*r + 110, -66 = 3*r + 3*n. Let s(y) = -2*y**2 + 5*y. Let c(o) = -8*o**2 + 19*o. Let w(f) = r*s(f) + 6*c(f). Factor w(i).
-4*i*(i - 1)
Let a(b) be the second derivative of 0 + 8/3*b**3 - 8/3*b**2 + 7/9*b**4 - 8*b. Factor a(q).
4*(q + 2)*(7*q - 2)/3
Determine q so that 6*q + 3/2*q**4 - 21/2*q**2 + 0 + 3*q**3 = 0.
-4, 0, 1
Let o(a) be the second derivative of a**6/6 - 7*a**5/4 + 25*a**4/6 - 16*a. Factor o(k).
5*k**2*(k - 5)*(k - 2)
Let t(j) be the second derivative of -j**6/480 + 9*j**4/32 - 2*j**3 + 41*j. Let w(f) be the second derivative of t(f). Determine k so that w(k) = 0.
-3, 3
Let f(k) be the first derivative of 0*k - 1/5*k**5 + k**2 + 0*k**4 + k**3 - 1. Suppose f(p) = 0. Calculate p.
-1, 0, 2
Suppose -3*h + 12 = -0*h. Suppose 4*g + 5*l - 11 = 2*g, -7 = -h*g + 5*l. Suppose 4*r**2 + 2 + 2*r**3 + 0*r**2 + 5*r - r**g = 0. Calculate r.
-2, -1
Let j(u) be the third derivative of u**8/1260 - u**7/630 - u**6/135 + 41*u**3/6 - u**2 + 20*u. Let d(z) be the first derivative of j(z). Factor d(g).
4*g**2*(g - 2)*(g + 1)/3
Factor -24*n - 28*n + 80*n**2 - 25*n**4 + 2*n + 5*n**2 + 110*n**3.
-5*n*(n - 5)*(n + 1)*(5*n - 2)
Let m be 2/(-9) - 58/(-18). Let z be -6 - -2 - (-7 + (-80)/(-28)). Factor 0 + 0*i**m + 1/7*i**2 + 0*i - z*i**4.
-i**2*(i - 1)*(i + 1)/7
Solve -2*s + 2*s**2 - 9*s - 1058 + 10306 - 261*s = 0.
68
Let d be ((-20)/(-250))/((-1)/(-1465)). Let y = d + -7578/65. Factor -2/13*v**3 - 6/13*v + 0 + y*v**2.
-2*v*(v - 3)*(v - 1)/13
Let t = 642 - 1145. Let k = t + 3527/7. Factor -2/7*o**4 + k*o**2 + 0*o**3 + 0 - 4/7*o.
-2*o*(o - 1)**2*(o + 2)/7
Let p be (-46)/529 - (20/115)/(-2). Factor p + 2/7*m**4 - 2/7*m**2 + 4/7*m - 4/7*m**3.
2*m*(m - 2)*(m - 1)*(m + 1)/7
Let l be (-2)/4*(0/3 + 0). Let y(s) be the second derivative of l - 3*s + 1/6*s**5 + 6*s**2 + 11/3*s**3 - 14/9*s**4. Factor y(u).
2*(u - 3)**2*(5*u + 2)/3
Suppose 2*p + 41 = 5*o + 6, 35 = 5*o + 4*p. Let d be 2/o*(-56)/(-24). Find h such that -4/9 - d*h - 2/9*h**2 = 0.
-2, -1
Let l(h) be the first derivative of -h**7/4200 - h**6/1800 - 20*h**3/3 + 16. Let d(r) be the third derivative of l(r). What is q in d(q) = 0?
-1, 0
Let x(f) = -2*f**3 + 302*f**2 - 10653*f - 22500. Let a(l) = -18*l**3 + 2716*l**2 - 95876*l - 202500. Let r(s) = -6*a(s) + 52*x(s). Factor r(i).
4*(i - 75)**2*(i + 2)
Let t(q) be the third derivative of 0 + 22*q**2 + 1/120*q**6 + 7/300*q**5 - 1/15*q**4 + 0*q - 2/15*q**3. Suppose t(d) = 0. Calculate d.
-2, -2/5, 1
Let i = 6 - 11. Let b(j) = -86 + 26 - j**3 + 39*j - 2*j**3 + 60*j**2. Let s(a) = a**3 - 17*a**2 - 11*a + 17. Let g(q) = i*b(q) - 18*s(q). Factor g(p).
-3*(p - 2)*(p - 1)*(p + 1)
Let i(x) be the first derivative of -4*x**2 + 2/5*x**5 + 0*x - 11 + 6*x**3 - 3*x**4. Factor i(n).
