r**2. Let o(a) be the second derivative of p(a). Factor o(c).
-(c - 1)**3/2
Let o(q) = 20*q**4 + 25*q**3 - 30*q**2 - 20*q. Let n(m) = 30*m**4 + 37*m**3 - 45*m**2 - 30*m. Let d(j) = -5*n(j) + 8*o(j). Factor d(l).
5*l*(l - 1)*(l + 2)*(2*l + 1)
Let t(a) = a**2 - 5*a - 3. Let o be t(6). Suppose 3*z = -z + 12. Factor n + z*n**2 + 2*n**3 + 0*n**o - 5*n**2 - n**3.
n*(n - 1)**2
Let o be (4/(-5))/((-4)/10). Factor 19*l**o + 4*l - 18*l**4 + 4*l**5 + 24*l**3 + 34*l**4 - 3*l**2.
4*l*(l + 1)**4
Let f be 16/6*(3 + 0). Suppose 5*j - 2 - f = 0. Factor -1/5*r**j + 0*r + 0.
-r**2/5
Let c(m) = 3*m - 6. Let d be c(4). Let j = d + -3. Factor 2*h**3 + j*h**3 + h - 6*h**3.
-h*(h - 1)*(h + 1)
Suppose -4*q - q = -15. Suppose 2*f + q*f - 10 = 0. Let -2/7*t**f + 2/7*t**3 + 0*t + 0 - 2/7*t**5 + 2/7*t**4 = 0. Calculate t.
-1, 0, 1
Let c be (1 - (-1)/2)/((-9)/(-18)). Let j(o) be the third derivative of 0*o**4 + 0 + 1/300*o**5 - 3*o**2 + 0*o**c + 0*o + 0*o**6 - 1/1050*o**7. Factor j(f).
-f**2*(f - 1)*(f + 1)/5
Suppose i - 33 = 4*i. Let a = -8 - i. Find v, given that -84*v - 69*v**a + 11*v**3 - 8 - 285*v**3 - 294*v**2 = 0.
-2/7
Suppose 5*p = 3 + 7. Factor 2*v + v**4 + v**3 - 2*v**4 - 3*v**p - v + 2*v**3.
-v*(v - 1)**3
Suppose -29*f + 27*f = 0. Factor 0 + 1/2*r**3 + f*r**2 + 0*r.
r**3/2
Let m(j) = -2 + 3 - j**2 - 3 - 8*j. Let l be -19 + (2 - 5 - 0). Let u(c) = c. Let k(o) = l*u(o) - 2*m(o). Factor k(v).
2*(v - 2)*(v - 1)
Let m(b) be the third derivative of -7*b**6/120 + b**5/12 + b**4/12 - 19*b**2. Find v such that m(v) = 0.
-2/7, 0, 1
Suppose 0 = 3*b + 3, 4*q - b = -3*b + 18. Factor 6*w**q + 0 + 18*w**4 + 38/9*w**2 + 4/9*w + 14*w**3.
2*w*(w + 2)*(3*w + 1)**3/9
Suppose 3*q = 2*q + 2. Determine a so that 2/13*a + 0 - 2/13*a**q = 0.
0, 1
Let g(u) be the second derivative of -u**4/3 - 2*u**3/3 + 9*u. Factor g(r).
-4*r*(r + 1)
Let f(a) = -4*a**3 - 6*a**2 + a. Let g(x) = -3*x**3 - 5*x**2. Let u(z) = -2*f(z) + 3*g(z). Factor u(w).
-w*(w + 1)*(w + 2)
Let a = 2392/1145 + 5/458. Let y(g) be the second derivative of 0 - 4*g**4 - g - a*g**5 + 0*g**2 + 49/15*g**6 - 4/3*g**3. Factor y(m).
2*m*(m - 1)*(7*m + 2)**2
Let w = -4221 - -12544/3. Let a = 40 + w. Solve a*c**2 + 1/3*c - 1/3*c**4 - 1/3*c**3 + 0 = 0 for c.
-1, 0, 1
Let s(z) = -z**3 + 7*z**2 - 13*z + 5. Let a be s(3). Factor 1/3*x**a + x**4 + 1/3*x**5 + 0 + x**3 + 0*x.
x**2*(x + 1)**3/3
Let d be ((-140)/(-6))/(-5) + 5. Solve 25/3*f**2 + 7/3*f**4 - 16/3*f + 4/3 - 19/3*f**3 - d*f**5 = 0.
1, 2
Let h(q) be the third derivative of -q**5/15 - q**4/6 - 11*q**2. Determine w so that h(w) = 0.
-1, 0
Let z be ((-9)/((-108)/16))/(2/6). Let c(f) be the second derivative of 0*f**2 - 4*f + 0 - 7/30*f**5 + 1/15*f**6 - 1/9*f**3 + 5/18*f**z. Factor c(o).
