(d) = d**2 - 11*d - 2. Let h(s) = 3*l(s) - 2*r(s). Suppose h(u) = 0. Calculate u.
-7, 0
Let h be 60/(-100)*3/(-27). Let g(u) be the third derivative of 2*u**2 + 0 - 1/120*u**6 + 0*u**3 - h*u**5 - 1/6*u**4 + 0*u. What is d in g(d) = 0?
-2, 0
Let v(y) be the third derivative of y**5/20 - y**4/2 - 45*y**3/2 - 851*y**2. Let v(p) = 0. Calculate p.
-5, 9
Solve 2/7*m**4 - 2 - 16/7*m**3 + 16/7*m + 12/7*m**2 = 0.
-1, 1, 7
Determine r so that 6*r**4 + 2/3*r**5 + 56/3*r**3 + 0 + 32/3*r + 24*r**2 = 0.
-4, -2, -1, 0
Let z(g) be the second derivative of -g**4/15 + 2*g**3/5 + 36*g**2/5 - 387*g. Solve z(t) = 0.
-3, 6
Factor 19*z**4 - 9 + 35*z - 4*z**4 + 25*z - 11 - 50*z**3 + 15*z**2.
5*(z - 2)**2*(z + 1)*(3*z - 1)
Let s = 5986 + -23941/4. Factor s*k - 1/4*k**2 - 1/2.
-(k - 2)*(k - 1)/4
Let i(y) = -y**5 - y**4 + y**2 + y + 2. Let n(c) = 6*c**5 + 10*c**4 + 6*c**3 - 9*c**2 - 13*c - 10. Let j(b) = 10*i(b) + 2*n(b). Factor j(q).
2*q*(q - 1)*(q + 2)**3
Let i = -2/153 - -932/1071. Let d = -138 + 968/7. Factor 4/7 - i*l + d*l**2.
2*(l - 2)*(l - 1)/7
Suppose -5*w + 2*g + 30 = 16, -2*g = -2*w + 2. Factor f**w + 2*f**2 + 0 - 1/6*f**5 - 2/3*f - 13/6*f**3.
-f*(f - 2)**2*(f - 1)**2/6
Let a(h) be the second derivative of 0 + 0*h**2 - 2/5*h**5 + 1/15*h**6 + 14*h + 5/6*h**4 - 2/3*h**3. Let a(b) = 0. Calculate b.
0, 1, 2
Let w(a) = -9*a**5 - 2*a**4 - 2*a**3 + 8*a**2 - 9*a. Let n(k) = -k**5 - 2*k**3 + k. Let g(f) = -7*n(f) + w(f). Solve g(p) = 0.
-2, 0, 1, 2
Let z(d) be the second derivative of d**8/6720 + d**7/3360 - d**6/1440 - d**5/480 - 2*d**3 - 11*d. Let x(c) be the second derivative of z(c). Factor x(u).
u*(u - 1)*(u + 1)**2/4
Suppose m = -4*u + 5*m + 20, -2*m = 10. Suppose 0 = -2*f - 3*l - 9, -f = -u*f + 2*l + 7. Factor 4/9*g**2 - 2/9*g**f + 0*g + 0.
-2*g**2*(g - 2)/9
Let b(x) = 17*x + 10. Let o be b(-6). Let c be 8/6*(o/(-20) + -4). Solve -6/5*k + c*k**3 - 2/5 - 4/5*k**2 + 6/5*k**4 + 2/5*k**5 = 0.
-1, 1
Let l(p) = 2*p**2 - 7*p + 21. Let f(i) = 2*i**2 - 8*i + 11 + 2 + 7. Let m(h) = -5*f(h) + 4*l(h). Factor m(x).
-2*(x - 4)*(x - 2)
Let f(o) = 2*o**3 - 50*o**2 - 156*o - 168. Let p(t) = t**3 - t**2 + 2. Let z(k) = -f(k) + 6*p(k). Factor z(j).
4*(j + 3)**2*(j + 5)
Let w = -69 - -72. Let t(z) be the first derivative of -2/33*z**w + 0*z + 1/11*z**2 - 8 + 2/55*z**5 - 1/22*z**4. Let t(a) = 0. What is a?
-1, 0, 1
Let t(i) = 18*i**3 + 146*i**2 + 260*i + 52. Let a(k) = -19*k**3 - 145*k**2 - 260*k - 50. Let s(y) = -2*a(y) - 3*t(y). Solve s(v) = 0 for v.
-7, -2, -1/4
Let f(r) be the second derivative of r**8/6720 - r**7/2520 + 4*r**4/3 + 30*r. Let y(d) be the third derivative of f(d). Factor y(i).
i**2*(i - 1)
Let n be 8/(-8) - 12/(-2). Suppose v - n*v + 108 = 0. Let 6*t - 3*t**2 + 6*t + 20*t**3 + v*t**2 + 2 + 6*t**4 = 0. What is t?
