) be the third derivative of 0*f + 0 - 1/60*f**5 - 1/24*f**4 + 1/210*f**7 + 1/120*f**6 + 0*f**u + 6*f**2. Factor h(c).
c*(c - 1)*(c + 1)**2
Let y(g) be the first derivative of g**4/24 + g**3/9 - 13*g**2/12 + 5*g/3 - 34. Suppose y(p) = 0. Calculate p.
-5, 1, 2
Let f = 8106 - 8104. Factor -1/6*q**3 - q**f - 3/2*q + 0.
-q*(q + 3)**2/6
Suppose -157*s + 24*s + 652 = 193*s. Solve -2/5*l**3 + 4/5*l**s + 0*l + 0 = 0 for l.
0, 2
Let h(p) be the third derivative of -13*p**8/1680 - 9*p**7/350 - p**6/40 - p**5/300 - 2*p**2 - 2. Factor h(f).
-f**2*(f + 1)**2*(13*f + 1)/5
Let m be (4071/(-18))/(8/(-12)). Let x = -334 + m. Solve -5/4*g**5 - 1/2*g + 0 - 17/4*g**4 - x*g**3 - 11/4*g**2 = 0.
-1, -2/5, 0
Let s(q) be the first derivative of 3/2*q**2 - 3 + 6*q - q**3. Factor s(b).
-3*(b - 2)*(b + 1)
Let v(f) be the first derivative of -1/3*f**2 + 1/2*f**4 - 2/15*f**5 + 32 + 0*f + 2/9*f**3 - 2/9*f**6. Find g, given that v(g) = 0.
-1, 0, 1/2, 1
Let d = 545 + -545. Solve 4/7*z**3 - 4/7*z - 1/7*z**2 + 1/7*z**4 + d = 0.
-4, -1, 0, 1
Let o(k) = k**4 + 23*k**3 - 53*k**2 - 5*k - 5. Let q(c) = 2*c**4 + 22*c**3 - 54*c**2 - 6*c - 6. Let l(x) = 6*o(x) - 5*q(x). Determine t, given that l(t) = 0.
0, 3, 4
Let s = 49 - 35. Let d(n) = n**2 - 43*n - 61. Let b(k) = 14*k + 20. Let i(c) = s*b(c) + 4*d(c). Factor i(y).
4*(y + 3)**2
Let d(n) = n + 3. Let l be d(2). Suppose -v + 1 + 3 = 0, -17 = j - l*v. Suppose -6*x**4 - 8*x**j + 88*x - 2*x**2 - 88*x = 0. Calculate x.
-1, -1/3, 0
Let m(g) be the third derivative of g**5/360 - 5*g**4/144 - g**3/6 - 70*g**2. Factor m(q).
(q - 6)*(q + 1)/6
Factor -15/2 - 135/2*w**2 + 65/4*w**3 + 235/4*w.
5*(w - 3)*(w - 1)*(13*w - 2)/4
Find p such that 5/3*p**2 + 35/3 + 40/3*p = 0.
-7, -1
Let v(p) be the second derivative of p**7/63 - p**6/15 - 3*p**5/2 - 9*p**4/2 - 115*p. Let v(i) = 0. Calculate i.
-3, 0, 9
Let i(q) = 5*q**5 - 8*q**4 + 13*q**3 + 18*q**2 - 88*q + 72. Let k(c) = -c**5 + c**3 - c**2 + c. Let p(t) = i(t) + 4*k(t). Factor p(a).
(a - 3)**2*(a - 2)**2*(a + 2)
Let v = -931/4 - -473/2. Let y(k) be the first derivative of -v*k**4 + 0*k + 2*k**5 + 12 + 0*k**2 - 10/3*k**3. What is n in y(n) = 0?
-1/2, 0, 2
Let y(k) be the third derivative of -2*k**7/105 - 47*k**6/15 - 2113*k**5/15 + 752*k**4 - 1536*k**3 + 76*k**2 + k. Find s such that y(s) = 0.
-48, 1
Let l be 3/2*(-42)/(-9). Suppose 12 = -3*r + l*r, 0 = 2*x + 4*r - 28. Let -3*y - 2 + 10 + 3*y**2 - x = 0. Calculate y.
0, 1
Let c = 28585 - 314431/11. Factor -2/11*p + 4/11 + 2/11*p**3 - c*p**2.
2*(p - 2)*(p - 1)*(p + 1)/11
Let t = -75 + 33. Let x be 23/7 + 12/t. Let 2*l**2 + 23*l**x - 4*l - 3*l**4 - 19*l**3 + l**4 = 0. What is l?
-1, 0, 1, 2
Let k(u) = u**2 + 6*u - 22. Let i be k(-9). Suppose -13 = 2*c + 3*l + 2, i*l + 25 = 0. Factor 2*j**3 - 2*j + c*j - 2 + 5 - 2 - j**4.
