3)/6
Let t = 34 - 22. Factor -6*f + t*f**2 + 18*f - 4*f**3 + 7*f**3.
3*f*(f + 2)**2
Let o(l) = 11*l**2 + 2*l - 6. Let h(a) = 20*a**2 + 3*a - 10. Let v(f) = 3*h(f) - 5*o(f). Factor v(s).
s*(5*s - 1)
Let r = -3 + 6. Let l(f) be the first derivative of 0*f + 2/3*f**r - 1/5*f**2 - 5 - 2/5*f**4. Factor l(x).
-2*x*(x - 1)*(4*x - 1)/5
Let f = 202175/9 - 22459. Let f*g - 16/9 - 14/9*g**3 + 46/9*g**2 = 0. What is g?
-1, 2/7, 4
Let q(w) = -15*w**2 + 4*w. Let l(u) = -u**2 - 6*u + 2. Let x be l(-6). Let p(z) = -z**2 + z**x - 3*z**2 + z. Let m(t) = -11*p(t) + 2*q(t). Solve m(n) = 0.
0, 1
Let j(s) = -s**4 + s - 1. Suppose 30 = 11*z - 5*z. Let i(p) = -11*p**4 - 8*p**3 + 7*p**2 - 6*p + 5. Let d(o) = z*j(o) + i(o). Factor d(x).
-x*(x + 1)*(4*x - 1)**2
Factor 105*s + 62*s - 42*s + 25*s**3 + 240*s**2 - 90.
5*(s + 1)*(s + 9)*(5*s - 2)
Let p(f) be the first derivative of -1/8*f**4 + 0*f + 1/6*f**3 - 28 + 3/2*f**2. Determine d, given that p(d) = 0.
-2, 0, 3
Let d(z) be the first derivative of -z**5/30 + z**4/6 + 2*z**3/3 - 8*z**2/3 - 32*z/3 + 133. Factor d(y).
-(y - 4)**2*(y + 2)**2/6
Let i(c) = -13*c**3 + 80*c**2 - 85*c + 27. Let k(g) = 3*g**3 - 20*g**2 + 21*g - 6. Let l(a) = 2*i(a) + 9*k(a). Find r, given that l(r) = 0.
0, 1, 19
Let z be 5 + -2 - 1112/(-1330)*-3. Let v = -6/95 + z. Solve 6/7*l + v + 3/7*l**2 = 0.
-1
Let i(q) be the first derivative of -2*q**3/3 + 16*q**2 - 128*q - 44. Factor i(b).
-2*(b - 8)**2
Find b, given that -4*b**4 - 675 - 13776*b - 9878*b**2 + 2494*b**2 - 336*b**3 - 6049 = 0.
-41, -1
Let z(x) be the first derivative of x**6/90 - x**5/20 - x**4/6 + 7*x**3/3 - 5. Let p(o) be the third derivative of z(o). What is r in p(r) = 0?
-1/2, 2
Let c(h) be the first derivative of 24*h**2 - 72*h + 1/2*h**4 - 47 + 22/3*h**3. Factor c(o).
2*(o - 1)*(o + 6)**2
Let u(t) = -6 - 62*t**2 - 1 + 69*t**2. Suppose -5*q = -1 - 19. Let p(y) = 3*y**2 - 3. Let h(m) = q*u(m) - 9*p(m). Factor h(f).
(f - 1)*(f + 1)
Let g(q) = -q**3 + 9*q**2 - 18*q - 10. Let r be g(5). Let k(z) be the first derivative of r*z - 1/6*z**3 + 6 - 1/2*z**2. Factor k(u).
-u*(u + 2)/2
Let j(g) be the first derivative of 9*g + g**3 - 32*g**2 + 6 + 16*g**2 + 10*g**2. Factor j(a).
3*(a - 3)*(a - 1)
Determine z so that 139105/4*z - 46225/4 - 1291/4*z**2 + 3/4*z**3 = 0.
1/3, 215
Let l(f) be the second derivative of f**5/35 + 2*f**4/21 - 16*f**3/21 - 9*f + 8. Suppose l(d) = 0. Calculate d.
-4, 0, 2
Suppose -4*p = -8*p + 16. Determine a, given that -2*a**2 - 2 + p*a - 2 + 4 = 0.
0, 2
Let a(r) = 24*r - 11 + 3*r**2 - 18 - 15 + 1. Let v(l) = -2*l**2 - 12*l + 22. Let b(x) = -4*a(x) - 7*v(x). Factor b(p).
2*(p - 3)**2
Let c(h) be the third derivative of 0 + 0*h + 0*h**3 + 0*h**4 - 9*h**2 + 1/20*h**5. Factor c(a).
