*(j + 13)
Let m = -153591/104 + 11859/8. Factor -24/13*c + m + 2/13*c**2.
2*(c - 6)**2/13
Let j(k) be the first derivative of -5 + 1/8*k**2 - 1/24*k**3 + 1/40*k**5 - 1/16*k**4 + 0*k. Factor j(r).
r*(r - 2)*(r - 1)*(r + 1)/8
Let c = -195 - -281. Suppose -4 - c = -30*b. Factor -1/3*i**4 + 0 - i**2 + 1/3*i + i**b.
-i*(i - 1)**3/3
Let 12/5*b**3 - 16/5*b + 0 + 4/5*b**4 + 0*b**2 = 0. Calculate b.
-2, 0, 1
Let x(k) = -k**2 + 3*k + 6. Let j be x(4). Factor -18*g**j - 3 - 4*g + 28*g**2 + 3.
2*g*(5*g - 2)
Let w(c) be the third derivative of 5/12*c**4 + 5/14*c**7 + 0*c - 4/3*c**5 + 2*c**2 + 5/6*c**3 + 15/28*c**8 - 19/12*c**6 + 2. Let w(h) = 0. Calculate h.
-1, -1/3, 1/4, 1
Determine b so that -6*b**2 - 32*b + 23*b**2 + 29*b**3 - 61 + 45 + 19*b**2 - 20*b**4 + 3*b**3 = 0.
-1, -2/5, 1, 2
Let s = 13 - 7. Let h be 3 - -2 - 12/s. Solve 70*l**2 + 36*l**h + 133*l**2 + 3*l**4 + 243 + 324*l - 41*l**2 = 0 for l.
-3
Let q(r) = 3*r - 52. Let s be q(18). Factor -164*f - 184*f + 335*f - f**s.
-f*(f + 13)
Solve -12656/3*k + 3136/3 + 449/3*k**2 - 4/3*k**3 = 0.
1/4, 56
Factor -6/5*d**3 - 1/5*d**4 + 0 - 12/5*d**2 - 8/5*d.
-d*(d + 2)**3/5
Let o = 216 + -213. Suppose 34*c = 27*c + 35. Solve -3/4*g**2 - 1/4*g**o + 1/2*g**c - 1/4*g + 3/4*g**4 + 0 = 0 for g.
-1, -1/2, 0, 1
Let x(m) = -7*m**2 + 68*m + 5. Let b(k) = 3*k**2 - 34*k - 2. Let n(g) = -5*b(g) - 2*x(g). Factor n(w).
-w*(w - 34)
Let f = -1 + 3. Suppose -4*i + 10 = -2*o - 9*i, -4 = 4*o + 2*i. Factor -1 + 0 - 1 - p + p**f + o.
(p - 2)*(p + 1)
Factor 2*l**5 - 486 + 66*l**2 + 6*l**2 + 181 - 12*l**4 - 4*l**5 + 197 + 54*l - 4*l**3.
-2*(l - 2)*(l - 1)*(l + 3)**3
Suppose 5*z - 13 + 3 = 0. Factor -9*l**2 + 9*l**5 + 22*l**4 + 0*l**3 - 8*l - l**4 - 2*l**3 - 11*l**z.
l*(l - 1)*(l + 2)*(3*l + 2)**2
Factor -4 - 1/2*o**2 + 1/2*o**3 - 5*o.
(o - 4)*(o + 1)*(o + 2)/2
Let h(f) be the second derivative of 0 - 5/12*f**4 + 5/6*f**2 - 1/9*f**6 - 5/12*f**5 + 5/18*f**3 - 16*f. Determine c, given that h(c) = 0.
-1, 1/2
Let d = -40 + 84. Suppose 3*q = -8*q + d. Determine s, given that 1/3*s**q + 0*s**3 - 2/3*s**2 + 1/3 + 0*s = 0.
-1, 1
Let k(h) = -126*h + 380. Let l be k(3). Solve -l*y**3 + y**2 + 4/3*y**4 + 0 - 1/6*y = 0.
0, 1/2
Suppose 4*q - 2 = -2*z + 12, -q - 3*z = -11. Factor 588*k**q - 9*k - 23*k - 8 - 570*k**2.
2*(k - 2)*(9*k + 2)
Let c(u) be the second derivative of 1/120*u**6 + 0 + 1/12*u**4 + 0*u**2 + 0*u**3 + 1/20*u**5 + 10*u. Factor c(b).
b**2*(b + 2)**2/4
Let v(x) be the second derivative of -8*x**5/5 - 10*x**4/3 + 26*x**3 - 18*x**2 - 18*x. Determine i so that v(i) = 0.
-3, 1/4, 3/2
Let a(g) be the third derivative of -g**7/1260 + g**6/60 - g**5/12 + g**4/8 - 13*g**2. Let z(v) be the second derivative of a(v). Let z(y) = 0. What is y?
