 -k(h) + 2*l(h). Let v(y) = 2*y**2 + 14*y - 2. Let m(z) = -2*g(z) + 3*v(z). Factor m(b).
4*b*(b + 4)
Suppose -y + 5 = 93*r - 90*r, 6*r + y = 14. Factor -r - 5/2*s - 1/2*s**2.
-(s + 2)*(s + 3)/2
Suppose 280 - 227 + 459 + 6*y**3 + 29*y**3 + 354*y**2 + 832*y + y**4 = 0. What is y?
-16, -2, -1
Let c(h) = h**3 + 6*h**2 + 6*h + 5. Let p be c(-5). Let o(k) = k**3 - 3*k - 2. Let v be o(2). Factor 0*a**2 + v*a**4 - 1/2*a**3 + p + 1/2*a**5 + 0*a.
a**3*(a - 1)*(a + 1)/2
Let m = 4 + -2. Let v be (-3 - -3)*(5/10 - 0). Determine k so that -2/5*k**3 + 0 - 2/5*k**5 + 4/5*k**4 + v*k + 0*k**m = 0.
0, 1
Let q be ((-12)/(-9))/(-17 - -18). Factor q*m**3 + 16/3*m**2 + 20/3*m + 8/3.
4*(m + 1)**2*(m + 2)/3
Let f(q) be the first derivative of -6*q**5/5 + 41*q**4/2 + 34*q**3/3 - 41*q**2 - 28*q - 421. Find p, given that f(p) = 0.
-1, -1/3, 1, 14
Suppose 52 = 7*x + 38. Determine d, given that d**5 - d**4 + 3*d**2 - 1 + d - x*d**3 - d**2 + 7*d**2 - 7*d**2 = 0.
-1, 1
Let g(r) = 4*r**4 - 9*r**3 + 11*r**2 + 3. Suppose 0*j + 39 = -13*j. Let y(s) = s**3 + s**2 + 1. Let w(q) = j*y(q) + g(q). Suppose w(x) = 0. What is x?
0, 1, 2
Let x(a) be the first derivative of 3*a - a**4 + a**2 - 20 - 5/3*a**3. Suppose x(v) = 0. Calculate v.
-1, 3/4
Determine x, given that 14*x + 37*x - 3*x**2 + 93*x - 1728 = 0.
24
Let k(c) be the first derivative of c**7/210 - 2*c**6/45 + c**5/10 + 10*c**3/3 - 7. Let n(w) be the third derivative of k(w). Suppose n(a) = 0. What is a?
0, 1, 3
Let c(z) be the third derivative of z**5/270 - z**4/54 - 8*z**3/27 - 92*z**2. Let c(w) = 0. Calculate w.
-2, 4
Let l(h) be the second derivative of 0 - 2*h**3 - 19*h + 2*h**2 + 13/12*h**4 + 1/30*h**6 - 3/10*h**5. Factor l(k).
(k - 2)**2*(k - 1)**2
Suppose 2*c - 2 = 0, -6*d = -d + 3*c - 48. Solve 15*t**2 + 0 + 0*t**2 - 2*t**3 - d*t**2 - 8 = 0 for t.
-1, 2
Let c = 2065/6177 - 2/2059. Factor 0*k + 0 + c*k**2 - 2/3*k**3.
-k**2*(2*k - 1)/3
Determine k so that -97*k**3 - 109*k**3 - 8*k + 6*k**4 + 220*k**3 = 0.
-2, -1, 0, 2/3
Determine m, given that 0 + 28/9*m**5 + 4/9*m**2 + 50/9*m**4 + 0*m + 26/9*m**3 = 0.
-1, -1/2, -2/7, 0
Let v(b) = 4*b**2 - 5*b - 5. Let d(f) = -f**2 + 2*f + 1. Let i(s) = 3*d(s) + v(s). Factor i(w).
(w - 1)*(w + 2)
Let d(i) = 30*i**3 - 1428*i**2 + 928*i - 168. Let m(g) = -59*g**3 + 2856*g**2 - 1854*g + 338. Let t(s) = 13*d(s) + 6*m(s). Factor t(u).
4*(u - 39)*(3*u - 1)**2
Factor 2*j**4 - j**3 + 4*j**3 - 3*j**5 - 6*j**2 + j**4 + 3*j**2.
-3*j**2*(j - 1)**2*(j + 1)
Let p(k) be the first derivative of k**4/6 - 10*k**3/3 + 21*k**2 - 54*k + 17. Determine u so that p(u) = 0.
3, 9
Suppose -h - 7 = -2*o, 3*o - 2 - 7 = 2*h. Let r(m) = 5*m - 21. Let z be r(o). Factor 0*v - 2/3*v**z + 2/3*v**3 + 0*v**2 + 0.