2*n*(n - 4)*(n - 1)**2
Let n = 2678/9 + -13381/45. Determine m, given that 4/5*m - n*m**4 + 3/5*m**2 - 4/5 - 2/5*m**3 = 0.
-2, 1
Factor 0 + 2/7*c**2 + 18/7*c.
2*c*(c + 9)/7
Let o = -439 - -879/2. Let z(l) be the second derivative of 1/3*l**3 + 0*l**4 - 2*l + 0 - 1/30*l**6 + o*l**2 - 1/10*l**5. Let z(a) = 0. What is a?
-1, 1
Let w be (6/4)/(1/(112/12)). Let f be (-30)/w*(-24)/20. Factor -10/7*h**2 + 6/7*h**3 + 0 + f*h**4 + 2/7*h.
2*h*(h + 1)*(3*h - 1)**2/7
Let o be (8/6)/(4/12). Suppose -2*y = 2*q - 46, 2*y - 16 = -0*y + o*q. Factor -12*x**4 - 2*x**4 + 6*x**2 + 3*x**3 - 10*x**4 - 3*x**5 + y*x**5.
3*x**2*(x - 1)**2*(5*x + 2)
Let x(v) be the third derivative of 1/42*v**4 + 14*v**2 + 0 + 0*v - 1/42*v**5 + 0*v**3 - 1/140*v**6. Determine a so that x(a) = 0.
-2, 0, 1/3
Suppose 0 = -15*j + 19*j - 84. Let r be (-2)/6 + 7/j. Suppose r*t**2 - 3/2*t**3 + 0 + 2*t - 1/2*t**4 = 0. What is t?
-2, 0, 1
Let b be ((-19)/(-60))/(24/(-60)). Let s = 9/8 + b. What is i in s*i**2 - 2/3*i + 1/3 = 0?
1
Suppose 0 = -4*w + 2*v + 264, 5*v - 11 = -31. Let t = w - 446/7. Suppose 2/7*u - t*u**2 + 0 = 0. Calculate u.
0, 1
Let a(o) be the third derivative of o**5/180 - o**4/12 - 91*o**3/18 - 55*o**2 - 2. Determine w so that a(w) = 0.
-7, 13
Let r be (224/(-5))/(1/(-5)). Factor 193*n - 192*n - 704*n**2 + r*n**3 - 34*n**4 - 512 + 1023*n + 2*n**5.
2*(n - 4)**4*(n - 1)
Let o = -2787 - -2791. Factor 0*j + j**2 + 2/3*j**o + 7/3*j**3 + 0.
j**2*(j + 3)*(2*j + 1)/3
Find z such that -10*z + 7 + 42*z**2 + 1 + 50*z + 48*z = 0.
-2, -2/21
Let t be (-168)/(-147)*35/25. Find n such that 8/5*n - 2/5*n**3 + 2/5*n**2 - t = 0.
-2, 1, 2
Suppose -8*f - j + 6 = -3*f, 2*j = -8. Determine g so that -5*g**3 - 3*g + 23*g - 31*g**2 + 11*g**f + 5*g**4 = 0.
-2, 0, 1, 2
Let n(o) = -o**3 + 4*o**2 - o + 3. Let r be n(3). Factor 0*f**2 + 3*f**2 - r - 46*f + 52*f.
3*(f - 1)*(f + 3)
Let u(z) be the first derivative of -1/27*z**3 + 0*z + 1/45*z**5 - 1/18*z**4 + 1/9*z**2 - 10. Factor u(t).
t*(t - 2)*(t - 1)*(t + 1)/9
Factor -3*j + 18/5 - 3/5*j**2.
-3*(j - 1)*(j + 6)/5
Solve 56*x**3 + 37 - 2*x**2 + 70*x**2 - 51*x**3 + 43 + 165*x + 22*x**2 = 0 for x.
-16, -1
Let p(y) be the second derivative of -22*y**4/3 + 50*y**3/3 - 6*y**2 + y + 36. Let p(o) = 0. Calculate o.
3/22, 1
Factor -43*d**2 + 10*d**3 - 58*d**2 - 20*d**2 - d**4 - 32*d**3.
-d**2*(d + 11)**2
Let l(h) be the third derivative of h**5/15 + 5*h**4/2 + 28*h**3/3 - 9*h**2 + 6. Find n, given that l(n) = 0.
-14, -1
Suppose -2*b + 9*j = 4*j + 49, 26 = -b + 2*j. Let c be ((-6)/4)/(16/b). Suppose -4*z**c + z**5 + z**5 + 2*z**5 = 0. What is z?
-1, 0, 1
Let p(t) be the third derivative of 0 - 5/6*t**3 + 4*t**2 + 3/40*t**5 - 1/120*t**6 + 0*t - 1/4*t**4. Let h(g) be the first derivative of p(g). Factor h(k).