2*o*(o - 1)**2*(3*o - 1)/3
Let u(v) = 5*v**2 - 16*v - 16. Let y(d) be the second derivative of -d**4/12 + 2*d**3/3 + 2*d**2 + 3*d. Let n(k) = -2*u(k) - 9*y(k). Factor n(l).
-(l + 2)**2
Let g = -47 - -47. Let c(l) be the first derivative of -l**3 - 3 + g*l**2 + 0*l - 3/4*l**4. Factor c(d).
-3*d**2*(d + 1)
Suppose -5*p - 1245 = -8*p. Let n = p - 2057/5. Solve -14/5*g**5 - 4/5*g - 2*g**4 + 0 + n*g**3 + 2*g**2 = 0.
-1, 0, 2/7, 1
Let t(u) be the first derivative of -2*u**3/3 + 2*u**2 - 3*u/2 - 3. Factor t(k).
-(2*k - 3)*(2*k - 1)/2
Let d be 1 - 412/140 - -2*1. Let c(a) be the third derivative of 0*a**4 + 1/30*a**5 - 1/40*a**6 - a**2 - 1/48*a**8 + 0*a + 0 + 0*a**3 - d*a**7. Factor c(x).
-x**2*(x + 1)**2*(7*x - 2)
Let q = -26 - -42. Factor -10*p**4 + 2*p + q*p**2 + 5*p + 0*p**2 + p - 14*p**3.
-2*p*(p - 1)*(p + 2)*(5*p + 2)
Let l(z) be the second derivative of -z**6/120 + z**4/8 - z**3/3 + 5*z. Let f(x) be the second derivative of l(x). Find s, given that f(s) = 0.
-1, 1
Let c = 2/161 + 228/161. Solve -6/7*r**5 + c*r**4 - 2/7*r**2 + 0 + 0*r - 2/7*r**3 = 0.
-1/3, 0, 1
Let j(y) be the third derivative of 0*y + 0 - 1/15*y**6 + 1/15*y**5 + 0*y**4 - 1/42*y**7 + 0*y**3 + 8*y**2. Factor j(u).
-u**2*(u + 2)*(5*u - 2)
Let y = 8 + -4. What is q in -q**2 - 20*q**4 + y*q**3 + q**2 + 25*q**5 = 0?
0, 2/5
Let s(x) be the third derivative of -x**7/840 + x**6/40 - 9*x**5/40 - x**4/24 - 2*x**2. Let o(a) be the second derivative of s(a). Find r, given that o(r) = 0.
3
Let f = -1 - -5. Let p = 5 - 3. Factor 2*j + 5 - f + 0*j**p + j**2.
(j + 1)**2
Suppose -8 - 1 = -3*b. Factor 3*y**2 + y**2 - 6*y**b - 5*y**4 - 19*y**4 - 14*y**5.
-2*y**2*(y + 1)**2*(7*y - 2)
Factor 0*n**2 + 0 + 3/7*n**3 - 3/7*n.
3*n*(n - 1)*(n + 1)/7
Let m(y) = y**4 - y**3 + y**2 + y - 1. Let k(o) = -2*o**4 - 2*o**3 - 12*o**2 - 4*o + 4. Let g(v) = -k(v) - 4*m(v). Factor g(u).
-2*u**2*(u - 4)*(u + 1)
Let g(y) be the third derivative of 5*y**8/1008 - 5*y**7/126 + y**6/9 - y**5/9 + 2*y**2 - 31*y. Find i such that g(i) = 0.
0, 1, 2
Let l(m) = -m**2 + 10*m - 10. Let v be l(9). Let r be -2*(6/v)/3. Determine d so that 2*d + d**r + d**4 - d**4 + 6*d**3 + 6*d**2 + d**4 = 0.
-1, 0
Let g(l) = l**3 + 9*l**2 + l + 10. Let f be g(-9). Let s(b) be the first derivative of 0*b + 1/3*b**3 + 1/2*b**2 - f. Solve s(r) = 0.
-1, 0
Let s be (-4)/(-6)*-3 + -2. Let k = s + 3. Let d(p) = -6*p**3 + 3*p**2 - 6. Let t(y) = -y**3 - y - 1. Let o(m) = k*d(m) + 3*t(m). Find v such that o(v) = 0.
-1, 1
Let n(w) be the third derivative of 0*w + 4/105*w**7 + 0*w**3 + 0 - 2/15*w**5 + 1/30*w**6 - 1/6*w**4 - 2*w**2. Find g, given that n(g) = 0.
-1, -1/2, 0, 1
Let c(g) be the first derivative of g**4/4 + 4*g**3/3 + 2*g**2 - 64. Suppose c(t) = 0. Calculate t.
