 + -10 + -1. Let t(l) = x*u(l) + 3*v(l). Factor t(p).
-2*p**2*(p - 1)
Let n = -33 - -35. Let y(z) be the second derivative of n*z - 1/18*z**4 + 0*z**3 + 0 + 1/3*z**2. Factor y(x).
-2*(x - 1)*(x + 1)/3
Let v(b) be the first derivative of -b**8/1008 - b**7/210 + b**5/45 + b**2 + 8. Let l(p) be the second derivative of v(p). Solve l(f) = 0 for f.
-2, 0, 1
Let p(h) be the first derivative of -2 + 0*h**4 - 1/9*h**6 + 1/3*h**2 - 4/9*h**3 + 0*h + 4/15*h**5. Factor p(o).
-2*o*(o - 1)**3*(o + 1)/3
Let h(f) be the first derivative of f**3/15 + 4*f**2/5 + 16*f/5 - 12. Factor h(r).
(r + 4)**2/5
Let y be 1/2*(-6 + 6). Let t = 3 + y. Find u such that 0*u + 0 + 3/2*u**t - 1/2*u**2 = 0.
0, 1/3
Suppose -3*f = 0, -5*f + f = -2*p + 10. Factor -1 + y + 2*y**2 + 1 + p*y + 4.
2*(y + 1)*(y + 2)
Suppose 2*t - 4 = 22. Suppose -18*w = -t*w. What is y in -2*y**4 + 10/3*y**5 + 2*y**2 + w + 4/3*y - 14/3*y**3 = 0?
-1, -2/5, 0, 1
Let q = -548 - -548. Solve 0*f - 1/4*f**3 - 1/4*f**2 + q = 0 for f.
-1, 0
Let h(l) = -22*l**4 - 40*l**3 - 12*l**2 + 172*l + 160. Let f(m) = 9*m**4 + 16*m**3 + 5*m**2 - 69*m - 64. Let c(v) = -12*f(v) - 5*h(v). Factor c(p).
2*(p - 2)*(p + 2)**3
Let n = -6 + 9. Suppose -4*x - 4 = q - 7*x, n*q = 2*x + 2. Factor 2*b**q - b**3 - 17*b**3 + 2*b**2 + 14*b**4.
2*b**2*(b - 1)*(7*b - 2)
Let s(q) be the first derivative of -q**5/150 + q**4/10 - 3*q**3/5 - 2*q**2 - 3. Let j(b) be the second derivative of s(b). Suppose j(h) = 0. Calculate h.
3
Let f(p) be the second derivative of -p**4/24 + p**3/3 - 3*p**2/4 + 16*p. Determine h so that f(h) = 0.
1, 3
Let r be 19/3 + (-1)/3. Let j = 9 - r. Factor -31 + k - 2*k**2 + k**j + 31.
k*(k - 1)**2
Let l = 19 - 16. Let m(z) be the first derivative of -1 + l*z**2 + 2*z + 4/3*z**3. Find w, given that m(w) = 0.
-1, -1/2
Suppose 116 - 122 = -3*b. Factor 2*l**b - 8/3*l**3 + l**4 - 1/3 + 0*l.
(l - 1)**3*(3*l + 1)/3
Let j(s) be the first derivative of 0*s**3 + 1/4*s**4 + 0*s**2 + 0*s + 1/5*s**5 - 3. Suppose j(g) = 0. Calculate g.
-1, 0
Factor -1/3*h**3 - 1/3*h**2 + 2/3*h**4 + 0*h + 0.
h**2*(h - 1)*(2*h + 1)/3
Let x = 149/3 - 49. Let 0*u**2 + 1/3*u**4 - x*u**3 - 1/3 + 2/3*u = 0. What is u?
-1, 1
Let y = 1/5 - -1/5. Let n be (-96)/(-30) - 9 - -7. Let 2*t**2 + 0 + 4/5*t - y*t**4 + n*t**3 - 2/5*t**5 = 0. Calculate t.
-1, 0, 2
Let z = 13/9 + 11/9. Let u(f) be the first derivative of 1/2*f**4 - 3 + z*f**3 + 0*f - 8/5*f**5 - f**2. Factor u(a).
-2*a*(a - 1)*(a + 1)*(4*a - 1)
Factor -w**2 + 3 + 0 + 3*w - 7 + 2.
-(w - 2)*(w - 1)
Factor -3/4*l + 0 - 3/4*l**2.
-3*l*(l + 1)/4
Suppose -3*g + 9 + 6 = 0. Suppose -3*j - g*i + 19 = 0, -j + 2*i + i = 3. Factor 1 - 3*u**2 + u + 2*u**2 + 0*u**2 - u**j.
-(u - 1)*(u + 1)**2
Let l(w) be the third derivative of -w**6/150 + w**5/75 + w**4/15 + 10*w**2. What is x in l(x) = 0?
