j = c. Factor -p*q + 12 - 6*q**2 + 4*q + 9*q**2.
3*(q - 2)**2
Determine s, given that -21/2*s**5 + 99/2*s**4 - 60*s**2 + 24 + 72*s - 48*s**3 = 0.
-1, -2/7, 2
Let a(d) = 5*d**2 + 5*d - 30. Let r(h) = -334 + 49*h**2 + 39*h**2 - 86 - 18*h**2 + 70*h. Let b(y) = -55*a(y) + 4*r(y). Factor b(p).
5*(p - 2)*(p + 3)
Let z(y) = -5*y**4 - 233*y**3 + 4797*y**2 - 4559*y + 4. Let m(g) = 2*g**4 - g**3 - g - 1. Let w(l) = 4*m(l) + z(l). Factor w(v).
3*v*(v - 39)**2*(v - 1)
What is k in -4*k + 6/5*k**2 - 16/5 + 8/5*k**3 - 2/5*k**4 = 0?
-1, 2, 4
Let m be 0/((-5 - -8)*-1). Let l(h) be the second derivative of -6*h + m + 0*h**2 - 1/20*h**5 - 1/12*h**4 + 0*h**3. Factor l(c).
-c**2*(c + 1)
Let w = 38 - 38. Let d(l) = 2*l**2 + l + 8. Let g be d(w). Factor -2*f**2 - g*f - 5*f + 4 + 15*f.
-2*(f - 2)*(f + 1)
Factor 89/2*h**4 - 9/4*h**5 - 4625/4*h - 625/2 - 655/2*h**3 + 1050*h**2.
-(h - 5)**4*(9*h + 2)/4
Let n(j) be the third derivative of 1/32*j**8 + 1/70*j**7 + 1/2*j**3 - 1/10*j**5 + 0*j + 30*j**2 + 7/16*j**4 - 7/40*j**6 + 0. Determine q so that n(q) = 0.
-1, -2/7, 1
Determine c so that 8112/5*c + 70304/5 + 4/5*c**3 + 312/5*c**2 = 0.
-26
Let x(g) be the second derivative of -g**4/3 - 32*g**3/3 - 110*g**2 - 111*g + 3. Factor x(k).
-4*(k + 5)*(k + 11)
Let t(v) = v**3 - 4*v**2 - 10*v - 10. Let z be t(6). What is j in -14*j + 5*j**z + 21*j - 17*j = 0?
0, 2
Let i(f) be the first derivative of -20 + 1/15*f**5 + 0*f**2 - 1/8*f**4 + 0*f + 0*f**3. Factor i(m).
m**3*(2*m - 3)/6
Let h(k) = 14*k**3 - 58*k**2 + 25*k - 1. Let j = 14 + -10. Let x = -2 + j. Let y(d) = 27*d**3 - 117*d**2 + 50*d - 1. Let o(w) = x*y(w) - 5*h(w). Factor o(g).
-(g - 3)*(4*g - 1)**2
Factor -156/7 + 8/7*q**2 - 4*q.
4*(q + 3)*(2*q - 13)/7
Suppose -1350 - 584*k**2 + 383*k**2 - 3*k**3 - 495*k + 285*k**2 = 0. What is k?
-2, 15
Let q = -50 + 32. Let w be q/(-3)*(-3)/(-27)*3. Solve 1/4*c**w + 0*c + 1/4*c**3 + 0 = 0 for c.
-1, 0
Suppose -5*x - 7*o + 24 = 0, 4*x - 5*o + 2 = -0. Let 8/5*u**x + 4/5*u**3 + 0 + 4/5*u = 0. Calculate u.
-1, 0
Let w(s) = -3*s**3 - 3*s**2 + 5*s - 5. Let y(v) = 13*v**3 + 13*v**2 - 20*v + 21. Let l = -50 + 41. Let m(j) = l*w(j) - 2*y(j). Suppose m(q) = 0. What is q?
-3, 1
Factor 3*w**2 - 3/7*w**4 + 0 - 12/7*w - 6/7*w**3.
-3*w*(w - 1)**2*(w + 4)/7
Let b = 36 + -41. Let z(c) = -14*c**2 + 12*c + 26. Let a(t) = 9*t**2 - 8*t - 17. Let k(h) = b*z(h) - 8*a(h). Factor k(i).
-2*(i - 3)*(i + 1)
Let l = -6 + -2. Let b(z) = -z**2 - 9*z - 6. Let c be b(l). Solve -2*t**c + 1 + 4*t**2 + 31 + 16*t = 0 for t.
-4
Let y(s) be the third derivative of s**7/945 + 2*s**6/15 + 36*s**5/5 + 216*s**4 + 3888*s**3 - 23*s**2 + 3. What is x in y(x) = 0?