-1, -1/3
Let c(x) be the third derivative of -2*x**7/105 + 7*x**6/30 - 16*x**5/15 + 2*x**4 + 5*x**2 + 6. Factor c(b).
-4*b*(b - 3)*(b - 2)**2
Let x = 331 - 328. Let q(m) be the first derivative of -1/10*m**4 - 2/15*m**x + 2/25*m**5 + 0*m + 1/5*m**2 - 6. What is i in q(i) = 0?
-1, 0, 1
Let w(x) be the third derivative of -9*x**2 + 2/45*x**5 + 0 + 0*x + 1/4*x**4 + 2/9*x**3. Factor w(k).
2*(k + 2)*(4*k + 1)/3
Let d be 93/2 + 12/8. Suppose 2*u - d = -4*u. Factor -30*p**2 + 0*p**2 - 42*p**2 + u*p + 20*p**2 + 84*p**3.
4*p*(3*p - 1)*(7*p - 2)
Let a = 831 - 411. Let z = a - 2091/5. Let 2/5*f - f**4 + 1/5*f**5 + 0 + z*f**3 - 7/5*f**2 = 0. What is f?
0, 1, 2
Let d(s) = -9*s**3 + s. Let f be d(-1). Let v be ((-12)/f - -2)*4. Factor -g**4 + 6*g**3 + g**v - 7*g**3 + 2*g**3 - g**5.
-g**2*(g - 1)*(g + 1)**2
Suppose 7*x - 1 = 27. Suppose -54 + 2*l**x + 12*l**2 + 16*l**3 + 20*l**2 + 4*l**2 = 0. Calculate l.
-3, 1
Find s, given that -5*s**2 + 2*s**2 + 108 + 9*s - 86 + 2*s**2 = 0.
-2, 11
Factor 16*p**5 - 44*p**5 + 4*p**2 + 4*p**3 + 11*p**5 - p**4 + 16*p**5.
-p**2*(p - 2)*(p + 1)*(p + 2)
Suppose 5*u + 3*j + 22 = 207, 2*u = j + 74. Let s = u - 35. Factor 2/7*z**s + 0*z + 0.
2*z**2/7
Let a = 581 - 6967/12. Let l = 1/4 + a. Factor 0 - 2/3*f**2 + l*f.
-2*f*(f - 1)/3
Factor 1020*p**2 + 69360*p + 642*p**3 - 320*p**3 + 1572160 - 317*p**3.
5*(p + 68)**3
Solve 4/3*v**3 + 2/3*v**4 - 10*v**2 - 64/3*v - 32/3 = 0 for v.
-4, -1, 4
Let g = -708 + 708. Let f(x) be the first derivative of g*x**3 + 6 - 3/4*x**4 + 9/2*x**2 + 6*x. Factor f(o).
-3*(o - 2)*(o + 1)**2
Let t = 13836 + -13836. Suppose c**2 - 2*c**3 + 0*c + 3/4*c**5 + t + 1/4*c**4 = 0. Calculate c.
-2, 0, 2/3, 1
Let n(c) be the third derivative of c**5/120 - 7*c**4/4 + 147*c**3 - 27*c**2 - 1. Determine t, given that n(t) = 0.
42
Let p = 12 - 9. Let k = 0 + p. Suppose 146 + 10*h**2 - 146 - 15*h**k = 0. What is h?
0, 2/3
Let d(a) be the second derivative of -a**7/140 - a**6/40 - a**5/40 + 37*a**2/2 - 18*a. Let m(g) be the first derivative of d(g). Factor m(c).
-3*c**2*(c + 1)**2/2
Suppose -6*u**4 + 11 + 35*u**3 + 16 + 16*u**4 - 82*u**2 + 2*u**5 - 61*u**3 + 24*u + 45 = 0. What is u?
-6, -2, -1, 1, 3
Solve 12*b**3 + 14821 - 29620 + 150*b - 2*b**5 + 14745 - 124*b**2 + 18*b**4 = 0 for b.
-3, 1, 9
Find m such that 106*m + 88*m - 9*m - 350*m**2 + 35*m - 40 + 125*m**3 = 0.
2/5, 2
Let v be (2 - (-9)/(-4))/(28/((-896)/12)). Let 4/3 + v*r - 2/3*r**2 = 0. Calculate r.
-1, 2
Factor 10*k**4 + 6*k**2 + 25*k**2 - 59 - 21 + 84*k**2 - 75*k**3 + 120*k.
5*(k - 4)**2*(k + 1)*(2*k - 1)
Factor -6/5 + 2/5*w**2 + 11/5*w.
(w + 6)*(2*w - 1)/5
Suppose -275*l = -282*l. Factor 2/11*z + l + 0*z**2 - 2/11*z**3.
-2*z*(z - 1)*(z + 1)/11
Let 3/4*x**2 - 27/4 + 6*x = 0. What is x?
