-1/2*a + 1 - 1/2*a**h.
-(a - 1)*(a + 2)/2
Factor 2*s**2 - 16*s + 46 - 3*s + 10*s - 25*s - 14*s.
2*(s - 23)*(s - 1)
Let v(z) = 28*z**2 + 32*z + 4. Let d(r) = 9*r**2 + 10*r + 1. Let y(p) = 16*d(p) - 5*v(p). Determine h, given that y(h) = 0.
-1, 1
Let j(l) = l**3 + 5*l**2 - 4*l - 5. Let c be j(-4). Let d be 890/6 + (c - 22). Factor 152/3*z - 208/3*z**4 - 16/3 + 482/3*z**3 + 32/3*z**5 - d*z**2.
2*(z - 2)**3*(4*z - 1)**2/3
Let j(q) be the first derivative of -q**4/30 - 44*q**3/45 - 121*q**2/15 - 101. Factor j(k).
-2*k*(k + 11)**2/15
Let u = 10 + -7. Suppose -4*v + 0*j = -5*j - 33, 3 = -v - j. Determine i so that 2*i**v - 8/9*i**u + 2/9 - 4/3*i = 0.
1/4, 1
Factor -2/13*x**4 + 0 - 14/13*x**2 + 6/13*x + 10/13*x**3.
-2*x*(x - 3)*(x - 1)**2/13
Let o(m) = m**3 - 2*m - 1. Let j(x) = -x**4 + 11*x**3 - 3*x**2 - 38*x + 25. Let u(r) = -j(r) + 3*o(r). Suppose u(h) = 0. Calculate h.
-2, 1, 2, 7
Let q(o) = o**4 - 36*o**3 - 72*o**2 + 107*o - 11. Let i(f) = 12*f**3 + 24*f**2 - 36*f + 4. Let r(c) = -11*i(c) - 4*q(c). Factor r(l).
-4*l*(l - 4)*(l - 1)*(l + 2)
Let i = -1720 - -1726. Let y(v) be the third derivative of 0*v + 1/120*v**5 + 1/140*v**7 + 3*v**2 + 1/48*v**4 + 0 - 1/48*v**i + 0*v**3. Factor y(o).
o*(o - 1)**2*(3*o + 1)/2
Let p(x) be the second derivative of -2*x**6/15 - 2*x**5 - 17*x**4/3 - 16*x**3/3 + 20*x + 3. Factor p(m).
-4*m*(m + 1)**2*(m + 8)
Let s(k) be the first derivative of -10*k**6/3 + 119*k**5 - 2455*k**4/2 + 7135*k**3/3 - 910*k**2 - 980*k - 900. Suppose s(c) = 0. What is c?
-1/4, 1, 14
Suppose y - 1 = -5. Let u be y/40*-22*2. Factor u*z**3 + 8/5*z**2 - 12/5*z**4 - 18/5*z**5 + 0 - 8/5*z.
-2*z*(z + 1)**2*(3*z - 2)**2/5
Let f be ((-19)/57*2)/(20/(-66)) + -2. Factor -1/5*y**2 + 3/5*y - f*y**4 + 2/5 - 3/5*y**3.
-(y - 1)*(y + 1)**2*(y + 2)/5
Factor 2/9*s**3 + 10/3*s - 50/9 + 2*s**2.
2*(s - 1)*(s + 5)**2/9
Let m = -113 + -46. Let t = m - -159. Factor 2/3*y + t + 2/3*y**2.
2*y*(y + 1)/3
Find x such that -25*x**2 + 32*x + 193*x**4 - 2*x - 188*x**4 - 10*x**3 = 0.
-2, 0, 1, 3
Let b = -30 + 28. Let z be (9/(-27) - b/(-2))/(-2). Factor -2/3*o + z*o**3 + 7/3*o**4 - 7/3*o**2 + 0.
o*(o - 1)*(o + 1)*(7*o + 2)/3
Let i(a) = a**5 + 5*a**3 - 14*a**2 - 6*a - 7. Let o(f) = f**3 - 2*f**2 - f - 1. Let u(m) = 5*i(m) - 35*o(m). Solve u(p) = 0 for p.
-1, 0, 1
Let n(y) = -y**3 + 8*y**2 + 9*y - 5. Let z be n(5). Let w be 1/20 - (z/(-20) - -5). Factor -w*i**2 + 2/5*i + 0 + 2/5*i**3.
2*i*(i - 1)**2/5
Let l(p) be the third derivative of -p**7/126 + p**6/24 + p**5/36 - 5*p**4/24 - 277*p**2. Factor l(t).
-5*t*(t - 3)*(t - 1)*(t + 1)/3
Let x(y) be the third derivative of 13*y**2 - 2*y - 1/6*y**4 + 0 + 0*y**3 - 1/15*y**5. Factor x(q).
