).
-3*l**4*(l + 1)/5
Suppose 4*b = -5*v + v + 36, 0 = -5*b - 4*v + 41. Factor 50*g + 39 + b*g**2 + 84 + 2.
5*(g + 5)**2
Solve -1/5*j**3 - 9/5*j + 0 - 2*j**2 = 0.
-9, -1, 0
Let q(g) = 13*g**3 - 57*g**2 + 64*g - 18. Let f(j) = -j**3 - j**2 + 2*j + 1. Let w(m) = 2*f(m) - q(m). Factor w(i).
-5*(i - 2)*(i - 1)*(3*i - 2)
Let t be (-9)/21 + 250/420. Let v(x) be the third derivative of 4/3*x**3 + 0*x - 1/15*x**5 + 0 - t*x**4 + 3*x**2. Suppose v(s) = 0. Calculate s.
-2, 1
Let r(j) be the first derivative of 0*j**2 + 0*j**3 + 1/25*j**5 + 1 + 1/30*j**4 + 1/75*j**6 - j. Let v(n) be the first derivative of r(n). Factor v(p).
2*p**2*(p + 1)**2/5
Let n(o) = 172*o**2 + 23*o + 1. Let p(s) = -173*s**2 - 22*s - 1. Let y = 94 - 97. Let f(c) = y*p(c) - 4*n(c). Factor f(j).
-(13*j + 1)**2
Let q(r) be the first derivative of r**4/20 + 19*r**3/15 + 42. Factor q(y).
y**2*(y + 19)/5
Let u(j) be the first derivative of -1/40*j**5 + 3/16*j**2 + 0*j + 5/24*j**3 - 36 + 1/32*j**4. Factor u(d).
-d*(d - 3)*(d + 1)**2/8
Let n(f) be the second derivative of -24/35*f**7 - 6*f + 0 + 259/30*f**4 + 68/15*f**6 + 4/5*f**2 - 1017/100*f**5 - 18/5*f**3. Suppose n(q) = 0. What is q?
2/9, 1/4, 2
Let x(m) be the third derivative of m**5/30 - 5*m**4/12 + 4*m**3/3 + 19*m**2. Suppose x(p) = 0. What is p?
1, 4
Suppose -26/9*z**2 + 98/9 + 70/9*z + 2/9*z**3 = 0. What is z?
-1, 7
Let g(w) be the first derivative of -w**6/48 + 7*w**5/20 + w**4 + w**3/12 - 31*w**2/16 - 2*w + 195. Factor g(x).
-(x - 16)*(x - 1)*(x + 1)**3/8
Let i(n) be the first derivative of -n**3/24 - 37*n**2/16 - 9*n/2 - 386. Factor i(t).
-(t + 1)*(t + 36)/8
Let m(l) be the first derivative of -3*l**5/5 - 11*l**4/4 + 4*l**3/3 + 90. Factor m(y).
-y**2*(y + 4)*(3*y - 1)
Let l(n) = n**2 + n. Let x = 4 - 18. Let z(q) be the second derivative of 2*q**4/3 + q**3/2 + 3*q**2/2 + 4*q - 11. Let s(a) = x*l(a) + 2*z(a). Factor s(b).
2*(b - 3)*(b - 1)
Factor -2*u**3 - 28*u - u**4 + 3 - 11 + 20 + 19*u**2.
-(u - 2)*(u - 1)**2*(u + 6)
Suppose i**2 - 2949 + 27*i + 2949 = 0. What is i?
-27, 0
Let d(k) be the third derivative of -k**6/720 - k**5/40 - 3*k**4/16 - 2*k**3/3 + 4*k**2. Let i(q) be the first derivative of d(q). Let i(p) = 0. Calculate p.
-3
Let m(v) be the second derivative of -v**4/4 - 8*v**3/3 + 7*v**2 - 5*v. Let u be m(-6). Factor -4/5 - 9*j**u + 5*j**3 + 24/5*j.
(j - 1)*(5*j - 2)**2/5
Suppose 4*y + y - 30 = 0. Find w such that 8*w + 3*w**2 + y + w**2 - 2*w**2 = 0.
-3, -1
Let y(h) = h**2 + 3*h - 2. Let w be y(-5). Suppose -6*t = -w - 10. Factor -k - 26*k**2 - 29*k**2 + 53*k**2 - k**t.
-k*(k + 1)**2
Let f = -821 - -826. Let d(o) be the third derivative of 2/3*o**4 + 10*o**2 + 0*o + 2/105*o**7 + 2/3*o**3 + 0 + 2/15*o**6 + 2/5*o**f. Factor d(x).
4*(x + 1)**4
Let w(c) be the second derivative of -c**7/21 + 6*c**6/5 - 37*c**5/5 + 62*c**4/3 - 31*c**3 + 26*c**2 - 514*c. What is h in w(h) = 0?
