- 1)
Let v = -59219 - -59221. Factor -3 - 1/3*r**3 - 7/3*r**v - 5*r.
-(r + 1)*(r + 3)**2/3
Let f(i) be the third derivative of -i**8/672 + 23*i**7/420 + 49*i**6/240 + 5*i**5/24 + 103*i**2. Factor f(y).
-y**2*(y - 25)*(y + 1)**2/2
Let d(f) be the second derivative of -f**5/30 + f**4/12 + 31*f**2/2 + 14*f. Let s(o) be the first derivative of d(o). Factor s(y).
-2*y*(y - 1)
Factor 5*t**2 - 2102 + 0*t**2 - t**3 + 32*t - t**2 + 2102.
-t*(t - 8)*(t + 4)
Factor 3/7*g**2 + 180/7 + 96/7*g.
3*(g + 2)*(g + 30)/7
Let y be (52/(-8))/(-13)*-8. Let s be -5 + (-27)/y - -2. Let 0*w**2 - 9/4*w**4 - 3/2*w**3 + 0 + s*w**5 + 0*w = 0. What is w?
-2/5, 0, 1
Suppose 3*n - 1/2*n**2 + 0 = 0. What is n?
0, 6
Let d(o) = -o**2 + o. Suppose -5*h - 3*b + 11 = -4*b, 0 = -5*b - 5. Let r(j) = -12*j**2 + 6*j + 8. Let i(a) = h*r(a) - 28*d(a). Factor i(p).
4*(p - 2)**2
Let i(j) = 5*j**3 - 37*j**2 + 93*j + 135. Let f(t) = -t**3 - t**2. Let a(w) = -2*f(w) - i(w). Suppose a(h) = 0. Calculate h.
-1, 5, 9
Let k(t) be the first derivative of -t**5/30 - t**4/6 - t**3/3 + 10*t**2 - 46. Let y(i) be the second derivative of k(i). Let y(w) = 0. Calculate w.
-1
Factor 732*y**2 - 2129*y**4 + 2204*y**4 + 0*y + 960*y**3 + 144*y.
3*y*(y + 12)*(5*y + 2)**2
Solve 828*o**3 + 756*o**2 - 1654*o**3 + 47628*o + 829*o**3 = 0.
-126, 0
Let a(q) be the third derivative of q**9/1008 - q**8/140 + q**7/70 - 5*q**3/6 + 9*q**2. Let g(b) be the first derivative of a(b). Find x such that g(x) = 0.
0, 2
Let w be 273/126 + (-11)/66. Factor -1/6*a**w + 0 - 1/2*a.
-a*(a + 3)/6
Let b be 4*48/448*((-4)/(-3) + 0). Suppose 0*h + 0 + 4/7*h**4 + b*h**2 - 2*h**3 + 6/7*h**5 = 0. Calculate h.
-2, 0, 1/3, 1
Let o(g) be the third derivative of g**8/84 + 22*g**7/105 + 6*g**6/5 + 16*g**5/15 - 32*g**4/3 - 67*g**2. Suppose o(j) = 0. Calculate j.
-4, 0, 1
Let q(p) = -2*p**2 + 15*p + 23. Let n(a) = -9*a**2 + 75*a + 114. Let t(d) = -5*n(d) + 24*q(d). Find c, given that t(c) = 0.
-3, -2
Let y(q) be the second derivative of -17*q - 1/6*q**4 + 0*q**2 + 2/3*q**3 + 0. What is b in y(b) = 0?
0, 2
Suppose 4*q - 2*d = 24, -d - 26 = -3*q - 10. Let x be 4/q + 1/(-1). Factor 0*u**4 - 3*u + x*u + 3*u**4 + 3*u**3 - 3*u**2 + 0*u**4.
3*u*(u - 1)*(u + 1)**2
Factor 19*z - 6*z**2 - 3*z**4 - 12*z**3 - 16*z + 9*z + 9.
-3*(z - 1)*(z + 1)**2*(z + 3)
Let f(n) be the first derivative of 2*n**3/9 - 47*n**2/3 - 32*n + 214. Factor f(l).
2*(l - 48)*(l + 1)/3
Let v(w) be the first derivative of 5*w**7/21 + 3*w**6/5 + 3*w**5/10 - w**4/6 + 14*w + 18. Let o(t) be the first derivative of v(t). Factor o(y).
2*y**2*(y + 1)**2*(5*y - 1)
Let i(t) = -t**2 - 6*t + 3. Let s be i(-6). Let 6*b + 13*b**2 + b + 7*b**3 - s*b + 3*b**2 = 0. Calculate b.
-2, -2/7, 0
Factor -95*f + 125*f**3 - 103*f - 102*f + 290*f - 115*f**2.
