 i - 14*b + 0*b + 12 = 0.
-3/5, 3
Let c(k) be the first derivative of -k**8/2160 - 19*k**7/7560 - k**6/405 + k**5/270 + k**3/3 - 2. Let y(w) be the third derivative of c(w). Factor y(r).
-r*(r + 1)*(r + 2)*(7*r - 2)/9
Let s(c) = 21*c**2 - 25*c + 4. Let g(i) = -20*i**2 + 24*i - 4. Let t = 3 + 4. Let r(q) = q + 6. Let w be r(0). Let f(b) = t*g(b) + w*s(b). Factor f(v).
-2*(v - 1)*(7*v - 2)
Let a = 379133/402883 - -3/23699. Let 8/17*t - 50/17*t**4 - 110/17*t**3 - a*t**2 + 0 = 0. Calculate t.
-2, -2/5, 0, 1/5
Let o(p) be the first derivative of p**4/6 + 86*p**3/45 + 112*p**2/15 + 184*p/15 - 110. Factor o(r).
2*(r + 2)**2*(5*r + 23)/15
Factor 5839 - 28*d - 2930 - 4*d**2 - 2949.
-4*(d + 2)*(d + 5)
Let z(v) = -17*v**2 + 84*v + 206. Let m(n) = 36*n**2 - 167*n - 413. Let a(j) = 6*m(j) + 13*z(j). Factor a(o).
-5*(o - 20)*(o + 2)
Let i(x) = -x**3 + 5*x**2 - x - 4. Let b be i(4). Suppose 0 = -3*s - a + b, -2*s + 5*a = 4 + 2. What is p in 2*p - 8*p**s + 6*p + 16*p**2 - 10*p**2 = 0?
0, 4
Let g(m) = m**3 + 10*m**2 + 1. Let i be g(-10). Factor -5*t**3 - i - 6*t**2 - 6*t**3 + 7 - 10*t**3 + 21*t.
-3*(t - 1)*(t + 1)*(7*t + 2)
Let d(r) = r**2 - 4*r - 8. Let h(g) = 2*g**2 - 8*g - 15. Let s(t) = -5*d(t) + 3*h(t). Factor s(m).
(m - 5)*(m + 1)
Let n(p) be the second derivative of -1/36*p**4 + 10*p + 1/9*p**3 + 0 + 4/3*p**2. Factor n(k).
-(k - 4)*(k + 2)/3
Let p(o) be the third derivative of o**7/945 - o**6/90 + o**5/54 + o**4/9 - 69*o**2 + o. Determine l so that p(l) = 0.
-1, 0, 3, 4
Suppose y + y = 0. Suppose y*s + 3*m = -s - 4, -2*s - 6 = 5*m. Find x such that x**4 - 13*x**2 - 3*x**4 + 0*x**4 + 15*x**s = 0.
-1, 0, 1
Let g(m) be the second derivative of -m**5/10 + 43*m**4/24 + 11*m**3/12 - 576*m. Suppose g(v) = 0. Calculate v.
-1/4, 0, 11
Let s(o) be the first derivative of -o**3/21 + 4*o**2/7 - 12*o/7 - 100. Factor s(v).
-(v - 6)*(v - 2)/7
Let -186*p**2 - 78*p + 211*p - 87*p + 8*p**3 = 0. What is p?
0, 1/4, 23
Let d(p) = p**4 + p - 1. Let q(l) = l**4 - 21*l**3 + 45*l**2 - 41*l + 14. Let w(v) = 3*v + 22. Let g be w(-8). Let o(y) = g*d(y) - q(y). Factor o(r).
-3*(r - 4)*(r - 1)**3
Let x be -1 + 2*6 + -3. Let h be 75/20 - 12/16. Find v, given that -x*v**h + 14*v**4 + 3*v**5 - 6*v**4 + v**5 - 6*v**5 = 0.
0, 2
Let b(z) be the first derivative of -z**8/784 + z**7/245 - z**5/70 + z**4/56 + 3*z**2 + 19. Let u(y) be the second derivative of b(y). Solve u(v) = 0.
-1, 0, 1
Determine b, given that -196/15 - 154/15*b - 32/15*b**2 - 2/15*b**3 = 0.
-7, -2
Let i(q) be the third derivative of -q**7/5040 + q**6/480 + q**5/60 + 3*q**4/8 + 5*q**2. Let u(k) be the second derivative of i(k). Factor u(m).
-(m - 4)*(m + 1)/2
Let z(m) be the second derivative of -2/3*m**3 - m**4 + 4*m**2 + 1/5*m**5 + 2/15*m**6 - 5*m + 0. Factor z(s).
