u**4 + 5/16*u**3. Factor i(b).
3*(b - 2)*(b - 1)**2/8
Let j(y) be the first derivative of 92/3*y**3 + 4/5*y**5 - 31 + 8*y**4 + 48*y + 56*y**2. Factor j(a).
4*(a + 1)*(a + 2)**2*(a + 3)
Let d be 20/9 - (-16)/(-72). Factor 4*s - 12 - 2*s - 577*s**d + 579*s**2.
2*(s - 2)*(s + 3)
Let w(c) be the second derivative of c**6/30 + 106*c**5/5 - 71*c**4/2 - 212*c**3/3 + 425*c**2/2 + 526*c - 2. Factor w(j).
(j - 1)**2*(j + 1)*(j + 425)
Let u(y) be the first derivative of -22*y**2 - 15*y**3 + 0*y - 1/4*y**4 - 178. Factor u(w).
-w*(w + 1)*(w + 44)
Let c(r) = -r - 26. Let m be c(-28). Factor 16 - s - m*s**2 - 3*s - 7*s + 7*s.
-2*(s - 2)*(s + 4)
Find x, given that -14 + 2/3*x**3 + 22/3*x + 6*x**2 = 0.
-7, -3, 1
Let n be (-3)/5 + 612/170. Factor 19*w**2 + w**2 + 7*w**4 + 18*w**n - 14*w**5 + 15*w**5 + 8*w.
w*(w + 1)*(w + 2)**3
Suppose 12 = -4*x, -11*t + 70 = -13*t + 2*x. Let n be ((-46)/32)/(t/684). Factor 3/2*g - 21/2*g**2 - 105/4*g**4 + 0 + n*g**3 + 75/8*g**5.
3*g*(g - 1)**2*(5*g - 2)**2/8
Let f(w) be the second derivative of 8*w + 1 - 1/160*w**5 - 21/16*w**3 - 49/16*w**2 - 5/32*w**4. Find d, given that f(d) = 0.
-7, -1
Let d be ((-36632)/(-41211))/(28/135). Factor d*n + 2/7*n**2 + 4.
2*(n + 1)*(n + 14)/7
Factor 980985*s - 1575*s**3 - 132*s**4 - 3*s**5 - 980985*s - 2646*s**2.
-3*s**2*(s + 2)*(s + 21)**2
Let p(l) be the second derivative of l**6/1260 - 3*l**5/140 + 2*l**4/21 - 23*l**3/6 - 44*l. Let s(b) be the second derivative of p(b). Factor s(o).
2*(o - 8)*(o - 1)/7
Let h(v) be the second derivative of -v**4/120 + 113*v**3/60 + 57*v**2/10 - 51*v + 3. Factor h(d).
-(d - 114)*(d + 1)/10
Let -12*f - 49859 + 4*f**4 + 49859 - 4*f**2 + 12*f**3 = 0. Calculate f.
-3, -1, 0, 1
Let y(o) = o**2 + 5*o - 3. Let h be y(-6). Let z = -59 - -93. Factor -z*u**5 + 4*u**2 + 31*u**5 - 15*u**h + 12*u**4 + 2*u**2.
-3*u**2*(u - 2)*(u - 1)**2
Let x = -33567 + 33569. Factor -32/3 - 92/3*i + 140/3*i**x - 16/3*i**3.
-4*(i - 8)*(i - 1)*(4*i + 1)/3
Factor -44/5*h - 20*h**2 + 56/5.
-4*(h + 1)*(25*h - 14)/5
Factor 9/2*i**2 - 7/2*i**3 - 4 - 1/2*i**4 + 7/2*i.
-(i - 1)**2*(i + 1)*(i + 8)/2
Let v(o) be the first derivative of -106 - 1/2*o**4 - 40/3*o**3 - 324*o - 117*o**2. Factor v(n).
-2*(n + 2)*(n + 9)**2
Let o(u) be the first derivative of u**3/2 + 513*u**2/2 + 1023*u/2 - 2797. Solve o(j) = 0 for j.
-341, -1
Let p = 346 - 330. Suppose -18*f = 5*l - 14*f + p, -20 = 5*l + 5*f. Factor 1 - 1/4*g**2 + l*g.
-(g - 2)*(g + 2)/4
Let l(s) = 1520*s + 39522. Let w be l(-26). Factor 0 - 6*k + 21/2*k**w.
3*k*(7*k - 4)/2
Let a(p) = -p**3 - 15*p**2 - 16*p + 2. Let w be a(-14). Suppose w*n = 26*n + 8. Find d, given that 0*d**n + 0 + 2/9*d - 2/9*d**3 = 0.
-1, 0, 1
Let d(i) be the first derivative of 4*i**5/5 - 55*i**4 + 468*i**3 - 1458*i**2 + 1728*i + 1656. Factor d(x).