1, 2, 13
Factor -14/5*n + 0 - 86/15*n**2 - 46/15*n**3 - 2/15*n**4.
-2*n*(n + 1)**2*(n + 21)/15
Suppose -5*k + 18 = -22. Let q be 18/4 - 4/k. Suppose 7*n - 4*n**3 + 2*n**4 + 3*n**2 - 4 - 3*n - 2*n**q + n**4 = 0. What is n?
-1, 1, 2
Let k(s) be the first derivative of -s**3/12 - 5*s**2/8 - 3*s/2 - 33. Factor k(y).
-(y + 2)*(y + 3)/4
Let j(m) be the second derivative of -1/210*m**6 - 12*m + 0 + 1/42*m**3 + 0*m**2 + 1/84*m**4 - 1/140*m**5. Factor j(k).
-k*(k - 1)*(k + 1)**2/7
Factor -4/5*l**2 - 236/5*l + 0.
-4*l*(l + 59)/5
Let j(f) be the third derivative of f**4/24 - 5*f**3/6 + 4*f**2. Let z be j(9). Factor z*d + 4*d**2 - 3*d**3 - 2*d**4 + 0*d - d**5 - 4*d**4 + 2*d**4.
-d*(d - 1)*(d + 1)*(d + 2)**2
Let q(b) = 3*b**3 + 431*b**2 + 21619*b + 352952. Let l(h) = 3*h**3 + 433*h**2 + 21617*h + 352951. Let u(z) = 5*l(z) - 4*q(z). Factor u(p).
3*(p + 49)**3
Let w(c) be the first derivative of -3*c**5/160 - 5*c**4/32 - 3*c**3/8 + 16*c + 24. Let x(z) be the first derivative of w(z). Factor x(r).
-3*r*(r + 2)*(r + 3)/8
Suppose -3*c + 8 = -4. Factor 40 + 3*f**2 - c*f**2 + 9*f**2 - 3*f**2 + 50*f - 5*f**3.
-5*(f - 4)*(f + 1)*(f + 2)
Let f be 6/27 + (-7)/(-9) - -4. Factor -9*y**2 - f*y**2 + 5*y**3 + 35*y - 11*y**2 + 0*y**2 - 15.
5*(y - 3)*(y - 1)**2
Find t such that 4*t**3 + 2 - 2/5*t**5 - 6/5*t**4 - 4/5*t**2 - 18/5*t = 0.
-5, -1, 1
Let a(s) be the second derivative of s**7/189 + s**6/45 - s**5/15 - 14*s**4/27 - 8*s**3/9 + 35*s. Factor a(y).
2*y*(y - 3)*(y + 2)**3/9
Let -50 - 4 + 79*k - 352*k**2 + 462*k**4 - 56*k**2 - 195*k**5 - 184*k - 246*k + 546*k**3 = 0. Calculate k.
-1, -2/5, -3/13, 1, 3
Suppose 4*j + 18 - 6 = 2*t, 0 = -j - 3*t - 3. Let b be (77 - 77)*-1*1/j. Determine f so that b - 2/3*f**2 + 2/3*f = 0.
0, 1
Let z be ((-36)/27)/((-4)/162). Factor 10*l**2 - z*l - 5*l**2 + 49*l.
5*l*(l - 1)
Let s be 69/138*(-1 + (-4 - -6 - 1)). What is k in -1/3*k**5 + 4/9*k**2 + 1/9*k + 2/9*k**3 - 4/9*k**4 + s = 0?
-1, -1/3, 0, 1
Suppose -22 = -5*c + s, -3*c - 14*s + 12*s + 8 = 0. Let n(d) be the second derivative of 6*d**2 + 0 + 9/4*d**4 - 6*d**3 - c*d. Let n(l) = 0. Calculate l.
2/3
Suppose 0 = -8*t + 45 + 11. Solve 11*r**2 - 6*r**3 - 4*r + r + 3*r**2 + 2 - t*r = 0.
1/3, 1
Suppose -n = 3*a + 9, -5*n - 2 = 4*a - 1. Let j(s) = -s**2 - 4*s + 2. Let q be j(a). What is h in 4*h**3 - h**2 - h**5 + 9*h**2 + 342 - 342 - q*h**4 = 0?
-2, 0, 2
Let 0 + 36/5*f**3 + 0*f**2 + 0*f + 38/5*f**4 + 2/5*f**5 = 0. What is f?
-18, -1, 0
Let a(q) = -12*q**2 + q + 3. Let g(l) = 6*l**2 - 2. Suppose 0 = -10*t + 9*t - 3*n + 19, -26 = -2*t - 2*n. Let h(w) = t*g(w) + 4*a(w). Factor h(d).