-(j - 1)**3*(j + 1)
Let p(b) = 6*b + 5. Let o(l) = l - 1. Let v be o(-4). Let s(r) = r**2. Let c(h) = v*p(h) - 5*s(h). Factor c(q).
-5*(q + 1)*(q + 5)
Let k(c) be the first derivative of 4*c**5/5 + 13*c**4 + 92*c**3/3 + 22*c**2 - 12. Find f, given that k(f) = 0.
-11, -1, 0
Let l(j) be the first derivative of -3/20*j**5 - 50 - 9/8*j**2 + 0*j + 9/16*j**4 + 1/4*j**3. Let l(r) = 0. Calculate r.
-1, 0, 1, 3
Let r(g) = -g**3 + 3*g**2 - 8*g + 10. Let d be r(5). Let h be 1/(-2)*d/110. Let -h*t**2 + 2/11*t**3 + 4/11 - 2/11*t = 0. What is t?
-1, 1, 2
Let y(q) be the first derivative of -2*q**7/7 - q**6/20 + 11*q**5/80 + q**4/16 - 22*q**2 + 10. Let u(w) be the second derivative of y(w). Factor u(p).
-3*p*(4*p + 1)**2*(5*p - 2)/4
Let a(s) = -125*s**2 - 265*s - 195. Let x be 0 + 4 + 21 + -21. Let j(r) = -9*r**2 - 19*r - 14. Let b(g) = x*a(g) - 55*j(g). Factor b(m).
-5*(m + 1)*(m + 2)
Let g = -2208 + 13249/6. Let f(b) be the third derivative of 1/15*b**5 + 0*b**3 + 13*b**2 + g*b**4 + 0 + 0*b. Factor f(t).
4*t*(t + 1)
Let t = -2631/7 + 377. Let i be (-3)/(-15) + (-306)/105 - -3. Solve 8/7*c - t - 2/7*c**4 + i*c**5 - 10/7*c**3 + 10/7*c**2 = 0.
-2, -1, 1, 2
Let s(w) = 4*w**3 - 4 + 40*w**2 + 4 + 20*w. Let c(y) = -4*y + 9*y**3 - 5*y**2 - 3*y**2 - 10*y**3. Let r(b) = -33*c(b) - 6*s(b). Solve r(i) = 0.
-2, -2/3, 0
Let n(r) be the third derivative of -2*r**7/735 - 2*r**6/105 - r**5/35 + 34*r**2. Solve n(q) = 0.
-3, -1, 0
Suppose 0 = -5*p + 2*o + 20, -p + 3*o + 13 = -2*p. Let z be 2/(8 - p)*18/15. Suppose -z*g + 0 + 8/5*g**2 = 0. What is g?
0, 1/4
Let x be (-15 - -16)/((-1)/(-6)*2). Let r(u) be the third derivative of 0*u + 0 - 1/108*u**4 + 1/270*u**5 + 0*u**x + u**2. What is c in r(c) = 0?
0, 1
Let h(s) = 14*s**2 + 225*s - 2925. Let n(v) = 6*v**2 + 112*v - 1462. Let g(k) = 4*h(k) - 9*n(k). Suppose g(q) = 0. What is q?
27
Suppose -162 = -o + 315. Factor 105*z + 122*z**3 + o*z**3 + 6 + 588*z**2 + 145*z**3 + 285*z**3.
3*(7*z + 1)**2*(7*z + 2)
Let m be -10*1/85 - (-116)/119. Factor -3/7 - m*x - 3/7*x**2.
-3*(x + 1)**2/7
Let a(w) be the first derivative of 4*w**5/5 + 7*w**4 + 8*w**3 - 64*w**2 - 128*w - 18. Factor a(r).
4*(r - 2)*(r + 1)*(r + 4)**2
Let y(h) be the third derivative of h**5/75 - h**4/10 - h**2 + 60*h. Factor y(s).
4*s*(s - 3)/5
Suppose 47 = 31*p - 15. Factor -4/11*j**p - 2/11*j + 0 + 6/11*j**3.
2*j*(j - 1)*(3*j + 1)/11
Let v(g) be the second derivative of -54*g**7/7 + 15*g**6/2 + 68*g**5/5 - 221*g**4/12 + 26*g**3/3 - 2*g**2 + g + 32. Let v(s) = 0. Calculate s.
-1, 2/9, 1/4, 1
Let v be ((-3)/(-9))/(1*2/24). Let m be ((-6)/24)/(-5 + v). Let -m*l + 0 + 1/4*l**5 + 1/2*l**4 + 0*l**3 - 1/2*l**2 = 0. Calculate l.
-1, 0, 1
Let f(n) be the first derivative of -2*n**3/9 - 2*n**2/3 - 257. Factor f(d).