4*(x - 48)*(x - 3)**2*(x - 1)
Let c = -37 + 39. Let o be (6/9)/c + (-22)/(-6). Find t, given that 10*t**4 + 18*t**3 + 3*t + 9*t**o + 12*t**2 - 7*t**4 + 3*t**5 = 0.
-1, 0
Let 1212/5 - 27/5*h**2 + 5448/5*h = 0. What is h?
-2/9, 202
What is u in 244*u - 2220 - 2420 + 4*u**2 + 4394 - 2*u**2 = 0?
-123, 1
Let d = -599344/5 + 119876. Factor d + 68/5*l - 4/5*l**3 + 28/5*l**2.
-4*(l - 9)*(l + 1)**2/5
Let p = -827 - -873. Suppose p*q - 131 - 7 = 0. Suppose 0 - 15/4*d**q - 9*d**2 - 3*d = 0. What is d?
-2, -2/5, 0
Let r be (-11)/((-36)/(1656/1771)). Factor 0*f - 2/7 + r*f**2.
2*(f - 1)*(f + 1)/7
Let a = 181 + -120. Suppose 0 = 43*r - a - 68. Factor -3/4*w + 0*w**2 + 3/4*w**r + 0.
3*w*(w - 1)*(w + 1)/4
Let s(b) be the second derivative of b**6/15 + b**5/2 - 16*b**4/3 + 12*b**3 - 37*b + 21. Find u such that s(u) = 0.
-9, 0, 2
Let p(c) be the first derivative of c**6/150 + 3*c**5/25 - c**4/30 - 6*c**3/5 - 11*c**2/2 - c - 30. Let s(d) be the second derivative of p(d). Factor s(l).
4*(l - 1)*(l + 1)*(l + 9)/5
Suppose 4*o - 540 - 300 = 0. Suppose -48*x**3 - 4*x**5 - 12*x + 7 - 7 - 9*x**4 + 170*x**2 - 15*x**4 - o*x**2 = 0. Calculate x.
-3, -1, 0
Let q(m) = 3*m**3 + 14*m**2 - 23*m - 26. Let g(d) = 16*d**3 + 74*d**2 - 117*d - 131. Let k(n) = 4*g(n) - 22*q(n). Find h such that k(h) = 0.
-8, -1, 3
Suppose 0 = -2*b + 4*b - 6. Let v = -5161 - -7492. Solve -6320*i**2 - v*i**b + 378*i**5 - 320 + 5156*i**3 - 4320*i**4 + 5095*i**3 + 2320*i + 297*i**5 = 0.
2/5, 2/3, 4
Let w = -13 - -8. Let x be 1/(-15)*w*39. Factor x*f**3 + f + 11*f**2 + 8*f**4 + 7*f**5 - 3*f**5 + 4*f**4 - 5*f**2.
f*(f + 1)**2*(2*f + 1)**2
Let t(j) be the first derivative of -2*j**5/45 + 117*j**4 - 109512*j**3 + 38438712*j**2 - 8283. Factor t(v).
-2*v*(v - 702)**3/9
Let p be (-162)/135 + 330/275. Factor p - l**2 + 3/4*l + 1/4*l**3.
l*(l - 3)*(l - 1)/4
Let h(l) be the second derivative of l**7/28 + 121*l**6/20 + 5397*l**5/20 - 1921*l**4/4 - 3599*l**3/4 + 11163*l**2/4 + 656*l. Solve h(i) = 0 for i.
-61, -1, 1
Let v = -30149/11 - -2741. Suppose -20 = 3*g - 32. Solve 0*d - 2/11*d**g + v*d**5 + 0 - 4/11*d**3 + 0*d**2 = 0.
-1, 0, 2
Suppose 4*w - 17*w - 1690 = 0. Let i = 214 + w. Solve -60*m**2 - 52*m**4 - i*m**2 - 32*m - 12*m**3 - 8*m**4 - 172*m**3 = 0 for m.
-2, -2/3, -2/5, 0
What is i in 75*i**3 + 78*i**3 - 95*i**2 + 75*i**3 - 303*i**3 + 80*i**3 = 0?
0, 19
Determine a, given that 134/3*a**2 + 0 + 0*a - 23*a**3 + 1/3*a**4 = 0.
0, 2, 67
Let b be (-8)/(-80) - (-363)/120. Let y = b - 3. Factor 1/4*w**3 + 0 + y*w**2 - 1/8*w.
w*(w + 1)*(2*w - 1)/8
Determine b, given that 16/3 - 454/3*b**3 - 56*b - 484/3*b**2 - 60*b**4 - 26/3*b**5 = 0.
-2, -1, 1/13
Let c(z) be the first derivative of 4*z**3/15 + 67*z**2/5 + 26*z + 827. Factor c(v).