-1, 0, 2
Let d(h) = -3*h**3 - h**2 - h. Let f be d(-1). Solve 8*b**3 - 5 + f*b**4 + 12*b**2 - 11 - 16*b - 3*b**4 - 4*b**4 = 0 for b.
-1, 2
Let q(r) be the second derivative of -r**5/80 - r**4/12 - 5*r**3/24 - r**2/4 + 32*r. Let q(p) = 0. What is p?
-2, -1
Let u(k) be the third derivative of -1/40*k**6 + 1/210*k**7 + 0 + 1/60*k**5 + 1/8*k**4 + 0*k - 1/3*k**3 - 8*k**2. Factor u(z).
(z - 2)*(z - 1)**2*(z + 1)
Let q(n) = 2*n**5 + 4*n**4 - 6*n**3 + 4*n - 2. Let i(m) = -4*m**5 - 9*m**4 + 12*m**3 - m**2 - 8*m + 5. Let c(f) = 2*i(f) + 5*q(f). Factor c(k).
2*k*(k - 1)**2*(k + 1)*(k + 2)
Factor 16*r**4 + 33*r**2 - r**2 + 12*r - 86*r**3 + 26*r**3.
4*r*(r - 3)*(r - 1)*(4*r + 1)
Let w(s) = -s + 15. Let k be w(15). Let b(n) be the first derivative of 1/3*n**6 + 0*n + k*n**5 + 0*n**3 + 2 + n**2 - n**4. Determine m, given that b(m) = 0.
-1, 0, 1
Let r(d) = -d**5 + d**4 - d**3 - d**2 - d + 1. Let i(w) = 2*w**5 - 2*w**4 + 4*w**3 + 4*w**2 + 4*w - 4. Let q(x) = -i(x) - 4*r(x). Factor q(v).
2*v**4*(v - 1)
Let n = -1 - -1. Determine c so that 2*c**3 + 3*c**2 + 2*c + 6*c**2 - 5*c**2 + n*c**3 = 0.
-1, 0
Suppose 15 = -5*m, -m = 4*v - 3*m - 6. Let k be (-1)/((-1)/4*2). Solve -n**2 + 3*n**3 + 6*n**2 + v*n + k*n = 0 for n.
-1, -2/3, 0
Let 3/5*r**4 + 54/5 - 27/5*r**3 - 117/5*r + 87/5*r**2 = 0. What is r?
1, 2, 3
Let g be (-4 - -4)*(7 + 88/(-12)). Factor g + 4/3*i + 5/3*i**3 - 4*i**2.
i*(i - 2)*(5*i - 2)/3
Let p(h) = -35*h**4 + 15*h**3 + 75*h**2 + 40*h. Let i(v) = 9*v**4 - 4*v**3 - 19*v**2 - 10*v. Let y(z) = -15*i(z) - 4*p(z). Factor y(l).
5*l*(l - 2)*(l + 1)**2
Let r be (-9 + 1)*(-20)/32. Let c(b) be the second derivative of -1/100*b**r + 0*b**2 + 0 + 1/15*b**4 + b - 2/15*b**3. Solve c(n) = 0 for n.
0, 2
Let d be (1 - (-2)/(-4))*10. Factor 5*p + 88*p**2 + 392*p**d + 354*p**3 + 544*p**4 + 72*p**4 + 3*p.
2*p*(2*p + 1)**2*(7*p + 2)**2
Let u be 12/3*(-9)/(-12). Factor -5*i**2 - 3*i**u + 2*i + 3*i - 7*i.
-i*(i + 1)*(3*i + 2)
Let i = -148 - -151. Factor -2/3*r - 8/3*r**i + 0 + 8/3*r**2.
-2*r*(2*r - 1)**2/3
Let l be 2/5 - (-10)/(-25). Suppose 8 = f + 3. Factor -14*m**2 + 5*m + 4 + f*m + l.
-2*(m - 1)*(7*m + 2)
Factor 1/4*d**3 - 1 + 2*d - 5/4*d**2.
(d - 2)**2*(d - 1)/4
Let j(f) be the third derivative of -f**6/160 + f**5/80 - 14*f**2. Let j(l) = 0. What is l?
0, 1
Suppose 0 + 0*c**2 - 1/5*c + 0*c**4 + 2/5*c**3 - 1/5*c**5 = 0. What is c?
-1, 0, 1
Let i(z) be the first derivative of 0*z**4 + 2 + 1/2*z**2 - 1/300*z**6 - 1/150*z**5 + 0*z**3 + 0*z. Let g(q) be the second derivative of i(q). Factor g(b).
-2*b**2*(b + 1)/5
Let c be (5 + 4)*1/3. Let x(l) be the first derivative of 1/11*l**2 + 1/33*l**6 + 1 + 2/11*l - 1/11*l**4 + 2/55*l**5 - 4/33*l**c. Factor x(m).
2*(m - 1)**2*(m + 1)**3/11
Factor -1/9*k**3 - 1/9 + 1/9*k + 1/9*k**2.