5*f*(f - 1)*(25*f + 2)
Let l(x) be the third derivative of -5/6*x**3 + 0 + 1/12*x**4 + 0*x**5 - 1/180*x**6 - 2*x**2 + 0*x. Let m(u) be the first derivative of l(u). Factor m(t).
-2*(t - 1)*(t + 1)
Let p(a) be the third derivative of a**7/2520 + a**6/90 + 2*a**5/15 + 8*a**4/9 - 11*a**3/2 + 29*a**2. Let x(w) be the first derivative of p(w). Factor x(c).
(c + 4)**3/3
Suppose 4*o + o = 0. Suppose o = -9*q + 14*q - 15. Factor -7*l**3 - l**3 - 10*l**2 - 4*l + 4*l**q.
-2*l*(l + 2)*(2*l + 1)
Suppose y - a - 130 = -2*y, -y + 55 = 2*a. Solve -47*j + j**3 + 2*j**2 + y*j + 0*j**2 - j**2 = 0 for j.
-2, 0, 1
Let n be 8 + 0 + 0 + (-8 - -4). Suppose -5*p - 3*u = -4*p - 40, -3*u = -12. Factor 4*g**3 + 15*g**n + 12*g**2 - 7*g**5 + 4*g**5 - p*g**3 + 0*g**4.
-3*g**2*(g - 2)**2*(g - 1)
Let d = 82 - 22. Suppose -d = -2*p + 136. Factor -252*n**3 - 143*n**2 - 4 - 37*n - p*n**4 - 4 - 75*n**2 - 35*n.
-2*(n + 1)**2*(7*n + 2)**2
Let y(u) = -95*u**3 + 34*u**2 + 90*u - 34. Let c(a) = -47*a**3 + 16*a**2 + 45*a - 16. Let i(j) = -5*c(j) + 2*y(j). Factor i(x).
3*(x - 1)*(x + 1)*(15*x - 4)
Let f(n) be the first derivative of -3*n**4 + 8*n**3/3 + 35*n**2/6 - 25*n/3 - 51. Suppose f(d) = 0. Calculate d.
-1, 5/6
Let b(x) be the third derivative of -x**6/210 + 2*x**5/15 - 43*x**4/42 + 20*x**3/7 - x**2 + 12*x. Let b(i) = 0. What is i?
1, 3, 10
Let q(j) be the first derivative of j**3/12 + 9*j**2/2 + 81*j + 97. Determine f, given that q(f) = 0.
-18
Let 2/5*n**2 - 48/5 - 4*n = 0. What is n?
-2, 12
Let g = 43/324 + -4/81. Let b(p) be the second derivative of 0 + 1/84*p**7 + 0*p**2 + 1/15*p**6 + 3*p + 3/20*p**5 + g*p**3 + 1/6*p**4. Solve b(n) = 0.
-1, 0
Let y be (-215)/(-43) - 2/((-4)/(-2)). Let l(d) be the second derivative of 4*d**3 + 0 + 24*d**2 + 4*d - 7/4*d**y + 3/20*d**5. Factor l(b).
3*(b - 4)**2*(b + 1)
Factor 2/3 - 1/3*k**2 - 1/3*k.
-(k - 1)*(k + 2)/3
Let o = -900/31 + 4624/155. Factor 2/5*h**5 + o*h**2 + 0*h + 0*h**4 - 6/5*h**3 + 0.
2*h**2*(h - 1)**2*(h + 2)/5
Let f(y) be the first derivative of y**6/18 + 2*y**5/15 - 2*y**4/3 + 2*y**3/9 + 7*y**2/6 - 4*y/3 - 324. Factor f(s).
(s - 1)**3*(s + 1)*(s + 4)/3
Let r be (3/21)/(9 - (-627)/(-77)). What is y in r*y + 0 - 1/6*y**3 - 1/6*y**4 + 1/6*y**2 = 0?
-1, 0, 1
Factor 24 + 0*y**2 - 37*y**3 + 13*y**3 + 7*y**3 + 3*y**2 + 30*y + 14*y**3.
-3*(y - 4)*(y + 1)*(y + 2)
Let u(f) be the first derivative of -2*f**3/27 - f**2/9 + 4*f/9 + 67. Factor u(j).
-2*(j - 1)*(j + 2)/9
Let b(v) be the first derivative of -2*v**3/3 - 2*v**2/7 - 14. Factor b(i).
-2*i*(7*i + 2)/7
Let a(p) be the third derivative of -p**5/60 + 11*p**4/12 - 121*p**3/6 - 48*p**2. Solve a(i) = 0.
11
Let w(b) be the third derivative of -3*b**5/20 - 13*b**4/8 - 2*b**3 - 3*b**2 + 6. Find d such that w(d) = 0.