-2, 0
Let q(g) be the second derivative of g**8/5040 + g**3/6 + 3*g. Let j(a) be the second derivative of q(a). Factor j(x).
x**4/3
Let d(u) = -u**4 - 5*u**3 + 5*u**2 + 9*u + 4. Let h(w) = -w**4 - 10*w**3 + 10*w**2 + 19*w + 9. Let i(f) = 9*d(f) - 4*h(f). Solve i(g) = 0 for g.
-1, 0, 1
Let m(f) be the second derivative of -f**6/420 + f**4/28 - 2*f**3/21 + f**2 + 6*f. Let t(j) be the first derivative of m(j). Solve t(z) = 0.
-2, 1
Let r(j) be the first derivative of -25*j**4/18 + 20*j**3/9 - 4*j**2/3 - 4*j - 1. Let y(o) be the first derivative of r(o). Factor y(m).
-2*(5*m - 2)**2/3
Let d(n) be the third derivative of -7*n**2 + 0*n**3 + 1/120*n**6 + 1/30*n**5 + 0 + 0*n + 0*n**4. Let d(c) = 0. What is c?
-2, 0
Let w(l) be the third derivative of 5*l**8/336 + l**7/42 - l**6/12 - l**5/6 + 5*l**4/24 + 5*l**3/6 + 37*l**2. Factor w(y).
5*(y - 1)**2*(y + 1)**3
Let h(o) be the first derivative of 5/3*o**3 - 1/12*o**6 + 1/2*o + 1/2*o**5 - 3 - 5/4*o**4 - 5/4*o**2. Factor h(u).
-(u - 1)**5/2
Factor 1/5*f**2 - 1/5*f**3 + f + 3/5.
-(f - 3)*(f + 1)**2/5
Let i(m) = -m**2 + m. Let p(u) = 3*u**2 - 3*u. Let h be ((-15)/9)/(1/(-3)). Let g be (-9)/(-6) - 2/(-4). Let r(s) = g*p(s) + h*i(s). Factor r(t).
t*(t - 1)
Let r = 2250 + -11202/5. Factor 72/5*f**2 - 96/5*f + 3/5*f**4 + r - 24/5*f**3.
3*(f - 2)**4/5
Let r(f) = -f**3 + f**2 + f. Let z(g) = -6*g**3 + 10*g**2 + 7*g - 4. Let p(i) = -21*r(i) + 3*z(i). Factor p(k).
3*(k - 1)*(k + 2)**2
Factor 2 + 15*a**3 + 2*a**4 + 24*a**2 - 2 + a**4 + 12*a.
3*a*(a + 1)*(a + 2)**2
Let g be (4 + 192/(-40))/(18/(-5)). Find p such that 2/3*p**4 + 2/9*p**2 + 0 + 0*p - g*p**5 - 2/3*p**3 = 0.
0, 1
Let o(n) be the second derivative of n**5/60 - n**4/18 - n**3/18 + n**2/3 + 3*n. Factor o(r).
(r - 2)*(r - 1)*(r + 1)/3
Let d(g) be the second derivative of 0*g**2 - 1/10*g**4 - 1/25*g**5 + 0 + g + 2/15*g**3 + 1/25*g**6. Find v such that d(v) = 0.
-1, 0, 2/3, 1
Let q(f) be the first derivative of 119/4*f**4 + 3 + 8*f + 49/5*f**5 + 6*f**3 - 22*f**2. Factor q(j).
(j + 1)*(j + 2)*(7*j - 2)**2
Let p(g) be the second derivative of g**6/40 - g**5/20 - g**2 + 4*g. Let o(v) be the first derivative of p(v). Solve o(y) = 0 for y.
0, 1
Let z(l) = -4 - 3*l**2 + 0*l + l**3 + l - 5*l**2. Let a be z(8). Let -r**2 - 8 + 50*r**5 - 82*r**3 + 17*r - r**2 + 10*r**a + 15*r = 0. Calculate r.
-1, 2/5, 1
Let z = -1 + 6. Factor 4*t**2 + t**2 - 3*t**3 - z*t**2.
-3*t**3
Factor 924*o**2 - 463*o**2 - 465*o**2 + 4.
-4*(o - 1)*(o + 1)
Determine a, given that 1/3*a**2 + 0 + 2/3*a = 0.
-2, 0
Let f(u) be the first derivative of u**4/12 - u**2/2 + 3*u + 2. Let v(n) be the first derivative of f(n). Determine t so that v(t) = 0.
-1, 1
Suppose -7*q + 2*q - 45 = 0. Let d(m) = -11*m**2 + 19*m - 17. Let t(j) = -6*j**2 + 10*j - 8. Let b(k) = q*t(k) + 4*d(k). Factor b(l).
2*(l - 1)*(5*l - 