4*(s - 1)**2*(s + 1)*(s + 2)
Let v = 21 + -17. Suppose 5*y = -4*g + 34, -3*g + v*y = 5*y - 20. Solve 2 - 35*d - 10*d**2 + 2 + 53*d**3 + g - 18*d**3 = 0.
-1, 2/7, 1
Let o = 13913/3 + -4635. Factor o*m + 2/3*m**2 + 0.
2*m*(m + 4)/3
Factor 15/8*p + 3/4 - 21/8*p**2.
-3*(p - 1)*(7*p + 2)/8
Let d(v) be the third derivative of v**7/30 + 2*v**6/15 + 11*v**5/60 + v**4/12 + 12*v**2 + 2*v. Solve d(i) = 0.
-1, -2/7, 0
Suppose -5*k + 4*j = 18, -9*k + 12*k + 29 = 5*j. Factor -2/15*z**4 + 2/15*z + 2/15*z**k - 2/15*z**3 + 0.
-2*z*(z - 1)*(z + 1)**2/15
Find r such that -4/3*r - 2/9*r**2 - 2 = 0.
-3
Let d = -109 + 112. Factor 40*m**4 - 12*m**2 + 6*m**d - 58*m**4 - 64*m**3.
-2*m**2*(m + 3)*(9*m + 2)
Let y(w) be the second derivative of -w**7/112 - 9*w**6/40 - 27*w**5/160 + 81*w**4/4 - 81*w**3 - 467*w. Solve y(r) = 0.
-12, 0, 3
Let r(c) = -23*c**2 - 59*c - 8. Let q(n) = 68*n**2 + 178*n + 24. Let t(k) = -3*q(k) - 10*r(k). Factor t(o).
2*(o + 2)*(13*o + 2)
Let n = 5236/3 + -1742. Let i(o) = 3*o - 10. Let s be i(4). Factor 5/3*w**5 + 15*w**3 - 35/3*w**s + n*w + 0 - 25/3*w**4.
5*w*(w - 2)*(w - 1)**3/3
Let j(r) be the third derivative of 0*r - 1/72*r**4 - 1/630*r**7 + 0*r**3 - 1/60*r**5 + 19*r**2 - 1/120*r**6 + 0. Solve j(a) = 0 for a.
-1, 0
Let g(a) be the third derivative of -a**8/336 - 4*a**7/105 - 11*a**6/120 + 2*a**5/15 + a**4/2 - a**2 + 162*a. Find r, given that g(r) = 0.
-6, -2, -1, 0, 1
Suppose -25 = 2*t - 33. What is u in -4*u**3 + 3*u**3 + t*u - 3 - 2*u**2 + 9 + 2 = 0?
-2, 2
Let s = 315/4 - 2771/36. Let t = s - 158/99. What is i in -2/11*i + 0*i**3 + 4/11*i**4 - 4/11*i**2 + t*i**5 + 0 = 0?
-1, 0, 1
Suppose -2 + 8 = -6*x. Let c(j) = -j**2. Let d(l) = 4*l**2 - 4*l - 3. Let t(y) = x*d(y) - 5*c(y). Factor t(i).
(i + 1)*(i + 3)
Let a(o) = o**2 + 3*o. Let p be a(0). Find q such that -2*q**4 + 6*q**3 + p*q + 5*q**2 - 11*q**2 + 2*q = 0.
0, 1
Suppose 16 - 20 = -2*s. Let x(i) be the first derivative of 1/35*i**5 + 2/7*i**3 - 1/7*i**4 + 1/7*i - 4 - 2/7*i**s. Suppose x(q) = 0. What is q?
1
Suppose -8*k + 45 = -3*k. Let g be (-3)/(-2)*12/k. Factor 0 + 2/9*m**3 + 2/9*m**g + 0*m.
2*m**2*(m + 1)/9
Let a(z) be the second derivative of -z**7/18 + z**6/45 + 7*z**5/15 - 2*z**4/9 - 3*z + 7. Suppose a(j) = 0. Calculate j.
-2, 0, 2/7, 2
Suppose 0*v + 3/2*v**3 - 3/2*v**4 + 0 + 1/2*v**5 - 1/2*v**2 = 0. What is v?
0, 1
Let h(n) = 4*n**5 + 5*n**4 + 11*n**3 + n**2 - 3*n. Let g(o) = 17*o**5 + 20*o**4 + 45*o**3 + 3*o**2 - 13*o. Let m(y) = 6*g(y) - 26*h(y). Factor m(f).
-2*f**2*(f + 1)*(f + 2)**2
Let n = 44 + -32. Suppose 6*l - n = -0. Factor c + 1/2*c**2 - 1/4*c**3 - l.
-(c - 2)**2*(c + 2)/4
Let n(u) = u**3 + u - 1. Let d(g) = 2*g**3 + g**2 - g - 1. Let r be (-12)/(-24) - 2/(-4). Let i(b) = r*n(b) - d(b). Suppose i(t) = 0. Calculate t.