-18
Let n(u) be the third derivative of -3125*u**6/24 + 125*u**5 - 50*u**4 + 32*u**3/3 + 266*u**2. Find k such that n(k) = 0.
4/25
Let f(t) = 2*t**2 + 12*t + 8. Let u be (-120)/96 + 1/4. Let g(h) = -1. Let k(b) = u*f(b) + 8*g(b). Factor k(v).
-2*(v + 2)*(v + 4)
Suppose -35/2*r**4 + 35/2*r**2 + 0*r + 0 + 5/2*r**5 - 5/2*r**3 = 0. Calculate r.
-1, 0, 1, 7
Suppose 4*k + 0*k = -3*l + 721, 0 = 2*k + 5*l - 343. Let u = k + -180. Factor -1/3*p**2 + 1/3*p**u + 1/3*p**3 + 0 - 1/3*p.
p*(p - 1)*(p + 1)**2/3
Let n be 1/4 + 12 + 588/(-48). Let c(m) be the third derivative of 0 + 0*m**3 + n*m - 1/105*m**5 + 14*m**2 - 1/420*m**6 - 1/84*m**4. Let c(d) = 0. What is d?
-1, 0
Let s be 4/(-34) - (-72)/34. Factor -9*o**3 + 3*o**s + 18*o + 3 + 9*o**4 + 39*o**3 + 33*o**2.
3*(o + 1)**3*(3*o + 1)
Let x be (4 - 34/10)/((-3)/(-15)). Find j such that -20*j**2 - x*j**3 - 14*j**3 - 6*j - 12*j**4 - 2*j**5 - 7*j**3 + 0*j = 0.
-3, -1, 0
Let g(w) be the third derivative of -7/9*w**3 + 0*w + 1/90*w**5 - 21*w**2 - 1/6*w**4 + 0. Factor g(d).
2*(d - 7)*(d + 1)/3
Let q(b) be the third derivative of -b**8/168 + 4*b**7/105 - 8*b**5/15 + 4*b**4/3 + 586*b**2. Factor q(f).
-2*f*(f - 2)**3*(f + 2)
Let m(u) be the second derivative of u**4/3 + u**3/2 + 5*u**2/2 + u. Let s(i) = i**2 + 1. Suppose -6*r + 13*r = 42. Let l(w) = r*s(w) - m(w). Factor l(b).
(b - 1)*(2*b - 1)
Let g = 14 + -20. Let k = -3 - g. Factor 3*v - 5*v - v**3 + 7*v**k - 3*v**5 - v.
-3*v*(v - 1)**2*(v + 1)**2
Suppose 0 = 5*p + 50 - 0. Let a be (1 - -4)*(-6)/p. Let -a*c**3 - 4*c**3 - 8*c**2 + 2*c**4 - 13*c**3 + 10*c**4 = 0. What is c?
-1/3, 0, 2
Let s(p) be the third derivative of p**6/300 + 4*p**5/75 - p**4/60 - 8*p**3/15 - 5*p**2. Factor s(w).
2*(w - 1)*(w + 1)*(w + 8)/5
Let l(p) be the second derivative of 1/2*p**3 - 1/4*p**4 + 0 + 0*p**2 + 19*p + 1/10*p**6 - 3/20*p**5. Factor l(u).
3*u*(u - 1)**2*(u + 1)
Let y be 56/912 + (-4)/(-38). Let w(c) be the second derivative of 0 + 0*c**2 - 1/20*c**5 + y*c**4 - 1/6*c**3 - 5*c. Factor w(n).
-n*(n - 1)**2
Let z = 313/20 + -78/5. Let m(f) be the second derivative of -f + 0 - z*f**4 - 3/10*f**2 + 1/5*f**3. Let m(o) = 0. Calculate o.
1
Let i(y) be the second derivative of -y**4/30 - y**3/5 + 4*y**2/5 - y + 1. Factor i(q).
-2*(q - 1)*(q + 4)/5
Let j(x) be the first derivative of -3*x**5/80 + 5*x**4/24 - 11*x**3/24 + x**2/2 + 7*x + 12. Let d(k) be the first derivative of j(k). Factor d(g).
-(g - 1)**2*(3*g - 4)/4
Let x(j) = -2*j**3 + 4*j**2 + 2*j - 8. Let l(v) = -2. Suppose -3*i + 28 = 4*r - 7*i, 0 = 2*r - 5*i - 29. Let m(w) = r*x(w) - 4*l(w). Factor m(a).
-4*(a - 2)*(a - 1)*(a + 1)
Solve 41*k**2 - 45*k**3 - 27*k**4 - 64 - 3*k**5 - 11*k**2 + 45*k**2 + 64 = 0 for k.