1, 5
Suppose t = -17 + 19. Let h be -4*(t/3)/((-44)/33). Factor 2/7*q - 2/7 - 2/7*q**3 + 2/7*q**h.
-2*(q - 1)**2*(q + 1)/7
Suppose -j + 2 = -13. Let w be 12/j*5/6. Factor 0 + 0*s**3 + 0*s + 4/9*s**5 - w*s**4 + 2/9*s**2.
2*s**2*(s - 1)**2*(2*s + 1)/9
Let t(s) be the second derivative of -4/3*s**3 - 25/27*s**4 + 0 - 3/10*s**5 - 21*s - 1/27*s**6 - 8/9*s**2. Let t(n) = 0. Calculate n.
-2, -1, -2/5
Let x(k) be the third derivative of k**8/84 - 2*k**7/21 - 7*k**6/15 - 2*k**5/15 + 13*k**4/6 + 14*k**3/3 - 36*k**2 + 2*k. Factor x(t).
4*(t - 7)*(t - 1)*(t + 1)**3
Let u(m) = 7*m**5 - 10*m**4 + 6*m**3 + 10*m**2 - 3*m. Let j(g) = g**5 + g. Let b(r) = -5*j(r) + u(r). Factor b(h).
2*h*(h - 4)*(h - 1)**2*(h + 1)
Let u(c) be the third derivative of 5*c**8/336 + c**7/21 - c**6/8 - 2*c**5/3 - 5*c**4/6 - 5*c**2. Solve u(i) = 0 for i.
-2, -1, 0, 2
Let v = -25 - -34. Suppose 2*m + 5 = v. Factor 13*o**2 - 21*o**m + 4*o**3 - 4*o - 8*o**3.
-4*o*(o + 1)**2
Let q(a) be the first derivative of a**4/22 + 8*a**3/33 + 3*a**2/11 - 225. Find r, given that q(r) = 0.
-3, -1, 0
Let a = -166/11 - -11963/792. Let u(g) be the third derivative of 5*g**2 - 1/9*g**3 + 1/90*g**5 + 0*g + 0 - 1/360*g**6 + a*g**4. Factor u(l).
-(l - 2)*(l - 1)*(l + 1)/3
Factor 2/7*f**3 - 26/7*f - 24/7 + 0*f**2.
2*(f - 4)*(f + 1)*(f + 3)/7
Determine g so that 0*g + 2/5*g**2 - 2/5 = 0.
-1, 1
Let -1/5*t**4 - 1/5*t**2 + 2/5 - 3/5*t + 3/5*t**3 = 0. What is t?
-1, 1, 2
Let l be (2/4)/(1/6). Let s(b) = -57*b - 508. Let m be s(-9). Find d such that -3/4*d**2 + 0 + 3/4*d**4 - 15/4*d**l + 9/4*d**m + 3/2*d = 0.
-1, 0, 2/3, 1
Suppose 0 = -17*p + 21*p + z - 24, 5*p - 41 = -4*z. Let l(d) be the first derivative of 0*d**3 + p + 4/9*d - 1/18*d**4 + 1/3*d**2. Factor l(m).
-2*(m - 2)*(m + 1)**2/9
Factor 1/10*d**4 - 7/10*d**3 + 13/10*d**2 - 9/5 + 3/10*d.
(d - 3)**2*(d - 2)*(d + 1)/10
Let 5 - 1/4*l**2 + 19/4*l = 0. Calculate l.
-1, 20
Let g(b) = -15*b**2 - 32*b + 2. Let r(i) = 14*i**2 + 30*i - 1. Let p(u) = -5*g(u) - 6*r(u). Find f, given that p(f) = 0.
-2, -2/9
Let m(x) = -x**2 + 7*x - 10. Suppose -2*p = -2 - 6. Let j be m(p). Find s, given that j*s**4 - 17*s**2 + 0*s**4 - 4 + 2*s**3 + 11*s**2 - 10*s = 0.
-1, 2
Let i(c) be the third derivative of 9*c**5/160 - c**4/32 + 61*c**2. Factor i(v).
3*v*(9*v - 2)/8
Suppose 0 = -705*n + 929*n. Let 7/6*h**3 + 0*h**2 + n + 1/2*h**4 - 2/3*h = 0. What is h?
-2, -1, 0, 2/3
Let m be ((-6)/(-30))/(13/((-195)/(-6))). Let h(x) be the first derivative of 1/2*x**2 + 0*x + m*x**3 + 1/8*x**4 - 11. Let h(z) = 0. Calculate z.
-2, -1, 0
Suppose -2 = -a - 10. Let w(x) = -x**3 - 7*x**2 + 6*x - 10. Let n be w(a). Factor 3*j**2 + j**2 + 2*j**2 - n*j - 4*j**2.