-2*d*(d + 2)/3
Factor 0 - 10/17*d**3 - 2/17*d**5 + 8/17*d**4 + 4/17*d**2 + 0*d.
-2*d**2*(d - 2)*(d - 1)**2/17
Let n(h) be the third derivative of 1/2*h**4 - 8*h**2 + 0*h + 0 + 0*h**3 - 1/30*h**5. Let n(j) = 0. Calculate j.
0, 6
Let v(r) = 2*r**3 - 3*r**2. Let g(k) = -2*k**3 + 2*k**2. Suppose 16*c + 14 = 9*c. Let i(b) = c*v(b) - 3*g(b). Suppose i(x) = 0. Calculate x.
0
Let a(q) = 2*q**3 + 25*q**2 + 58*q + 59. Let z(x) = -x**2 + 2*x - 1. Let w(i) = a(i) + 3*z(i). Factor w(l).
2*(l + 2)**2*(l + 7)
Let m(b) be the first derivative of 0*b**2 + 2 + 8*b + 1/3*b**4 - 1/10*b**5 - 1/3*b**3. Let r(l) be the first derivative of m(l). Factor r(h).
-2*h*(h - 1)**2
Let z be 78/351*9*1. Let r(p) be the first derivative of 0*p**2 - 1 - z*p**3 - 3/4*p**4 + 3/5*p**5 + 0*p. Factor r(x).
3*x**2*(x - 2)*(x + 1)
Let s(f) be the first derivative of 2*f**6/75 + f**5/10 + f**4/30 - 2*f**3/15 + 18*f - 25. Let l(h) be the first derivative of s(h). What is d in l(d) = 0?
-2, -1, 0, 1/2
Let x(d) be the first derivative of -15*d**4/4 - 13*d**3 - 9*d**2 - 179. Solve x(v) = 0.
-2, -3/5, 0
Let s(k) = k**3 - 15*k**2 + 12*k + 10. Let c be s(14). Let j = c + 34. Suppose -291*b**2 - 297*b**2 - 918*b**3 + 232*b**3 - j - 123*b - 45*b = 0. What is b?
-2/7
Let l(k) = -k**3 - k. Let h = -25 - -30. Suppose 2*j + 3*y = y - 4, 2*y + 1 = -h*j. Let u(w) = -3*w**3 - 2*w. Let r(i) = j*u(i) - 2*l(i). Factor r(b).
-b**3
Let p(l) be the second derivative of -2/45*l**6 + 3*l - 16/3*l**2 - 2*l**4 - 40/9*l**3 + 0 - 7/15*l**5. Factor p(v).
-4*(v + 1)*(v + 2)**3/3
Let h(y) be the third derivative of 1/12*y**3 + 0*y + 1/120*y**5 + y**2 + 0 - 1/24*y**4. Factor h(n).
(n - 1)**2/2
Let r(a) = a. Let g(z) = -z**5 - 47*z**4 - 619*z**3 - 1585*z**2 - 1499*z - 484. Let d(y) = 2*g(y) + 6*r(y). Factor d(j).
-2*(j + 1)**3*(j + 22)**2
Let b be (4 - (-3 + 2))*(-10)/(-25). Suppose 2*s**3 + 2*s + 9 + 6*s**2 + 3 - 14*s**b = 0. What is s?
-1, 2, 3
Suppose 0*s**2 + 2/3*s**3 - 2/3*s + 1/3*s**4 - 1/3 = 0. What is s?
-1, 1
Let p = 2/55 + 1/33. Let g = p + 1/10. Factor 1/6*y - 1/6 - 1/6*y**4 - 1/3*y**3 + 1/3*y**2 + g*y**5.
(y - 1)**3*(y + 1)**2/6
Let s = -96 - -101. Suppose -l = -3*n + 14, -2*n - 3*n = s*l - 10. Find d such that 0*d + 0 + 1/2*d**2 + 0*d**3 - 1/2*d**n = 0.
-1, 0, 1
Factor 100*c**3 + 102*c**3 + 2*c**5 + 30*c**4 + 915*c**2 - 375*c**2 + 486 - 22*c**3 + 810*c.
2*(c + 3)**5
Let k(p) be the third derivative of -p**8/84 - 34*p**7/105 - 13*p**6/5 - 142*p**5/15 - 113*p**4/6 - 22*p**3 + 723*p**2. Suppose k(l) = 0. Calculate l.
-11, -3, -1
Let p be -8 - (-155)/15 - 2/6. Let l(v) be the first derivative of 4/5*v**5 + 10 + 0*v + 4*v**2 - p*v**4 - 4/3*v**3. What is g in l(g) = 0?
-1, 0, 1, 2
Suppose -10*g = -15 - 25. Let n(s) be the fir