-2, 0, 1
Let a(l) be the second derivative of 6*l + 2/33*l**3 + 2/55*l**5 - 5/66*l**4 - 1/165*l**6 + 0*l**2 + 0. Factor a(x).
-2*x*(x - 2)*(x - 1)**2/11
Let h(m) be the first derivative of m**6/1980 - m**4/132 - 5*m**3/3 - 2. Let f(l) be the third derivative of h(l). Factor f(o).
2*(o - 1)*(o + 1)/11
Let q(z) be the first derivative of 2*z**3 - 9*z**2/2 - 6*z + 56. Factor q(a).
3*(a - 2)*(2*a + 1)
Find k such that 15*k - 5/2*k**3 + 55/4 - 105/4*k**2 = 0.
-11, -1/2, 1
Let g(y) be the third derivative of y**9/60480 + y**8/8960 - y**7/10080 - y**6/960 - 3*y**4/2 - 14*y**2. Let q(f) be the second derivative of g(f). Factor q(d).
d*(d - 1)*(d + 1)*(d + 3)/4
Suppose -4*y = -5*i - 14, 3*i - 4*y - 59 = -77. Factor 40/3*b - 100/3 - 4/3*b**i.
-4*(b - 5)**2/3
Factor 0 - 210/13*p + 2/13*p**2.
2*p*(p - 105)/13
Let -16*w - 5 + 3*w**3 - 1 + 7*w = 0. What is w?
-1, 2
Let v = 22973/332 + 9/166. Let -49/4*i**5 - 4 + 19*i - 133/2*i**4 + 8*i**2 - v*i**3 = 0. Calculate i.
-4, -1, 2/7
Let m(u) = u**3 + u**2 + u - 1. Let t(o) = 3*o**4 - 3*o**3 + 3*o**2 + 3*o - 2. Let v(a) = 6*m(a) - 3*t(a). Factor v(p).
-3*p*(p - 1)**2*(3*p + 1)
Let d = 80 - 33. Let f = d - 42. Suppose 0*h**2 + 0 + h**3 + 0*h - 1/2*h**4 - 1/2*h**f = 0. Calculate h.
-2, 0, 1
Let q(d) = 35*d**3 - 20*d**2 - 5*d. Let s(p) = p. Let h(a) = -q(a) - 5*s(a). What is n in h(n) = 0?
0, 4/7
Let o(w) be the first derivative of -7*w**3/18 - 29*w**2/12 - 2*w/3 + 218. Factor o(n).
-(n + 4)*(7*n + 1)/6
Let g(w) be the first derivative of w**4/2 + 12*w**3/7 + 15*w**2/7 + 8*w/7 + 82. Solve g(l) = 0.
-1, -4/7
Solve 0 - 3*p**2 + 12/5*p**3 - 3/5*p**4 + 6/5*p = 0 for p.
0, 1, 2
Let f(a) be the second derivative of a**4/36 - 7*a**3/4 - 8*a**2/3 + 104*a. Let f(n) = 0. What is n?
-1/2, 32
Let w be 8/(-108)*3 - (-20)/(-210)*-7. Solve 2/9*z**2 - 2/3*z**4 + 0*z + w*z**3 + 0 = 0.
-1/3, 0, 1
Determine l so that -1/6*l**4 + 4/3*l - 4/3*l**3 + 0 + 1/6*l**2 = 0.
-8, -1, 0, 1
Suppose 81*d - 80*d + 3*k = 11, 3*d - k = 3. Let b(q) be the first derivative of -4*q**3 - 8 + 3*q**4 - 4/5*q**5 + 2*q**d + 0*q. Factor b(z).
-4*z*(z - 1)**3
Let d(b) be the first derivative of 2*b**6/3 + 12*b**5/5 - 4*b**4 + 170. Determine q so that d(q) = 0.
-4, 0, 1
Let q(m) = m**3 + 7*m**2 - 7*m + 8. Let f be q(-8). Suppose f = -2*z + 4. Factor 2*p**z + 2*p + 2*p**2 - 3*p**2 - 2*p**3 - 3*p**2 + 2.
-2*(p - 1)*(p + 1)**2
Let u = -221472 - -3319831/15. Let o = u - -457/3. Determine l so that -24/5*l + 16/5 - 2/5*l**3 + o*l**2 = 0.
2
Let n be (5 - (4 + -1))/(-3 + 4). Let i(w) be the second derivative of 0 + 1/9*w**3 - 1/36*w**4 - 1/6*w**n + w. Solve i(x) = 0.
1
Let i be 18/(-24) - 62/(-8). Factor -21*m**2 + 15*m - 3 - i + 16*m**2.
-5*(m - 2)*(m - 1)
Let m(a) be the first derivative of a