-(k - 1)**2*(k + 1)/9
Let m(g) be the first derivative of g**6/27 - 4*g**5/45 + 4*g**3/27 - g**2/9 + 4. Factor m(r).
2*r*(r - 1)**3*(r + 1)/9
Suppose -11*g = -18 - 4. What is f in 0*f + 0 - 8/7*f**3 + 2/7*f**g = 0?
0, 1/4
Suppose -5*x - 16 = -5*f - 4*x, 24 = 3*f + 3*x. Solve 4*o**2 + 9*o**5 + 4*o - 12*o**f - 3*o - 9*o**3 + 7*o**3 = 0 for o.
-1/3, 0, 1
Let v(c) be the first derivative of -c**6/105 - c**5/70 + c**4/42 + c**3/21 + c + 1. Let w(z) be the first derivative of v(z). Factor w(m).
-2*m*(m - 1)*(m + 1)**2/7
Let r be (10/15)/((-20)/(-90)). Solve 13/6*t**2 + 2/3 + 2*t + t**r + 1/6*t**4 = 0.
-2, -1
Suppose 10 = 4*w + w. Let 2*q**3 + 4*q - 4*q - w*q**4 = 0. What is q?
0, 1
Let o be (-5)/(-1) - 9/3*1. Let t(f) be the second derivative of 0*f**2 + 1/30*f**4 - o*f + 1/15*f**3 + 0. Solve t(m) = 0 for m.
-1, 0
Let l(a) = 11*a**3 - 14*a**2 - 15*a + 14. Let w(j) = -65*j**3 + 85*j**2 + 90*j - 85. Let r(z) = 25*l(z) + 4*w(z). Factor r(q).
5*(q - 1)*(q + 1)*(3*q - 2)
Let w(n) = -22*n**3 + 42*n**2 - 18*n + 22. Let t(p) = 9*p**3 - 17*p**2 + 7*p - 9. Let b(v) = 12*t(v) + 5*w(v). Solve b(d) = 0 for d.
1
Let k(r) be the third derivative of 8/735*r**7 + 0 + 4/105*r**5 - 1/42*r**4 - 1/588*r**8 - 1/35*r**6 + 0*r**3 + 0*r + 6*r**2. Factor k(l).
-4*l*(l - 1)**4/7
Suppose -3*c + 12 = 3*l, c - 3*l + 0*l + 12 = 0. Suppose q = -2*r + 4, 4*r - 5*q - 3 - 5 = c. Factor -2*w**4 + 0*w**3 - 2*w**3 - r*w**2 + 2*w**5 + 4*w**2.
2*w**2*(w - 1)**2*(w + 1)
Let j(f) = 9*f**4 - 12*f**3 - 6*f**2 + 5. Let x(i) = 18*i**4 - 24*i**3 - 11*i**2 + i + 9. Let q(w) = 7*j(w) - 4*x(w). Factor q(s).
-(s - 1)**2*(3*s + 1)**2
Let j = 1 + 6. Let t = -7 + j. Factor 2/5*a**3 + t + 4/5*a**2 + 0*a.
2*a**2*(a + 2)/5
Let c(i) be the first derivative of 0*i**2 + 1/4*i**4 + 0*i - 1/5*i**5 + 2 + 0*i**3. Factor c(x).
-x**3*(x - 1)
Suppose -885 - 8*j**3 + 885 - 6*j**2 + 4*j - 2*j = 0. Calculate j.
-1, 0, 1/4
Suppose 0 = -3*t - j + 38, 4*t - 33 + 9 = 4*j. Solve -21*s**3 + t*s**3 + 2*s**2 + 12*s**3 = 0 for s.
-1, 0
Let 12*f + 70*f**3 + 5*f**5 + 80*f**2 + 3*f + 28*f + 10 + 2*f + 30*f**4 = 0. What is f?
-2, -1
Let l(n) be the first derivative of -n**9/12096 + n**7/1680 - n**5/480 + n**3 + 1. Let y(r) be the third derivative of l(r). Factor y(w).
-w*(w - 1)**2*(w + 1)**2/4
Let u = 409/9 + -45. Factor -22/9*w + 2*w**2 + u.
2*(w - 1)*(9*w - 2)/9
Let k(g) be the second derivative of 7/18*g**4 + 13/45*g**6 + 4/63*g**7 + 1/9*g**3 + 0 + 0*g**2 + 1/2*g**5 - 2*g. Factor k(n).
2*n*(n + 1)**3*(4*n + 1)/3
Let i(q) be the first derivative of q**6/12 - 3*q**5/10 + q**4/8 + q**3/2 - q**2/2 - 9. Factor i(u).
u*(u - 2)*(u - 1)**2*(u + 1)/2
Let l be 1*0/(5/((-15)/6)). Let h(f) be the second derivative of l*f**3 + 0*f**2 - 1/6*f*