2*j*(j - 3)
Let a(y) be the third derivative of y**8/336 + 13*y**7/735 - 43*y**6/840 + y**5/42 - 107*y**2. Suppose a(c) = 0. What is c?
-5, 0, 2/7, 1
Suppose g - 2*g - 13 = 0. Let j = g + 32. Let -27*p**2 - 6 - j*p - 2*p**4 + 16*p - p**4 - 18*p - 15*p**3 = 0. Calculate p.
-2, -1
Let t(s) be the third derivative of 0*s + 0*s**3 - 1/16*s**4 - 1/40*s**5 + 0 - s**2. Find k such that t(k) = 0.
-1, 0
Let z(r) be the second derivative of -r**6/1080 + r**5/180 + r**4/9 + 29*r**3/6 - 39*r. Let f(p) be the second derivative of z(p). Solve f(y) = 0 for y.
-2, 4
Solve 19*h**3 + 27789*h**2 + h**4 - 27702*h**2 + h + 116*h = 0.
-13, -3, 0
Let j = 1/9 + 4/45. Let n be 1/(-5) + (7/(-2) - (-215)/50). Factor -j*x**2 - 2/5 - n*x.
-(x + 1)*(x + 2)/5
Let p(n) be the first derivative of -n**5/60 + 9*n**2/2 + 6. Let y(x) be the second derivative of p(x). Factor y(a).
-a**2
Let k(n) be the second derivative of -2*n + 1/36*n**4 + 7/2*n**2 + 1/180*n**5 + 0 + 0*n**3. Let u(d) be the first derivative of k(d). Factor u(o).
o*(o + 2)/3
Let y(q) be the first derivative of 9*q**4/16 + 2*q**3 - 15*q**2/2 - 12*q + 163. Factor y(b).
3*(b - 2)*(b + 4)*(3*b + 2)/4
Let f be (-5)/(-35) + 5056/2240. Factor 0 - f*y - 3/5*y**2.
-3*y*(y + 4)/5
Factor -107 - 560*x - 2*x**5 - 86*x**3 - 53 - 482*x**2 + 21*x**4 + 13*x**4 - 40.
-2*(x - 10)**2*(x + 1)**3
Suppose -4*y + 60 = 21*y - 10*y. Determine c so that 4/5 - 2/15*c**3 + 14/15*c**2 + 26/15*c - 2/15*c**y = 0.
-2, -1, 3
Let z(p) be the third derivative of p**7/945 + p**6/270 - 2*p**5/135 - p**4/54 + p**3/9 + 108*p**2. Factor z(f).
2*(f - 1)**2*(f + 1)*(f + 3)/9
Let o = 20 - 15. Suppose -3 = 3*w, -g + 4*w - 52 = -o*g. Let 2*z**2 + 8*z + z - g*z**2 + 11*z - 8 = 0. What is z?
2/3, 1
Let p = 170 - 156. Suppose 36 = -2*v + p*v. Factor 8/3*i**4 + 0 - 2/3*i**5 + 8/3*i**2 - 2/3*i - 4*i**v.
-2*i*(i - 1)**4/3
Let h = 42 - 33. Let a = 29/3 - h. Factor -a*j - 1/6*j**2 + 5/6.
-(j - 1)*(j + 5)/6
Factor 1/8*k**5 + 0*k + 3*k**3 + 0 + 0*k**2 + 5/4*k**4.
k**3*(k + 4)*(k + 6)/8
Let o(r) be the first derivative of 2/3*r**2 + 5/36*r**4 - 3 - 4/9*r**3 - 1/60*r**5 + 3*r. Let p(a) be the first derivative of o(a). Factor p(h).
-(h - 2)**2*(h - 1)/3
Let a(w) be the third derivative of w**5/45 - 19*w**4/9 + 74*w**3/9 - 637*w**2. Factor a(y).
4*(y - 37)*(y - 1)/3
Let b = -682/15 - -691/15. Factor -b*a**3 + 0*a + 1/5*a**4 + 2/5*a**2 + 0.
a**2*(a - 2)*(a - 1)/5
Let 4/3*y**2 + 0 + 1/3*y**5 - y**4 + 0*y + 0*y**3 = 0. Calculate y.
-1, 0, 2
Let v(b) = 3*b + 27. Let y = -52 + 43. Let u be v(y). Factor 1/7*q**2 + 3/7*q**4 + 3/7*q**3 + 0 + 1/7*q**5 + u*q.
q**2*(q + 1)**3/7
Let l = 160 - 155. Let p(v) be the first derivative of 0*v**3 + 0*v - l + 1/2*v**4 - v**2. Solve p(j) = 0.
-1, 0, 1
Let i(p) = p**4 - p**3 - 2*p**2 - p - 1. Let v(q) = q**4 - 21*q**3 + 38*q**2 + 24*q - 36. Let a(u) = 4*i(u) + v(u). Suppose a(t) = 0. What is t?
-1, 2
Let