-4*q*(q + 1)
Let v = -92 - -95. Find z such that -8*z**2 + 3 - 16*z - 3 - 4*z**v + 24*z**2 = 0.
0, 2
Let u = -68 + 72. Let 14*k + u*k**3 - 13 + 0*k**4 - 2*k**5 + 9 + k**4 - 16*k**2 + 3*k**4 = 0. Calculate k.
-2, 1
Let p(k) be the first derivative of -93/2*k**2 + 33/5*k**5 + 45/4*k**4 - 18*k - 2*k**6 - 25*k**3 + 12. Solve p(m) = 0 for m.
-1, -1/4, 2, 3
Let v(q) be the first derivative of 8/21*q**3 + 4/7*q + 9/7*q**2 - 14. Suppose v(l) = 0. What is l?
-2, -1/4
Suppose 3 = 2*p - z, 0 = 2*p - 4*z - 3 + 9. Determine q, given that -1265 + 12*q**2 + 15*q**p + 1265 = 0.
-4/5, 0
Solve -806*g - 261*g**2 - 4*g**3 + 114*g - 60*g**2 - 375*g**2 = 0.
-173, -1, 0
Let f(j) be the third derivative of 32*j**2 - 1/60*j**6 + 0 + 1/35*j**7 - 4/3*j**3 - j**4 - 11/30*j**5 + 0*j + 1/168*j**8. Factor f(a).
2*(a - 2)*(a + 1)**3*(a + 2)
Determine y, given that 39/7*y + 0 + 3/7*y**2 = 0.
-13, 0
Let x be 6/10 + 24/(-40). Let v(r) be the third derivative of 0 + 1/90*r**5 + x*r + 1/9*r**3 - 2*r**2 + 1/18*r**4. Solve v(k) = 0 for k.
-1
Let m(l) = l**5 + 29*l**4 + 44*l**3 - 4*l**2 - 45*l - 23. Let z(c) = c**5 + 59*c**4 + 89*c**3 - 7*c**2 - 90*c - 47. Let d(g) = -5*m(g) + 2*z(g). Factor d(n).
-3*(n - 1)*(n + 1)**3*(n + 7)
Let j be 22/(-2200)*7/(-14). Let m(s) be the third derivative of -1/100*s**5 - j*s**6 + 0*s + 0 - 14*s**2 + 0*s**4 + 0*s**3. Suppose m(r) = 0. What is r?
-1, 0
Factor 2/7*t**3 + 0 - 16/7*t + 2*t**2.
2*t*(t - 1)*(t + 8)/7
Let -18 - 20*n**2 + 19*n**2 + 238*n - 257*n = 0. Calculate n.
-18, -1
Suppose -5*v + 2*p = 4*p - 16, 3*v - 4*p = -6. Solve -17*c + 4 + 0*c - 7*c + 20*c**v = 0.
1/5, 1
Let n(t) be the second derivative of t**5/60 - t**4/3 + 8*t**3/3 + 7*t**2/2 - 12*t. Let k(w) be the first derivative of n(w). Factor k(i).
(i - 4)**2
Let u = -13 - -25. Factor -122*w**5 + 36*w + 11*w**4 - u - 2*w**4 - 33*w**2 + 119*w**5 + 3*w**3.
-3*(w - 2)*(w - 1)**3*(w + 2)
Let x = -8 + 12. Suppose r + 20 = 5*r - 3*q, -2*q + 20 = x*r. Factor -2*t**4 + 5/2*t**3 + 0 + 0*t + 1/2*t**r - t**2.
t**2*(t - 2)*(t - 1)**2/2
What is j in 4020*j - 1127*j**2 + 757*j**2 - 2*j**3 - 16928 - 16535*j - 4781*j = 0?
-92, -1
Suppose -2*p + 31 = -5*s, 3*s + 4 = -4*p + 1. Let o be (4/s)/((-48)/120). What is c in -2*c + 4 - o*c**2 + 2*c - 2*c = 0?
-2, 1
Suppose -409*v + 3*v**2 - 2*v**2 + 6 + 404*v = 0. Calculate v.
2, 3
Let h(q) = -65*q**2 + 170*q - 65. Let d(m) = 32*m**2 - 85*m + 33. Let z(c) = -5*d(c) - 3*h(c). Suppose z(t) = 0. Calculate t.
3/7, 2
Let b(x) be the third derivative of -x**8/504 - x**7/45 - x**6/18 - x**2. Solve b(y) = 0 for y.
-5, -2, 0
Let h(x) be the third derivative of -x**5/20 + x**4 - 492*x**2. Determine t, given that h(t) = 0.
0, 8
Let y(d) = -7*d**4 - 16*d**3 - 15*d**2. Let h(f) = 8*f**4 + 16*f**3 + 16*f**2. Let q(o) = -3*h(o) - 4*y(o). Solve q(t) = 0 for t.