-9, 1
Let g(i) be the first derivative of -i**3/7 + 3*i**2/14 + 6*i/7 - 73. Factor g(o).
-3*(o - 2)*(o + 1)/7
Let w be (2/(-6))/(22 - (-2136)/(-96)). Determine o, given that -w + 11/3*o + o**2 = 0.
-4, 1/3
Let i be 12/14*(-18)/(-4). Let b be 2 - 176/(-140) - (-6)/10. Factor i*u + 1/7*u**3 + 9/7*u**2 + b.
(u + 3)**3/7
Let h be (-1 + -1)/((-9)/18). Suppose h = -x + 10. Factor -3*w + 0*w - x*w**5 + 0*w**5 + 3 + 3*w**4 - 6*w**2 + 3*w**5 + 6*w**3.
-3*(w - 1)**3*(w + 1)**2
Let m(y) = 3*y**2 + 40*y - 10. Let q be m(-14). Suppose q*r - 50 = -7*r. Factor -9/5*d**r - 3*d**3 - 3/5*d**4 + 27/5*d + 0.
-3*d*(d - 1)*(d + 3)**2/5
Factor -11/4*g**2 + 1/8*g**3 - 27/4 + 75/8*g.
(g - 18)*(g - 3)*(g - 1)/8
Determine l so that 0 + 8/3*l + 2/3*l**5 - 2*l**2 - 10/3*l**3 + 2*l**4 = 0.
-4, -1, 0, 1
Suppose -3*u - 4*g - 1 = 0, -5*g = -g + 16. Suppose 12*l**u - 7*l**4 - 36*l**3 + 17*l**4 - 16*l - 2*l**4 - 48*l**2 = 0. What is l?
-1, -2/3, 0, 2
Let c(o) be the first derivative of 1/24*o**4 + 1/3*o + 0*o**3 - 1/4*o**2 + 16. Factor c(l).
(l - 1)**2*(l + 2)/6
Let h(l) be the third derivative of -49*l**6/24 - 2569*l**5/12 + 925*l**4/3 - 530*l**3/3 - 267*l**2. Factor h(r).
-5*(r + 53)*(7*r - 2)**2
Let f = -1387 + 1388. Determine k, given that -1/2*k + 1/2*k**2 - f = 0.
-1, 2
Let l be 18/5 - 6/(-15). Let r(w) = w**3 + 4*w**2 + 4*w + 2. Let y be r(-2). Factor g**4 - 6*g**3 + g**5 + 1 + g + l*g**3 - y*g**2 + 0*g**4.
(g - 1)**2*(g + 1)**3
Let m(q) be the first derivative of -3/2*q + 3/4*q**4 + 3/10*q**5 - 17 - 3/2*q**2 + 0*q**3. Factor m(g).
3*(g - 1)*(g + 1)**3/2
Let k = -6 - -9. Factor 5*r**5 + 8*r**5 + 8*r**5 - 24*r**5 - k*r + 6*r**3.
-3*r*(r - 1)**2*(r + 1)**2
Suppose 5*s = 9 + 11. Let b(g) be the third derivative of 1/24*g**6 + 0*g**3 + 12*g**2 - 1/6*g**5 + 0 + 0*g**s + 0*g. Solve b(c) = 0.
0, 2
Let u(x) be the second derivative of -4/33*x**3 + 27*x - 1/66*x**4 + 0 - 4/11*x**2. Let u(q) = 0. Calculate q.
-2
Let g(a) = -47*a**4 + 7*a**3 + 32*a**2 + 8*a. Let d = -35 + 34. Let n(y) = -y**4 + y**3. Let x(p) = d*g(p) - 3*n(p). Factor x(s).
2*s*(s - 1)*(5*s + 2)**2
Let g = 196 - 191. Let d(m) be the first derivative of 4*m - 4*m**2 + 0*m**3 + 3 - 4/5*m**g + 2*m**4. Factor d(b).
-4*(b - 1)**3*(b + 1)
Suppose -4*t**2 + 11184*t**5 + 12*t**2 - 8*t**4 + 4*t**3 - 11188*t**5 = 0. What is t?
-2, -1, 0, 1
Let u = -868 - -2608/3. Let p(t) be the first derivative of 9 - u*t**3 + 0*t**2 + 2/5*t**5 + 1/2*t**4 + 0*t. Determine f, given that p(f) = 0.
-2, 0, 1
Let i(r) = 5*r**2 + 65*r - 114. Let k(z) = -5*z**2 - 60*z + 113. Let h(v) = 3*i(v) + 4*k(v). Determine a, given that h(a) = 0.
-11, 2
Suppose 3 = -d + 15. Suppose -w + d = 5*w. Let -2*z - w*z**4 + 8 - 6*z**2 + 8*z**3 - 6*z + 0 = 0. Calculate z.
-1, 1, 2
Let c = -146 + 149. Factor -c*f**