-4, -1/3
Let x(s) be the second derivative of -1/6*s**6 + 5/2*s**3 + 11*s - 3/4*s**5 + 5*s**2 - 5/12*s**4 + 0. Factor x(c).
-5*(c - 1)*(c + 1)**2*(c + 2)
Let y(h) be the second derivative of h**4/4 + 3*h**3 - 406*h. Suppose y(f) = 0. Calculate f.
-6, 0
Factor 74088 + 11641*r - 48823*r + 144*r**4 + 19950*r**2 - 3*r**5 - 28086*r - 2547*r**3.
-3*(r - 14)**3*(r - 3)**2
Suppose 3*u = -2*x + 9, -3*x + 2 = -10*u + 3*u. Factor 0 - 6/7*p + 27/7*p**2 - 27/7*p**x.
-3*p*(3*p - 2)*(3*p - 1)/7
Factor 0*c**3 + 0 + 8/7*c**2 - 2/7*c**4 + 0*c.
-2*c**2*(c - 2)*(c + 2)/7
Let m(n) = -7*n**3 + 12*n**2 - 5*n + 3. Let t(x) = 2*x**3 - 2*x - 1. Let k(r) = -5*m(r) - 15*t(r). Let k(u) = 0. What is u?
0, 1, 11
Let m(z) = 3*z**2 - 19*z + 9. Let i be m(6). Determine q, given that i*q - 5*q + 0*q**2 - 12*q**2 = 0.
-1/6, 0
Let y(l) be the second derivative of 0 - 2*l - 1/45*l**6 + 1/18*l**4 - 1/15*l**5 + 0*l**2 + 2/9*l**3. Find n, given that y(n) = 0.
-2, -1, 0, 1
Let f(u) be the second derivative of 0 + 13*u - 5/3*u**3 - 5/12*u**4 + 1/4*u**5 + 0*u**2. Factor f(m).
5*m*(m - 2)*(m + 1)
Let n(p) be the second derivative of p**5/390 - p**4/39 - 5*p**3/39 + 3*p**2 + 2*p. Let x(d) be the first derivative of n(d). Let x(j) = 0. What is j?
-1, 5
Suppose -3*f + y + 53 + 33 = 0, -8 = -2*y. Let o = f + -28. Solve -4/5*a**o - 2/5*a + 2/5 = 0 for a.
-1, 1/2
Solve 16 + c + 14*c - 33*c + 0 + 2*c**2 = 0.
1, 8
Solve 7*o - 16*o**4 + 22*o**5 + 57*o + 64*o**2 - 26*o**5 = 0 for o.
-2, 0, 2
Let x(i) be the second derivative of 1/10*i**5 - 1/2*i**4 - 2*i**2 + 7*i + 0 + 1/15*i**6 - 5/3*i**3. Solve x(m) = 0 for m.
-1, 2
Let g = 1 + 1. Let a be 1550/(-1705) + 2672/616. Factor 16/7*o - a*o**g - 4/7*o**4 + 16/7*o**3 - 4/7.
-4*(o - 1)**4/7
Let w(d) = -7*d**3 - 45*d**2 + 13*d + 48. Let u(g) = -8*g**3 - 45*g**2 + 12*g + 47. Let f(n) = 3*u(n) - 2*w(n). Suppose f(p) = 0. What is p?
-9/2, -1, 1
Suppose -49*l + 158 = 60. Let r(z) be the first derivative of l*z + 1/3*z**3 - 3 - 3/2*z**2. Factor r(m).
(m - 2)*(m - 1)
Factor 5/3*x**4 + 7*x**3 + 0 + 8*x**2 + 4/3*x.
x*(x + 2)**2*(5*x + 1)/3
Suppose 0 = -o + 23 - 19. Solve -o*d + 6 - 10 + 3*d**2 + 16 + 16*d = 0.
-2
Let a(m) = 7*m**2 - 1100*m + 101576. Let t(r) = 15*r**2 - 2199*r + 203154. Let z(b) = 9*a(b) - 4*t(b). Factor z(l).
3*(l - 184)**2
Suppose k + 1 = 5*o, 5*k + 3*o = 11 + 12. Let s(g) = -2*g**3 + 20*g**2 + 3*g - 28. Let b be s(10). Determine y so that 4*y + 2*y - k*y**b + y**2 = 0.
0, 2
Let d = -1 + 10. Factor -11*o**3 - 8*o**2 + 23 + 16*o + d + 7*o**3.
-4*(o - 2)*(o + 2)**2
Let i(o) = -o**4 + o**3 + o**2 + 2*o - 1. Let g(p) = -16*p**4 + 60*p**3 + 216*p**2 + 306*p - 18. Let a(f) = 2*g(f) - 36*i(f). Factor a(d).
4*d*(d + 3)**2*(d + 15)
Let z be (-6)/((-504)/(-161)) - -2. Let i(f) be the first derivative 