4*(d + 1)*(3*d - 2)
Suppose 2*t = 2*i + 80, -2*t = 2*i + t + 85. Let c = i - -42. Determine k so that c - 1/2*k - 1/2*k**2 = 0.
-2, 1
Let i = 2/54719 - -164147/273595. Suppose 0*v + 0 + 6/5*v**2 - i*v**4 - 3/5*v**3 = 0. Calculate v.
-2, 0, 1
Let h = 176 - 176. Let a be ((-3)/25)/((-48)/80). Factor h*c + 1/5 - a*c**2.
-(c - 1)*(c + 1)/5
Let q(p) = -p**3 + 12*p**2 - 3*p - 13. Let f(n) = -n**3 + n - 1. Let g be -2 - (23/(-7) - (-10)/35). Let b(m) = g*q(m) + 3*f(m). Solve b(i) = 0 for i.
-1, 2
Let l be (-13)/(-24) + (-11)/(-12)*(-99)/(-726). Factor -l*a + 0 + 7*a**3 + 3*a**5 + 25/3*a**4 + a**2.
a*(a + 1)**3*(9*a - 2)/3
Solve 0 + 0*f - 2/7*f**2 - 2/7*f**3 = 0.
-1, 0
Let a(d) be the first derivative of -d**5/12 + 5*d**4/12 + 5*d**3/2 + 11*d**2/2 - 13. Let u(p) be the second derivative of a(p). Factor u(f).
-5*(f - 3)*(f + 1)
Let b(f) be the second derivative of f**7/56 - 9*f**5/80 + f**4/8 - 158*f. Find m such that b(m) = 0.
-2, 0, 1
Let q = -33 + 22. Let c = q - -11. Factor -2 - 3*z**4 + 5*z**2 + z**2 + c - 1.
-3*(z - 1)**2*(z + 1)**2
Suppose 2 = -2*h - 5*v + 35, -2*v + 2 = 0. Suppose 3*o - h = o. Determine m, given that 4*m**2 + 5*m**2 - 12 - o*m**2 - 32*m + 8*m**3 - 14*m**2 = 0.
-1, -1/2, 3
Let k(v) be the second derivative of v**6/40 - v**5/20 - v**4/4 + 6*v**2 + 5*v. Let t(w) be the first derivative of k(w). Let t(z) = 0. What is z?
-1, 0, 2
Let j(b) be the second derivative of 11*b**7/105 - 7*b**6/120 - b**5/30 - 12*b**2 + 8*b. Let c(g) be the first derivative of j(g). Factor c(x).
x**2*(2*x - 1)*(11*x + 2)
Let c(r) be the second derivative of 0*r**4 + 0 + 1/2*r**3 - 3/20*r**5 + 0*r**2 + 7*r. Factor c(z).
-3*z*(z - 1)*(z + 1)
Let p(k) be the first derivative of 9685/6*k**4 + 3500/3*k**6 + 297/2*k**2 - 20 + 6380/3*k**5 + 653*k**3 + 18*k. Suppose p(n) = 0. What is n?
-1/3, -3/10, -2/7
Let u(a) = a**5 + a**4 - a. Let f = -192 + 188. Let y(g) = 0*g - g**5 + 3*g**2 + 4*g - 3*g**3 - 7*g**4 + 0*g. Let o(v) = f*u(v) - y(v). Solve o(i) = 0.
-1, 0, 1
Let r = 590/129 + 4/43. Factor r*b**2 + 16/3*b**3 + 0 + 2*b**4 + 4/3*b.
2*b*(b + 1)**2*(3*b + 2)/3
Suppose -3*g = -44 - 28. Factor 11*z**3 + 39*z**3 + g - 8*z - 10*z**2 - 24*z - 32.
2*(z - 1)*(5*z + 2)**2
Let x(z) be the second derivative of z**4/18 + 8*z**3/3 + 23*z**2/3 - 6*z + 7. Factor x(k).
2*(k + 1)*(k + 23)/3
Let k = 183/10 + -109/6. Let d = k - -11/30. Determine n so that d*n + 1/4 + 1/4*n**2 = 0.
-1
Let f(t) be the second derivative of -t**4/4 + 10*t**3 - 153*t**2/2 + 403*t. Factor f(q).
-3*(q - 17)*(q - 3)
Suppose b - 3*w - 6 = 0, b + b + 4*w - 32 = 0. Suppose -u - 2*q + b = 0, 0 = -4*u - 0*u + 3*q - 7. Factor 0 + 0 - 6*i**2 + 3*i**u - 9 - 12*i.
-3*(i + 1)*(i + 3)
Let q = 14 - 12. Factor 10*s**2 - 19 - 1 - 5*s**q.
5*(s - 2)*(s + 2)
Let y(j) be the third derivative of 13*j**2 +