b - 3)**2
Suppose 7*q = 3*m + 2, -58 = -5*m + 21*q - 17*q. Factor 3/2*d**2 + 12*d + m.
3*(d + 2)*(d + 6)/2
Let w = 6 - 0. Suppose 5*l + 6 = 26. What is g in -3*g - w - 24*g**2 + 12*g**3 - 10*g - 2*g**l + 33*g = 0?
1, 3
Let s(y) be the second derivative of -y**6/30 + y**4/12 + 9*y - 6. Suppose s(r) = 0. Calculate r.
-1, 0, 1
Suppose -14*s + 28*s**2 - 25*s - 4*s**3 - 17*s + 32 = 0. Calculate s.
1, 2, 4
Let g(b) = -b**2 + 23*b - 129. Let x be g(12). Factor 1/5*f**4 + 3/5*f + 1/5*f**2 - 2/5 - 3/5*f**x.
(f - 2)*(f - 1)**2*(f + 1)/5
Suppose 12*u**4 - 2*u**5 + 3 + 165*u**3 - u**5 - 177*u**3 - 3 = 0. Calculate u.
0, 2
Let q be 24/(-60) + 9519/60. Let t = q - 158. Let -3/4*d**2 + 3/4*d + 1/4*d**3 - t = 0. What is d?
1
Let h(t) be the third derivative of 5*t**8/336 - t**6/6 - t**5/6 + 5*t**4/8 + 5*t**3/3 - 103*t**2. Solve h(d) = 0.
-1, 1, 2
Let g(t) be the second derivative of -11*t - 1/225*t**6 - 1/30*t**4 + 4/15*t**2 + 0 + 4/45*t**3 - 2/75*t**5. Solve g(w) = 0 for w.
-2, -1, 1
Let b = 319 - 316. Let s(j) be the third derivative of 0 + 0*j**4 - 2*j**2 + 0*j + 0*j**b - 1/240*j**5. Factor s(d).
-d**2/4
Let f(z) = 4*z**2 - 8*z + 4. Let a(w) be the third derivative of -w**4/24 + w**3/6 + 22*w**2. Let o(d) = 16*a(d) - f(d). Factor o(v).
-4*(v - 1)*(v + 3)
Factor -8*i**4 - 1450 - 34*i + 28*i**2 + 1462 + 0*i**5 + 2*i**5.
2*(i - 3)*(i - 1)**3*(i + 2)
Suppose 7 + 18 = 5*v. Suppose -t = -6*t + 15, j - 17 = -v*t. What is i in 3*i**4 + 8 - 1 + 27*i**j - 2 + 15*i**3 + 1 + 21*i = 0?
-2, -1
Let x(h) = -5*h**2 + 76*h - 1367. Let o(f) = 7*f**2 - 77*f + 1366. Let z(b) = 2*o(b) + 3*x(b). Factor z(n).
-(n - 37)**2
Let l(y) be the first derivative of y**6/27 - 8*y**5/45 + y**4/3 - 8*y**3/27 + y**2/9 + 443. Suppose l(m) = 0. Calculate m.
0, 1
Let y(q) = -5*q**3 + 1537*q**2 + 133117*q + 3816347. Let t(h) = 3*h**3 - 768*h**2 - 66558*h - 1908174. Let r(z) = 11*t(z) + 6*y(z). Let r(p) = 0. What is p?
-86
Let d(h) = -h**3 + 88*h**2 - 169*h + 78. Let z(v) = -v**3 - 87*v**2 + 171*v - 77. Let r(s) = -3*d(s) - 2*z(s). What is k in r(k) = 0?
1, 16
Solve -15393*r**2 - 22*r**4 - 4*r**5 + 17*r - 8*r**3 + r - 5*r**3 - 9*r**3 + 15423*r**2 = 0 for r.
-3, -1/2, 0, 1
Let a(c) be the second derivative of -5*c**4/48 + 25*c**3/12 - 15*c**2 + 110*c. Factor a(x).
-5*(x - 6)*(x - 4)/4
Let -3*n**5 + 221779 + 24*n**4 - 221779 - 42*n**2 - 15*n**3 = 0. Calculate n.
-1, 0, 2, 7
Suppose s - 5 + 1 = 0. Let v be 10/s*72/45. Determine l so that 6*l**2 - l**3 - v*l + 3*l**3 - 4*l**3 = 0.
0, 1, 2
Let f(m) = m**2 - 21*m + 4. Let h be f(18). Let y = 52 + h. Factor -2/7*z**4 + 0 + 0*z**3 + 0*z + 2/7*z**y.
-2*z**2*(z - 1)*(z + 1)/7
Let a = 63 + -84. Let l(x) = -15*x**3 - 66*x**2 + 15*x + 24. Let k(d) = -3*d**3 - 13*d**2 + 3*d + 5. Let v(i) = a*k(i) + 4*l(i). Let v(z) = 0. Calculate z.