2*(v + 1)*(2*v + 65)/5
Suppose -114 = 7*b - 44. Let r be 10 + (b - (-24)/42). Factor 4/7*g**2 + 0 + r*g.
4*g*(g + 1)/7
Let x be -14*(-7 + 10)*2/(-4). Let c be ((-20)/105 + (-3)/x)/(-1). Solve 2 - 4/3*g**2 + c*g + 1/3*g**3 = 0.
-1, 2, 3
Suppose -38*a + 34*a = 49*a + 60*a. Let h be (-3)/12 + 18/8. Factor 5/2*z + a + 0*z**h - 5/2*z**3.
-5*z*(z - 1)*(z + 1)/2
Suppose 3*v + b - 3912 = 0, -3*v + 15*b = 14*b - 3918. Factor -8*i**2 + 649*i - v*i + 652*i.
-4*i*(2*i + 1)
Suppose -735*u = 739*u - 1479*u + 10. Factor -2809/3 - 1/3*b**u - 106/3*b.
-(b + 53)**2/3
Factor -1/5*r**4 + r**3 + 32/5*r**2 + 36/5*r + 0.
-r*(r - 9)*(r + 2)**2/5
Let y(a) = 125*a**3 - 575*a**2 + 1455*a. Let b(j) = 9*j**3 - 41*j**2 + 104*j. Let r(z) = 55*b(z) - 4*y(z). Factor r(i).
-5*i*(i - 5)*(i - 4)
Let w(o) be the first derivative of 11/18*o**3 + 57 - 11/6*o + 1/12*o**2 - 1/24*o**4. What is u in w(u) = 0?
-1, 1, 11
Let z(t) be the third derivative of -t**5/300 + 69*t**4/20 + 83*t**3/6 + 106*t**2. Solve z(i) = 0.
-1, 415
Suppose 0 = 5*u - p - 19, -11 = -3*u - u + 5*p. Factor -2*h**3 + 96*h - 8*h**3 + 3*h**u - 5*h**3 - 3*h**3.
3*h*(h - 4)**2*(h + 2)
Let g be 3/((-9)/(-7) - 50/175). Suppose -g*o + 20 = -2*o - 4*f, -o = f. Factor -10*u - 9*u**2 - 7/2*u**3 - 1/2*u**4 - o.
-(u + 1)*(u + 2)**3/2
Let m(u) = -1450*u**2 + 12320*u - 189728. Let c(d) = -175*d**2 + 1540*d - 23716. Let a(j) = 50*c(j) - 6*m(j). Let a(x) = 0. What is x?
154/5
Let y(u) = -u**3 + 15*u**2 - 24*u + 6. Let g(z) = 2*z**3 - 32*z**2 + 48*z - 15. Let v(s) = 2*g(s) + 5*y(s). Factor v(t).
-t*(t - 8)*(t - 3)
Let p(z) be the first derivative of 1/7*z**4 + 20/21*z**3 + 0*z**2 + 0*z + 131. Factor p(t).
4*t**2*(t + 5)/7
Let m = -107748 - -107753. Determine c so that -4*c - m*c**2 - 1/2*c**3 + 0 + 1/2*c**4 = 0.
-2, -1, 0, 4
Solve 216/5*d + 177/5*d**3 + 3/5*d**5 - 9*d**4 - 291/5*d**2 - 12 = 0.
1, 2, 10
Find b, given that -112/11*b**3 + 0 + 0*b**2 + 0*b - 2/11*b**4 = 0.
-56, 0
Suppose 0 = -5*m - 6*q + 3*q + 44, -3*q = -2*m - 16. Let d(r) be the first derivative of -35 + 8/3*r**3 + r**m + 0*r + 0*r**2. Suppose d(t) = 0. Calculate t.
-2, 0
Let k be (-55)/(-11) - (3 - (7 + 0)). Let 15*n + k*n + 72 - 111*n**2 - 114*n**2 + 227*n**2 = 0. Calculate n.
-6
Let z(a) be the third derivative of a**7/70 + a**6/40 - 59*a**5/20 + 111*a**4/8 - 27*a**3 + 672*a**2. What is i in z(i) = 0?
-9, 1, 6
Suppose -1438*g - 2159*g + 398592 = -829*g. Factor -304*b - g - 1588/9*b**2 - 152/9*b**3 - 4/9*b**4.
-4*(b + 1)**2*(b + 18)**2/9
Let n be 0/(27/(135/(-10))). Let t(k) be the first derivative of -1/2*k**6 + n*k**2 - k**3 + 3/4*k**4 + 0*k + 3/5*k**5 + 28. Factor t(d).
-3*d**2*(d - 1)**2*(d + 1)
Let a = -71086/13 - -100590174/18395. Let s = a + 3/283. What is v in s*v**2 + 36/5 + 12/5*v = 0?
-6
What 