3*a**2
Let g(a) = -15*a**2 + 7*a. Let u = 38 - 43. Let h(d) = 8*d**2 - 4*d. Let y(b) = u*h(b) - 3*g(b). Solve y(v) = 0 for v.
0, 1/5
Let c(y) be the third derivative of y**7/1120 + 7*y**6/2880 - y**5/240 - 5*y**4/24 - y**2. Let g(l) be the second derivative of c(l). Factor g(m).
(m + 1)*(9*m - 2)/4
Suppose 3*r + 3*n + 0 = 12, -2*n = 5*r - 17. Determine h, given that -3*h**3 + 7*h + 0*h**2 - r*h**2 - 4*h + 3*h**4 = 0.
-1, 0, 1
Solve 3*v + 3/2*v**2 + 3/2 = 0.
-1
Let p be (-4296)/(-9845) - (-6)/(-165). Solve -8/5*s**2 - 16/5*s**3 - p*s**5 - 2*s**4 + 0 + 0*s = 0 for s.
-2, -1, 0
Let f(h) be the second derivative of 7*h**6/6 - 17*h**5/2 + 20*h**4/3 + 55*h**3 + 45*h**2/2 - 119*h. Factor f(q).
5*(q - 3)**2*(q + 1)*(7*q + 1)
Let h(k) be the second derivative of -1/14*k**7 + 0 - 4*k + 0*k**3 + 0*k**4 + 0*k**2 - 1/15*k**6 + 1/20*k**5. Determine c so that h(c) = 0.
-1, 0, 1/3
Let m be 2/((2*1/1)/5). Let l(c) be the second derivative of 1/54*c**4 + 1/90*c**m - 2/27*c**3 - 5*c + 0 + 0*c**2. Factor l(t).
2*t*(t - 1)*(t + 2)/9
Let c(h) be the first derivative of h**5/40 - h**4/12 - h**3/3 + 2*h**2 - 5*h - 8. Let k(b) be the first derivative of c(b). Solve k(t) = 0 for t.
-2, 2
Suppose -2*y - 3*n + 8 = -0, -2*n = -y + 4. Let d(x) be the first derivative of 12/5*x - 5 - 12/5*x**2 + x**3 - 3/20*x**y. Solve d(w) = 0 for w.
1, 2
Let y = 468 - 2333/5. Let z(v) be the first derivative of -5 + 1/2*v**6 + v + 2*v**3 - 5/2*v**2 - y*v**5 + 1/2*v**4. Factor z(b).
(b - 1)**3*(b + 1)*(3*b - 1)
Let i(g) be the first derivative of g**4/4 + 10*g**3/3 + 4*g**2 - 64*g + 373. Determine p so that i(p) = 0.
-8, -4, 2
Let d = -60/127 - -367/508. Suppose d*l - 1/12*l**2 + 0 = 0. Calculate l.
0, 3
Suppose b + 2 = 7. Let g be 12/b + 8/(-20). Factor d - 1 - 5 - d**2 + 2*d + 4*d**g.
3*(d - 1)*(d + 2)
Factor -1/8*l**2 + 7/2 + 3/2*l.
-(l - 14)*(l + 2)/8
Let d(t) be the first derivative of 3*t**5/10 - t**3/2 - 189. Find a, given that d(a) = 0.
-1, 0, 1
Let i = 154/3 - 51. Let h(f) be the first derivative of 5 + i*f**3 + 1/4*f - 1/2*f**2. Factor h(m).
(2*m - 1)**2/4
Let j(r) = 36*r**3 + 84*r**2 - 10*r - 58. Let t(m) = 7*m**3 + 17*m**2 - 2*m - 12. Let c(n) = 3*j(n) - 14*t(n). Factor c(l).
2*(l + 1)**2*(5*l - 3)
Let m(x) = -25*x**3 + 61*x**2 - 47*x + 8. Suppose 3*c = 15, 2*l - 8 = l - c. Let r(p) = -p**3 + p**2 + p. Let j(t) = l*r(t) + m(t). Find w such that j(w) = 0.
2/7, 1
Factor 0 + 8*o + 2/3*o**2.
2*o*(o + 12)/3
Let r(l) be the third derivative of -l**5/4 - 11*l**4/4 - 4*l**3 - 10*l**2. Determine b, given that r(b) = 0.
-4, -2/5
Suppose -46*n = 68*n + 38*n. Factor -3/2*q + n - 39/2*q**2.
-3*q*(13*q + 1)/2
Let h(p) be the third derivative of -p**7/525 + p**6/75 - p**5/50 + 18*p**2 + 1. Suppose h(q) = 0. What is q?