-3, -1, 1
Suppose 0 = -5*v + r - 1, 27*r = -2*v + 23*r + 4. Solve v + 0*u - 2/15*u**3 + 0*u**2 = 0.
0
Let f(c) be the first derivative of c**6/960 + c**5/160 + c**4/64 - 4*c**3/3 - 19. Let g(w) be the third derivative of f(w). Find v such that g(v) = 0.
-1
Let k(i) be the first derivative of -2*i**7/105 + i**6/30 + 4*i**5/15 - 2*i**4/3 - 18*i**2 + 17. Let v(g) be the second derivative of k(g). Factor v(b).
-4*b*(b - 2)*(b - 1)*(b + 2)
Let t(j) = 12*j**2 - 1275*j + 35013. Let f(s) = -3*s**2 + 319*s - 8753. Let r(c) = 21*f(c) + 5*t(c). Factor r(q).
-3*(q - 54)**2
Let a(f) = -13*f**4 + 22*f**3 - 20*f**2 + 5*f. Let i(p) = p**4 + p**3. Suppose -1 = -4*g + 3*g. Let x(o) = g*a(o) + 3*i(o). Factor x(c).
-5*c*(c - 1)**2*(2*c - 1)
Suppose -250*p**3 - 7812500 - 18750*p**2 - 625000*p - 5/4*p**4 = 0. Calculate p.
-50
Let l(m) be the third derivative of -m**8/168 + 3*m**7/7 - 12*m**6 + 144*m**5 - 20736*m**3 + 138*m**2. Factor l(f).
-2*(f - 12)**4*(f + 3)
Let m(g) be the second derivative of -2*g**6/15 + 12*g**5/25 + g**4/15 - 8*g**3/5 + 8*g**2/5 + 74*g - 3. What is d in m(d) = 0?
-1, 2/5, 1, 2
Let s(o) be the third derivative of -o**8/144 + o**7/70 + 2*o**6/45 + o**5/5 - 5*o**2. Let q(t) be the third derivative of s(t). Determine a so that q(a) = 0.
-2/7, 4/5
Let -52*y**2 + 5*y**3 + 3*y - 9*y**3 - 3*y + 6*y**3 = 0. What is y?
0, 26
Let v(o) = -o. Let p(l) = -l**2 + 7*l + 7. Let m be p(8). Let j(h) = -2*h**2 + 4*h. Let t(c) = m*j(c) - 6*v(c). Let t(x) = 0. What is x?
-1, 0
Suppose -4 = -2*q + 2. Factor 8*f**2 - 36*f**4 - 12*f**q - 6*f**2 - 2*f**2 - 27*f**5.
-3*f**3*(3*f + 2)**2
Let p(o) be the third derivative of -o**8/120 - 47*o**7/525 - 7*o**6/50 + 64*o**5/75 - 8*o**4/15 - 351*o**2. Find r, given that p(r) = 0.
-4, 0, 2/7, 1
Let w(j) be the first derivative of -9/4*j**4 + 6*j**2 + 3 + 5*j**3 - 12*j. Factor w(c).
-3*(c - 2)*(c + 1)*(3*c - 2)
Let w be 2/(3*4/32 + 315/56). Factor 0*g + 0 + 2/3*g**2 + w*g**3.
g**2*(g + 2)/3
Factor 126*m - 96*m**2 + 30*m**3 - 21*m**3 - 1232*m - 11*m**3 - 46*m.
-2*m*(m + 24)**2
Let y(p) = 3*p**4 + 28*p**3 + 47*p**2 + 22*p - 2. Let q(o) = -5*o**4 - 55*o**3 - 95*o**2 - 45*o + 5. Let c(x) = -2*q(x) - 5*y(x). Determine m so that c(m) = 0.
-4, -1, 0
Let d(g) = -104*g - 1248. Let v be d(-12). Let r(q) be the first derivative of -4/55*q**5 - 1/22*q**4 + v*q + 1 + 0*q**3 + 0*q**2 - 1/33*q**6. Factor r(y).
-2*y**3*(y + 1)**2/11
Suppose 2*p = -5*u + p + 16, -5*u + 4*p + 36 = 0. Suppose 0 = -j + m + 1 + u, 2*j = -m + 7. Factor x + 4*x**2 + 0*x**3 + x - j - 2*x**3.
-2*(x - 2)*(x - 1)*(x + 1)
Let g = -28/29 + 547/116. Factor -g*n - 3/2 - 3*n**2 - 3/4*n**3.
-3*(n + 1)**2*(n + 2)/4
Let d = -83 - -203. Let x = -350/3 + d. Factor 0 + x*w**2 + 2*w.