-3*(k - 2)*(k - 1)
Let x(r) be the first derivative of r**4/6 - 8*r**3/9 + 5*r**2/3 - 4*r/3 + 65. Factor x(j).
2*(j - 2)*(j - 1)**2/3
Factor 2*s**2 - 126 + 14*s + 67 + 71.
2*(s + 1)*(s + 6)
Let c = -9 + 24. What is x in x**2 - 9*x + c - 9 - 13 - 3 = 0?
-1, 10
Suppose -4*s - 14 = -5*j, -5*j + 3*s = -16 + 3. Suppose 2*r**2 - 4*r**j - 172*r**3 - r**2 + 166*r**3 - 3*r**4 = 0. What is r?
-1, 0
Factor 4*w - 2*w**3 - 2*w + 154 - 303 + 14*w**2 + 135.
-2*(w - 7)*(w - 1)*(w + 1)
Let h = 182 - 182. Let k(i) be the third derivative of 0*i**4 + 0*i + 10*i**2 + 2/105*i**5 + 0*i**3 + h - 1/420*i**6. Let k(s) = 0. Calculate s.
0, 4
Let u(p) be the first derivative of 4*p**3/3 + 32*p**2 + 60*p + 77. Determine n, given that u(n) = 0.
-15, -1
Let b be 1/4 - 4/16. Let h = 3/3640 + 3631/10920. Factor 0 + b*o + 2/3*o**2 - h*o**3.
-o**2*(o - 2)/3
Let y(f) be the second derivative of f**8/17920 - f**7/5040 - f**6/1440 - f**4/6 - 11*f. Let b(g) be the third derivative of y(g). Find q, given that b(q) = 0.
-2/3, 0, 2
Let o(v) = -9*v**2 - 69*v - 66. Let t(x) = -8*x**2 - 68*x - 65. Let r(q) = -5*o(q) + 6*t(q). Factor r(z).
-3*(z + 1)*(z + 20)
Let x = -151 - -154. Let y(m) be the first derivative of m**4 + 1/24*m**6 + 2 - 2*m**2 - 2/3*m**x - 7/20*m**5 + 4*m. Let y(v) = 0. What is v?
-1, 2
Let j(x) be the second derivative of -5/39*x**3 + 1/13*x**2 + 2/39*x**4 + 2 - 5*x. Let j(t) = 0. Calculate t.
1/4, 1
Let o(l) be the first derivative of -l**6/39 - 14*l**5/65 + 11*l**4/13 + 56*l**3/39 - 72*l**2/13 + 395. Find f, given that o(f) = 0.
-9, -2, 0, 2
Let n(i) be the third derivative of -3267*i**5/70 + 33*i**4/7 - 4*i**3/21 - 78*i**2 - i. Factor n(y).
-2*(99*y - 2)**2/7
Let o = -1 - -1. Suppose 0 = 5*d - 2*h - 2*h, -5*d + 2*h = o. What is b in 6*b + 0*b + 3*b**2 + d*b**2 = 0?
-2, 0
Factor 26 - 48*i**2 - 8*i**2 + 4*i**2 + 4*i**3 + 86 - 64*i.
4*(i - 14)*(i - 1)*(i + 2)
Suppose 0 = 21*x - 22*x + 3. Suppose 6 = x*s - l - 5, 0 = 5*l + 10. Find u, given that 0*u + 3/7*u**s + 3/7*u**2 + 0 = 0.
-1, 0
Let j(y) = -20*y**3 + 9*y**2 + 47*y - 31. Let g(r) = -10*r**3 + 5*r**2 + 23*r - 15. Let l(b) = 5*g(b) - 3*j(b). Factor l(k).
2*(k - 1)**2*(5*k + 9)
Suppose -4*t = 5*m + 15, -3*m + t = -0 - 8. Let j be (5 - (-10)/(-2))/(m + 0). Factor 0 - 3/5*f**3 + j*f + 3/5*f**2.
-3*f**2*(f - 1)/5
Let q = 541/3 - 3811/21. Let l = q + 55/42. Factor -1/3*t - l*t**2 - 1/6.
-(t + 1)**2/6
Let s(p) = p - 23. Let d be s(9). Let c be (0 - d/(-90)) + (-3)/(-5). Suppose -2/9*l**2 + c*l + 0 = 0. Calculate l.
0, 2
Let p(v) be the second derivative of 0*v**4 - 4/225*v**6 + 0*v**3 + 4*v + 1/50*v**5 + 1/315*v**7 + 1 + 0*v**2. Factor p(r).
2*r**3*(r - 3)*(r - 1)/15
Let y(x) be the second derivative of 15*x - 1/40*x**5 + 0 + 3/2*x**2 + 1/4*x**4 - 11/12*x**3. Factor y(g).
-(g - 3)*(g - 2)*(g - 1)/2
So