-2*v**3*(v - 1)/3
Let d(g) = -g**3 - 15*g**2 - 16*g - 28. Let n be d(-14). Factor 1/3*r**4 - 1/3*r**2 + 0*r**3 + 0*r + n.
r**2*(r - 1)*(r + 1)/3
Determine r, given that 155*r**3 + 20*r - 27*r**4 - 250*r**3 - 8*r**4 - 40*r**2 = 0.
-2, -1, 0, 2/7
Let 6*a + 3/4*a**2 - 195/4 = 0. Calculate a.
-13, 5
Let g be 2 - (0 - (-1204)/(-20)). Let k = g - 62. Find b such that -3/5*b + 2/5 + k*b**2 = 0.
1, 2
Let z = 47 - -6. Let c = z - 50. Factor 3/2*u**c + 1/2*u - 1/2*u**4 - 3/2*u**2 + 0.
-u*(u - 1)**3/2
Let x = -2/13 + 17/26. Suppose -3*s + 4 = -z, -2*s - 5*z = -33 + 2. What is r in -r**2 + 1/2 + r**s - x*r - 1/2*r**5 + 1/2*r**4 = 0?
-1, 1
Suppose 21*s = 38 + 67. Let q(c) be the third derivative of 0*c - 1/4*c**4 + 0 - 3/2*c**3 - 1/60*c**s - 11*c**2. Factor q(p).
-(p + 3)**2
Let d be (-28)/(-7)*(-195)/(-6). Factor d*p**2 - 6*p - 69*p**2 - 3 - 64*p**2.
-3*(p + 1)**2
Let g(k) be the third derivative of -k**8/112 + 3*k**7/70 - k**6/40 - 3*k**5/20 + k**4/4 - 23*k**2 - 1. Let g(x) = 0. Calculate x.
-1, 0, 1, 2
Let i(l) be the first derivative of 2*l**4 - 500*l**3/3 - 126*l**2 + 261. Let i(o) = 0. Calculate o.
-1/2, 0, 63
Suppose -58/3*p + 40 - 1/3*p**2 = 0. Calculate p.
-60, 2
Factor -4/9*i**3 + 16/9*i**2 + 0 + 28/3*i.
-4*i*(i - 7)*(i + 3)/9
Let r(i) = 5*i**2 + 680*i - 46128. Let v(p) = 9*p**2 + 1368*p - 92256. Let u(y) = -15*r(y) + 8*v(y). Factor u(b).
-3*(b - 124)**2
Suppose -2*u + 54 = 7*u. Let d(x) = -3*x**3 + 4*x**2 - 12*x + 8. Let y(f) = 4*f**3 - 3*f**2 + 12*f - 8. Let l(k) = u*d(k) + 4*y(k). Let l(i) = 0. Calculate i.
2
Let u be (-3346)/3*32/(-84). Let a = 426 - u. Factor 0 + 4/9*r + 14/9*r**2 + a*r**3.
2*r*(r + 1)*(5*r + 2)/9
Let s(h) be the second derivative of -h**6/120 - 3*h**5/40 - 3*h**4/16 + h**3/6 + 3*h**2/2 - 17*h - 19. Suppose s(l) = 0. Calculate l.
-3, -2, 1
Suppose -2*s + 185 = -s - 5*q, 5*q = 2*s - 360. Solve -176 + 351 - s - 4*w - 2*w**2 = 0.
-2, 0
Let m(v) be the first derivative of v**6/30 - v**5/20 - v**4/12 + v**3/6 - 34*v + 10. Let w(l) be the first derivative of m(l). Factor w(b).
b*(b - 1)**2*(b + 1)
Let u(m) be the first derivative of 3*m**5/5 - 6*m**4 + 24*m**3 - 48*m**2 + 48*m - 22. Factor u(c).
3*(c - 2)**4
Let f(n) be the third derivative of -2/35*n**5 + 0*n + 1/105*n**6 + 13*n**2 + 0 - 1/1470*n**7 + 4/21*n**4 - 8/21*n**3. Determine w, given that f(w) = 0.
2
Suppose 121*j = 33*j. Let -8/3*p + 0*p**2 + j + 2/3*p**3 = 0. What is p?
-2, 0, 2
Let y(a) be the second derivative of -a**5/110 - 19*a**4/66 - 6*a**3/11 - 85*a. Determine x so that y(x) = 0.
-18, -1, 0
Let u be ((-3)/(3 + 672))/(36/(-27)). Let v(p) be the third derivative of 0*p + 0*p**3 + 1/120*p**4 + 5*p**2 + 0 - u*p**5. Let v(x) = 0. Calculate x.
0, 1
Let v = -64 - -64. Let p be -3*(-1)/(-6)*v. Factor 4/9*s**2 + 4/9*s**4 + 0 + p*s - 10/9*s**3.