-3, -1, 0
Let y(t) be the second derivative of -t**7/630 + t**6/120 + t**5/30 + t**4/3 + 13*t. Let r(i) be the third derivative of y(i). Factor r(b).
-2*(b - 2)*(2*b + 1)
Find c such that -60/7*c**4 - 36/7 + 39/7*c**3 + 222/7*c**2 + 87/7*c = 0.
-1, 1/4, 12/5
Let q(p) = p**2 - p. Let k = -75 - -72. Let r(g) = 7*g**2 + 61*g + 256. Let z(a) = k*q(a) + r(a). Factor z(x).
4*(x + 8)**2
Suppose -3*b + 21 = -3*t, -3*b - t - 4*t - 19 = 0. Let z = -20113 - -100569/5. Factor a - 1/5*a**b - z.
-(a - 4)*(a - 1)/5
Let j = -294 + 294. Let x(u) be the first derivative of 0*u + 0*u**2 + j*u**3 + 0*u**5 + 1/16*u**4 - 1/24*u**6 - 4. Factor x(l).
-l**3*(l - 1)*(l + 1)/4
Let c(m) be the second derivative of m**9/6048 - m**8/1680 - m**7/1680 + m**6/360 - 5*m**3/3 - 29*m. Let l(x) be the second derivative of c(x). Factor l(h).
h**2*(h - 2)*(h - 1)*(h + 1)/2
Let h(o) be the first derivative of 0*o - 34 + 0*o**2 - 2/17*o**5 - 7/34*o**4 - 1/51*o**6 - 2/17*o**3. Factor h(u).
-2*u**2*(u + 1)**2*(u + 3)/17
Let n(g) = 3*g - 12. Let i = 8 - 3. Let q be n(i). Factor 3*r**q + 4*r**2 - 1 + 3 + 5*r - 2*r**3.
(r + 1)**2*(r + 2)
Let o = 4 + -4. Let a(f) be the second derivative of o - 5/48*f**3 + 3/16*f**2 + 1/96*f**4 + 1/160*f**5 + 6*f. Solve a(s) = 0.
-3, 1
Let x(f) be the first derivative of -10 + 0*f + 2/7*f**3 + 2/35*f**5 + 3/14*f**4 + 1/7*f**2. Solve x(h) = 0.
-1, 0
Factor f**2 - 69*f - 2285 - 3160 - 261*f - f**2 - 5*f**2.
-5*(f + 33)**2
Let p(v) be the third derivative of -5*v**8/144 - 19*v**7/126 + v**6/12 + 12*v**2 + 4. Solve p(k) = 0 for k.
-3, 0, 2/7
Let p(z) be the first derivative of 17 + 10*z - 2/3*z**3 + 4*z**2. Let p(c) = 0. What is c?
-1, 5
Factor 2/9*h**2 + 8/3 - 16/9*h.
2*(h - 6)*(h - 2)/9
Suppose -2*p = 3*c + 1, p - 5*c + 4 + 3 = 0. Let u(j) = 4*j**2 + 12*j - 10. Let w(y) = y**3 + 4*y**2 + 13*y - 9. Let l(z) = p*w(z) + 3*u(z). Factor l(m).
-2*(m - 3)*(m - 1)*(m + 2)
Let b be 0*2/(-18)*(-2)/(-4). Let r(u) be the third derivative of 0*u**3 + 1/105*u**5 + 0 + 4*u**2 + b*u - 1/420*u**6 - 1/84*u**4. Factor r(v).
-2*v*(v - 1)**2/7
Let c = 65 - 61. Suppose 0 = -c*j + 7 + 1. Factor -4/7*o + 0 - 4/7*o**j.
-4*o*(o + 1)/7
Let s be (-13 - -13)/((15/3)/1). Factor s*k - 1/2 + 1/8*k**2.
(k - 2)*(k + 2)/8
Let i = -1093 + 1096. Let r(z) be the second derivative of 7*z + 1/24*z**4 - 1/6*z**i - 3/4*z**2 + 0. Factor r(g).
(g - 3)*(g + 1)/2
Let m(d) be the third derivative of d**7/35 - 3*d**6/40 + d**4/8 - 39*d**2. Factor m(a).
3*a*(a - 1)**2*(2*a + 1)
Let b = 91/18 + -601/126. Suppose -2/7*p**5 + 10/7*p**3 - b*p**4 - 16/7*p + 2/7*p**2 + 8/7 = 0. What is p?
-2, 1
Let j(a) = 9*a**2 - 17*a. Let y(n) = -6*n**2 - 8*n + 6*n**2 + 4*n**2. Let z(o) = 6*j(o) - 13*y(o). Factor z(g).
2*g*(g + 1)
Factor 2/7*g**2 - 48/7*g + 288/7.
2*(g - 12)**2/7
Let r(i) be the first deriva