g, given that 0*g + 4/5*g**5 - 8/5*g**2 + 0 - 16/5*g**4 + 4*g**3 = 0.
0, 1, 2
Let w(h) be the first derivative of 3*h**5/5 + 3*h**4/8 - 21*h**3/2 + 39*h**2/2 - 12*h - 34. Find o such that w(o) = 0.
-4, 1/2, 1, 2
Factor 0*y + 3*y**4 - 9/4*y**3 + 0*y**2 - 3/4*y**5 + 0.
-3*y**3*(y - 3)*(y - 1)/4
Suppose -41*a - 2*q = -43*a + 14, 12 = a - 2*q. Factor 35/2*y**a + 2 + 11*y + 25/4*y**3.
(y + 2)*(5*y + 2)**2/4
Let t(h) = h. Let s(c) = 45*c**2 - 100*c - 30. Let m(w) = -s(w) + 25*t(w). Factor m(f).
-5*(f - 3)*(9*f + 2)
Let -3*o + 2*o**2 + o**2 - 5*o + 2*o = 0. Calculate o.
0, 2
Let m(i) be the first derivative of i**5/20 - i**4/4 + i**3/3 - 7. Factor m(g).
g**2*(g - 2)**2/4
Let p(v) be the first derivative of -v**6/2 + 12*v**5/5 - 15*v**4/4 + 2*v**3 - 1. Factor p(c).
-3*c**2*(c - 2)*(c - 1)**2
Let r(p) be the third derivative of p**5/140 + p**4/28 + p**3/14 - 10*p**2. Factor r(l).
3*(l + 1)**2/7
Let d(n) be the third derivative of -n**8/588 - n**7/147 - n**6/105 - n**5/210 + 18*n**2. Let d(k) = 0. What is k?
-1, -1/2, 0
Let w(l) = -2*l - 54. Let q be w(-27). Find n such that -3/4*n**3 + 3/4*n**4 - 1/4*n**5 + 1/4*n**2 + 0*n + q = 0.
0, 1
Let y(o) be the first derivative of o**5/20 + 3*o - 3. Let q(r) be the first derivative of y(r). Factor q(m).
m**3
Determine z so that 3/8*z**2 + 3/2*z - 9/2 = 0.
-6, 2
Suppose 3*m + 8 = -1. Let v = 0 - m. Factor -1/3*y + 0 + 2/3*y**2 - 1/3*y**v.
-y*(y - 1)**2/3
Let j(c) = -c**3 - 19*c**2 + 2*c + 40. Let h be j(-19). Factor 10/3*i + 4/3 - h*i**2.
-2*(i - 2)*(3*i + 1)/3
Let l(d) be the first derivative of 7*d**3/3 - d**2 - 6. Factor l(r).
r*(7*r - 2)
Suppose 0 = 5*o - 1 + 6. Let l be (-3 - 6*o) + 1. What is m in 11/4*m**2 + 7/4*m**3 - 7/4*m - 1/2 - 9/4*m**l = 0?
-1, -2/9, 1
Let u = -109 - -112. Solve -u*k**3 - 1/2 - 3*k - 11/2*k**2 = 0 for k.
-1, -1/2, -1/3
Let j(i) be the first derivative of -18*i**6 - 36*i**5 - 39*i**4/4 + 10*i**3 - 3*i**2/2 - 22. Solve j(c) = 0.
-1, 0, 1/6
Let g(f) = -4*f**3 - 13*f**2 + f**3 - 9 + 14 + 13*f. Let o(y) = 8*y**3 + 38*y**2 - 38*y - 14. Let p(d) = -14*g(d) - 5*o(d). Determine x so that p(x) = 0.
0, 2
Let -14/11*s**4 - 8/11*s + 38/11*s**3 - 16/11*s**2 + 0 = 0. What is s?
-2/7, 0, 1, 2
Suppose 0 = 4*p - p. Factor v + v**2 - 3*v**2 + p*v**2 + v**2.
-v*(v - 1)
Let n(j) be the third derivative of j**5/20 + j**4/4 + j**3/2 - j**2 + 9. Factor n(x).
3*(x + 1)**2
Let g = -187/5 + 39. Factor 8/5*y**3 - 2/5*y**4 - g*y**2 + 0*y + 0.
-2*y**2*(y - 2)**2/5
Let h = -12/77 - -1487/154. Let l = -9 + h. Suppose -l*x**4 - 3/2*x**3 - 1/2*x**2 + 3/2*x + 1 = 0. Calculate x.
-2, -1, 1
Suppose -2*x = -u - 5, x + 4*x - 20 = -5*u. Let 0 - 1/6*h**4 + h**x + 4/3*h - 2*h**2 = 0. Calculate h.
0, 2
Let r(m) = -m**2 - 3*m - 5. Let t(a) = 18*a - 4*a + 6 + a**2 - 11*a. Let w(o) = -4*r(o) - 3*t(o). Factor w(x).
(x + 1)*(x + 2)
Let r(n) = n**4 + 5*n - n**2 + 6*n**2 + 2*n**3 + 6 - 13*n. Let u(m) = m**4 + m**3 + 5*m**2 - 7*m + 5. Let p(z) = -5*r(z) + 6*u(z). Solve p(t) = 0 for t.
0, 1, 2
Let l be 12/(-108)*(-9)/2. Suppose l*x - 1 + 1/2*x**2 = 0. Calculate x.
-2, 1
Let w(y) = 3*y. Let h be w(-5). Let f = h + 47/3. Find p such that f*p**2 + 2/3 + 4/3*p = 0.
-1
Factor 180*f**2 + 149*f**3 + 22*f**4 + 102*f + 60*f + 2*f**5 - 57*f**3 + 54.
2*(f + 1)**2*(f + 3)**3
Suppose 0 = 5*b + 12 - 7. Let g be 1/5 + b/(-20). What is i in -3/4*i**2 - 1/4*i**3 + 3/4*i**4 + 0 + g*i = 0?
-1, 0, 1/3, 1
Let a = -510428/21 + 24311. Let c = a - 25/7. What is w in c*w - 4/3 - 1/3*w**2 = 0?
2
Let t(f) be the first derivative of -f**3 - 12*f**2 - 48*f - 5. Determine r, given that t(r) = 0.
-4
Let z = -3/76 + 629/532. Factor -2/7*i**2 + 0*i + 0 - 10/7*i**3 - z*i**4.
-2*i**2*(i + 1)*(4*i + 1)/7
Let j(q) be the first derivative of -7*q**4/10 + 8*q**3/5 + 4*q**2/5 + 24. Factor j(w).
-2*w*(w - 2)*(7*w + 2)/5
Let p be (5 - 4)/((-10)/(-14)). Let x be (1/(-3))/(10/(-6)). Determine i, given that p*i + 8/5*i**2 + x - 16/5*i**3 = 0.
-1/4, 1
Let w(m) be the first derivative of 2*m**4/9 + 2*m**3/3 + 2*m**2/3 + 2*m/9 + 3. Find a such that w(a) = 0.
-1, -1/4
Factor 0*b**2 + 1/9 - 2/9*b**3 + 2/9*b - 1/9*b**4.
-(b - 1)*(b + 1)**3/9
Let a be 2/15 - (-420)/225. Let z(p) be the first derivative of -1/8*p**a + 1/24*p**6 - 1/10*p**5 + 1/6*p**3 - 1 + 0*p + 0*p**4. Factor z(k).
k*(k - 1)**3*(k + 1)/4
Let g be 2 - (-9)/(9/(-2)). Let n(k) be the third derivative of -2*k**2 + 0*k**3 + g - 1/20*k**6 