2*s**2*(s - 2)*(2*s - 1)/9
Suppose 0 = 5*h + 2*m - 18, -5 = -3*h + 3*m - 11. Let i be 1/1*2 + 1. Factor 66 + 1746*c**2 + 1372*c**i - 12 + 18*c**h + 756*c + 54.
4*(7*c + 3)**3
Let w(n) = -23*n**2 + 116*n - 8. Let h(m) = 22*m**2 - 116*m + 9. Let z(s) = 4*h(s) + 3*w(s). Factor z(x).
(x - 6)*(19*x - 2)
Let d = 4567/13737 - -4/4579. Determine x so that 0 + d*x**4 + 4/3*x + 5/3*x**3 + 8/3*x**2 = 0.
-2, -1, 0
Let f(p) be the second derivative of -p**5/5 - 7*p**4/3 + 56*p**3/3 - 40*p**2 - 211*p. Solve f(m) = 0 for m.
-10, 1, 2
Let d be 29085/12 + 6/(-8). Factor d*g**4 + 19*g**3 - 39*g**2 + 18*g + 5*g**3 - 2426*g**4.
-3*g*(g - 6)*(g - 1)**2
Let o(m) = -m**3 + 41*m**2 + 103*m + 108. Let w(z) = -z**3 + z**2 - z. Let f be (2 + 10)*2/3. Suppose 5*b = -f - 17. Let x(u) = b*w(u) + o(u). Factor x(l).
4*(l + 3)**3
Let n be (1/18)/(14/210). Determine s so that n*s**2 + 10/3 - 25/6*s = 0.
1, 4
Let v(w) be the second derivative of w**6/15 + w**5/5 - w**4/6 - 2*w**3/3 - 166*w. Let v(s) = 0. What is s?
-2, -1, 0, 1
Let a(m) be the first derivative of -m**2 - 5*m + 4. Let z be a(-4). Solve -4*x**2 - 2*x**4 + 10*x**2 + x**3 + 2*x**z - x**4 = 0 for x.
-1, 0, 2
Let g(f) be the third derivative of 3*f**7/490 - 137*f**6/70 + 18493*f**5/105 + 12604*f**4/21 + 16928*f**3/21 - 606*f**2. Factor g(a).
(a - 92)**2*(3*a + 2)**2/7
Determine u, given that 42*u + 64/3 - 2/3*u**3 + 20*u**2 = 0.
-1, 32
Let a(f) = 3*f - 9. Let u be a(4). Solve 4*w**2 - 4*w**u - 7 + 20*w - 1 + 20 = 0.
-1, 3
Let f be (-4 + 8 + -4)/1. Let x(b) be the third derivative of 0 + f*b - 1/20*b**5 + 3*b**2 - 1/120*b**6 + 0*b**4 + 2/3*b**3. Factor x(s).
-(s - 1)*(s + 2)**2
Let s be (-2)/(-7) + (-14)/49 - -2. Factor -2*q**3 - 45*q - 3*q**3 - 25*q**s - 15 + 10*q.
-5*(q + 1)**2*(q + 3)
Let z(f) = -f**2 - 3*f + 20. Let h be z(-6). Let l be 2 - 5 - (-703)/222. Find u, given that l*u**3 + 0 + 2/3*u**h - 1/6*u**4 - 2/3*u = 0.
-2, 0, 1, 2
Let w = 20116 - 101282/5. Let g = w + 141. Factor 0 + 0*t + g*t**2.
3*t**2/5
Let r(k) be the third derivative of -k**6/600 - 13*k**5/150 - 2*k**4/5 - k**2 - 146*k. Factor r(q).
-q*(q + 2)*(q + 24)/5
Let j(b) be the first derivative of 1/2*b**3 - 1/10*b**5 - 1/8*b**2 - 1/16*b**4 - 1/2*b - 9. Determine f so that j(f) = 0.
-2, -1/2, 1
Let r(m) be the first derivative of 91*m**3/18 - m**2 - 2*m/3 - 82. Find x such that r(x) = 0.
-2/13, 2/7
Let a(d) = 17*d**3 + 20*d**2 + d - 32. Let k(y) = 2*y**3 + y - 2. Let s(m) = -a(m) + 6*k(m). Solve s(p) = 0 for p.
-4, -1, 1
Let y(d) be the second derivative of -5*d**7/42 + 17*d**6/2 - 97*d**5/2 + 715*d**4/6 - 315*d**3/2 + 235*d**2/2 - 109*d + 5. Factor y(l).
-5*(l - 47)*(l - 1)**4
Let m(w) be the second derivative of -2*w - 1/9*w**3 + 0*w**5 + 0*w**2 + 0 + 1/12*w**4 - 1/90*w**6. Let m(a) = 0. Calculate a.
-2