2*w*(5*w + 3)/3
Let l = -62/77 - -12/11. Let d(y) = y + 2. Let v be d(1). Solve -6/7 - l*c**2 + 10/7*c - 2/7*c**v = 0.
-3, 1
Let z(u) be the second derivative of u**6/6 - u**5/4 - 5*u**4/4 + 5*u**3/6 + 5*u**2 + u + 2. Factor z(m).
5*(m - 2)*(m - 1)*(m + 1)**2
Let w be 1*(-8 - (1 - 6)). Let f be w/(-1*27) + (-92)/(-144). Find c such that -1/4*c**3 + 0*c + f*c**2 - 1 = 0.
-1, 2
Let o(i) be the first derivative of 5/2*i**2 + 5/9*i**3 + 10/3*i - 40. Determine x, given that o(x) = 0.
-2, -1
Let p = -609 + 611. Factor -1/3*d**3 - 4/3*d**p + 1/3*d + 4/3.
-(d - 1)*(d + 1)*(d + 4)/3
Factor 10*p - 66*p - 71*p + 37*p + 3*p**2 + 675.
3*(p - 15)**2
Factor 0 - 37/7*h - 1/7*h**2.
-h*(h + 37)/7
Let -18 + 121*y + 121*y - 253*y - y**2 = 0. Calculate y.
-9, -2
Factor -40/7 - 2/7*m**2 - 6*m.
-2*(m + 1)*(m + 20)/7
Let w(j) be the first derivative of 2*j**6/3 - 28*j**5 + 355*j**4 - 1300*j**3/3 - 13520*j**2 - 35152*j + 178. Find m such that w(m) = 0.
-2, 13
Let f(s) = -5*s**2 + 5. Let q(r) = -10*r**2 + 5*r + 1. Let n(x) = 5*x**2 - 2*x - 1. Let h(j) = 7*n(j) + 3*q(j). Let u(c) = -4*f(c) - 5*h(c). Factor u(k).
-5*k*(k + 1)
Let b(v) be the third derivative of 4*v**5/15 - 53*v**4/6 - 28*v**3 + 179*v**2. Factor b(k).
4*(k - 14)*(4*k + 3)
Let p(v) be the third derivative of 2/105*v**5 - 8/735*v**7 + 0 + 4/21*v**3 + 5/42*v**4 + 0*v - 1/588*v**8 + 21*v**2 - 2/105*v**6. Let p(z) = 0. Calculate z.
-2, -1, 1
Let m = -5566 - -133619/24. Let q = -1/8 + m. Let -q*i**2 + 1/3*i**5 - 4/3*i**4 + 0 + 1/3*i + 2*i**3 = 0. What is i?
0, 1
Let m(o) be the second derivative of -2*o + 216/5*o**2 + 12/5*o**3 + 1/20*o**4 - 23. Factor m(n).
3*(n + 12)**2/5
Suppose 5 = -2*n + n + 3*w, 0 = 2*n - 5*w + 7. Suppose n*a + a = 0. Find y, given that -5*y**2 + 3*y**2 - 1 + 3 + a*y**2 = 0.
-1, 1
Determine c, given that 12/5 - 183/5*c**2 + 81/5*c**5 - 12/5*c - 69/5*c**3 + 171/5*c**4 = 0.
-2, -1, -1/3, 2/9, 1
Let y = -35 + 38. Let u(m) be the third derivative of 0 + 0*m**4 + 0*m + 0*m**y - 1/120*m**5 - 2*m**2. Solve u(f) = 0 for f.
0
Let f = -1165 + 1172. Let h(p) be the second derivative of -4/21*p**3 + 0 + 2/21*p**4 - f*p + 1/7*p**2. Find v such that h(v) = 0.
1/2
Let b = 19388/15 + -1292. Let r = 278/579 - -36/193. Determine w, given that -b*w + 0 - r*w**3 + 32/15*w**2 - 14/15*w**4 = 0.
-2, 0, 2/7, 1
Let h = 138 + -132. Let u be (-21)/70*(-8)/h. Factor -16/5*k**3 + 32/5*k**4 - u*k - 14/5*k**2 + 0.
2*k*(k - 1)*(4*k + 1)**2/5
Let c(v) = -v**3 - v**2 + 2*v + 2. Let u(x) = 18*x**2 - 36*x - 4. Let b(z) = 2*c(z) + u(z). Factor b(j).
-2*j*(j - 4)**2
Determine u so that 40*u - 28/3*u**2 - 48 + 2/3*u**3 = 0.
2, 6
Suppose -5 - 15 = -10*j. Let q(s) be the first derivative of 1/8*s**4 - 1/4*s**j - 2 + 0*s - 1/6*s**3 + 1/10*s**5. Factor q(u).
u*(u - 1)*(u +