-5, 0, 1
Let a(k) be the second derivative of k**7/504 + k**6/72 + k**5/24 - 17*k**4/6 + 14*k. Let u(v) be the third derivative of a(v). Find f, given that u(f) = 0.
-1
Let m be 11*(-38)/209 - (-10128 + 1). Let s = 7 + 6. Let 224*u + 23 + 4050*u**2 - 764*u - m*u**3 - s + 14 = 0. Calculate u.
2/15
Factor 2809856/11 - 75264/11*y - 2/11*y**3 + 672/11*y**2.
-2*(y - 112)**3/11
Let p be (-1)/((-14)/8) + 200/(-56). Let b be p/2*(-44)/231. Factor 0 - 2/7*f - b*f**5 + 8/7*f**4 - 12/7*f**3 + 8/7*f**2.
-2*f*(f - 1)**4/7
Let l = -17583/112 - -157. Let z(f) be the third derivative of 0*f + 3/70*f**7 + 3/40*f**6 - 5*f**2 + 0*f**4 + 0 + 1/20*f**5 + l*f**8 + 0*f**3. Factor z(i).
3*i**2*(i + 1)**3
Let m = 6 - 4. Let w = -13 + 17. Determine x, given that -5/2*x**3 + 1/2*x**m + 3/2*x**w + 0*x + 0 + 9/2*x**5 = 0.
-1, 0, 1/3
Let l = 32 - 59. Let b = l + 30. Let -4*u**5 - 2*u**4 + 6*u**4 + b*u**3 + 4*u**4 - 7*u**3 = 0. What is u?
0, 1
Let s = 2251/54 + -125/3. Let l(f) be the second derivative of 8/27*f**3 + 16/9*f**2 + s*f**4 + 0 + 9*f. What is a in l(a) = 0?
-4
Let n(z) = -z**2 - 2*z + 1. Let h(l) = 6*l**2 + 20*l - 2. Let m(d) = -h(d) - 8*n(d). What is p in m(p) = 0?
-1, 3
Let i(f) be the third derivative of 23*f**2 - 32/3*f**3 + 0*f + 1/168*f**8 + 20/3*f**4 + 2/3*f**6 - 8/3*f**5 + 0 - 2/21*f**7. Factor i(s).
2*(s - 2)**5
Let u(p) = -8*p**4 - 78*p**3 - 219*p**2 - 247*p - 76. Let m(d) = -3*d**4 - 26*d**3 - 72*d**2 - 82*d - 25. Let b(f) = 11*m(f) - 4*u(f). What is l in b(l) = 0?
-1, 29
Let b be (21/(-6) + 3)*(-8 - -8). Let c(k) be the third derivative of 0*k + b + 1/40*k**5 - 1/240*k**6 + 0*k**3 - 1/24*k**4 - 4*k**2. Factor c(r).
-r*(r - 2)*(r - 1)/2
Suppose 0 = -45*k + 49*k - 32. Factor -k*d**3 + 0*d**3 + 3*d**3 - d**3 - 2*d**2 + 4*d.
-2*d*(d + 1)*(3*d - 2)
Let g(h) be the third derivative of 4*h**2 + 0 + 1/660*h**6 + 2/1155*h**7 + 1/1848*h**8 + 0*h**5 + 0*h + 0*h**3 + 0*h**4. Let g(r) = 0. What is r?
-1, 0
Let v be (84/378 - 17/9)*-2. Let x(p) be the second derivative of v*p**4 - 10/3*p**3 + 2*p**2 + 0 + 2/3*p**6 - 2/21*p**7 + 5*p - 2*p**5. Solve x(h) = 0 for h.
1
Let m(o) be the first derivative of -2*o**3/51 + o**2/17 + 34. What is j in m(j) = 0?
0, 1
Let o(i) be the third derivative of -i**5/15 + 40*i**4/3 - 3200*i**3/3 - 2*i**2 - 23. Find l, given that o(l) = 0.
40
Let f(s) be the first derivative of s**6/660 - s**4/132 - 19*s**2/2 - 13. Let t(x) be the second derivative of f(x). Suppose t(r) = 0. What is r?
-1, 0, 1
Let i(y) be the first derivative of -15*y**3/2 + 5*y**2/4 + 25*y - 3. Determine k, given that i(k) = 0.
-1, 10/9
What is m in -22 + 6*m**2 + 23 - 4*m**4 - 58*m**3 + 29*m**4 + 18*m**3 + 8*m = 0?
-1/5, 1
Let y = -683 - -32785/48. Let q(g) be the third derivative of 0*g + 3*g**2 - y*g**4 + 1/240*g**5 + 0 + 1/24*g**3. Factor q(x).
(x - 1)**2/4
Let d = 11/15 - 29/60. Let q(k) be the first derivative of 3 + k - d*k**2 - 1/6*k**3. Let q(c) = 0. What is c?
-2, 1