0, 1, 3
Let g(j) = j**2 - 34*j + 4. Let w(l) = 3*l**2 - 11*l - 8. Let h be w(6). Let r be g(h). Solve 8/3*b**3 - 4*b + 1/2*b**r - 3/2 + 7/3*b**2 = 0.
-3, -1/3, 1
Factor -144/7*c**2 - 256/7 + 4*c**3 + 320/7*c - 2/7*c**4.
-2*(c - 4)**3*(c - 2)/7
Suppose -51*y + 53*y - 6 = 0. Let u(g) be the first derivative of 2/3*g**y + 1/5*g**5 - 3*g + 5 + 2*g**2 - g**4. Determine p so that u(p) = 0.
-1, 1, 3
Let g(h) be the second derivative of -h**5/10 - 5*h**4/6 - h**3 + 9*h**2 + 7*h + 6. Let g(m) = 0. What is m?
-3, 1
Let w(d) be the first derivative of -3*d**5/10 + 5*d**4/6 - 13*d**3/18 + d**2/6 + 133. Solve w(a) = 0.
0, 2/9, 1
Suppose 1/2*b**2 + b - 1/2*b**4 - 3/2*b**3 + 0 + 1/2*b**5 = 0. Calculate b.
-1, 0, 1, 2
Let n be 3/(-6)*8/(-2). Let -6*j - 15 + n*j**3 - 13 + 32 + 0*j**3 = 0. What is j?
-2, 1
Let x(g) be the second derivative of -1/15*g**2 - 12*g + 0 - 2/45*g**4 - 1/9*g**3. Suppose x(b) = 0. What is b?
-1, -1/4
Let k(j) be the second derivative of j**6/55 + 3*j**5/22 + 9*j**4/22 + 7*j**3/11 + 6*j**2/11 + 124*j. Factor k(r).
6*(r + 1)**3*(r + 2)/11
Suppose -3*x = 5*u - 2, -3*u = 6*x - 10*x + 22. Let k(o) be the third derivative of -o**2 + 0 - 1/50*o**6 + 0*o - 1/20*o**5 - 1/40*o**x + 0*o**3. Factor k(d).
-3*d*(d + 1)*(4*d + 1)/5
Let r(z) = -5*z**3 - 25*z**2 - 15*z + 5. Let s(d) be the third derivative of d**4/24 + d**3/6 - 5*d**2. Let b(a) = -r(a) + 20*s(a). Factor b(n).
5*(n + 1)**2*(n + 3)
Let s(w) = -9*w**2 + 73*w + 80. Let l(n) = 30*n**2 - 218*n - 241. Let k(d) = 2*l(d) + 7*s(d). Factor k(h).
-3*(h - 26)*(h + 1)
Let c(z) = -z**3 + z**2 + 3*z + 1. Let k be c(-2). Factor 504*v - k*v**3 - 75*v**2 + 12*v**3 - 625 - 129*v.
5*(v - 5)**3
Let q(g) be the third derivative of -g**8/1680 - g**7/210 - g**6/90 - 7*g**4/24 - 2*g**2. Let l(w) be the second derivative of q(w). Solve l(a) = 0.
-2, -1, 0
Suppose 157*k = 117*k. Determine t, given that 4/5*t + 2/5*t**2 + k - 2/5*t**3 = 0.
-1, 0, 2
Let l be ((2/4)/((-91)/(-104)))/((-12)/(-56)). Factor 0*q**2 + l*q**3 + 0*q - 2*q**4 - 2/3*q**5 + 0.
-2*q**3*(q - 1)*(q + 4)/3
Let x be 18/(-108)*18 + (-10)/(-2). Let 2/5*d**3 + 0*d + 1/5*d**x + 0 + 1/5*d**4 = 0. Calculate d.
-1, 0
Let b = 354 - 352. Let u = -6 + 10. Determine z, given that -1/4*z**u - 1/2*z - 1/2*z**5 - 1/4 + 1/2*z**b + z**3 = 0.
-1, -1/2, 1
Let g(i) be the second derivative of i**10/120960 - i**9/60480 - i**8/13440 - i**4/3 - 14*i. Let m(x) be the third derivative of g(x). Factor m(w).
w**3*(w - 2)*(w + 1)/4
Let u(p) be the third derivative of 0*p + 5/36*p**5 + 0 + 5/24*p**4 + 1/72*p**6 - 5/2*p**3 - 6*p**2. Factor u(b).
5*(b - 1)*(b + 3)**2/3
Let u = -3/23 - -29/46. Let s = -28 - -32. Let 4/3*x**3 + u*x**s + 0*x + x**2 - 1/6 = 0. Calculate x.
-1, 1/3
Let d(a) be the second derivative of 1/90*a**5 - 11*a + 4/135*a**6 + 0 + 0*a**3 + 0*a**2