)*(l + 5)
Let i(d) be the first derivative of -d**4/32 - d**3/6 - 3*d**2/16 + 759. Factor i(q).
-q*(q + 1)*(q + 3)/8
Let -21*c**2 + 5*c**2 + 6*c**3 + 8*c + 4*c**4 + 12 - 14*c**3 = 0. What is c?
-1, 1, 3
Let c(r) be the third derivative of r**8/2240 + r**7/140 + r**6/20 + r**5/5 + 7*r**4/24 + 4*r**2. Let o(b) be the second derivative of c(b). Solve o(u) = 0.
-2
Let k(l) be the second derivative of l**6/30 + 3*l**5/2 + 27*l**4/4 - 2*l**3/3 - 54*l**2 - 40*l + 1. Solve k(a) = 0 for a.
-27, -2, 1
Let t(b) = -b + 1. Let w(c) = -4*c**2 - 32*c - 108. Suppose 9*y = 4*y - 5. Let l(a) = y*w(a) - 8*t(a). Factor l(h).
4*(h + 5)**2
Suppose 0 = -29*a + 3682 - 3595. Suppose -4/7*p**a + 10/7*p**4 + 18/7 - 2/7*p**5 - 4*p**2 + 6/7*p = 0. Calculate p.
-1, 1, 3
Solve 10*k**3 - 129 - 54*k + 34*k**2 - 7*k**3 + 39 - 5*k**3 = 0 for k.
-1, 3, 15
Suppose 5*f - 5 = 0, 0 = b + 2*f - 11 - 1. Suppose 4*m + 0*m - b = -2*p, -5*m = -p - 16. Let 3 + 6 + m*k**4 - 9 - 3*k**2 = 0. What is k?
-1, 0, 1
Let d(m) = -20*m**4 - 105*m**3 + 130*m**2 + 120*m - 95. Let k(x) = -x**4 + x**2 + x + 1. Let l(n) = -d(n) + 15*k(n). Factor l(z).
5*(z - 1)**2*(z + 1)*(z + 22)
Suppose -7*g + 2*g + 3*r = 12, 0 = 4*r - 16. Suppose -p + 5*p = g. Let 16*t**3 - 101*t**2 + p*t**5 + 10*t**4 + 2*t**5 + 109*t**2 = 0. Calculate t.
-2, -1, 0
Determine h, given that -481*h**3 - 34*h + 632*h**2 - 156*h**2 + 42*h**4 - h**5 - 366*h + 391*h**2 - 27*h**2 = 0.
0, 1, 20
Suppose k = -4*k + 350. What is v in 0 - 3 - k*v**2 + 80*v**4 + 20*v**3 + 10*v**5 - 55*v - 7 + 25*v**5 = 0?
-1, -2/7, 1
Suppose 5*t - t = -12. Let y be (t/3)/(4/(-356)). What is a in -41*a - 486*a**3 + 2 - 10 + 54*a**2 + y*a = 0?
-1/3, 2/9
Let u(l) = l**3 + 6*l**2 - 4*l + 11. Let i be u(-5). Let t be 6/(-4) + ((-1116)/i)/(-9). What is y in -2/7*y - t*y**2 + 0 = 0?
-2/5, 0
Suppose -2 - 11/2*b + 11/2*b**3 + 3/4*b**2 + 5/4*b**4 = 0. Calculate b.
-4, -1, -2/5, 1
Let p(l) = -l**2 - 3*l + 44. Let r be p(5). Let b(x) be the second derivative of 5/48*x**r + 1/2*x**2 - 1/80*x**5 + 0 - 1/3*x**3 - 5*x. Solve b(i) = 0 for i.
1, 2
Suppose -12 = -8*m + 12. Suppose -5*l + m*l = -4*l. Factor 0*s**2 - 3/5*s**3 + 1/5*s**4 + l + 4/5*s.
s*(s - 2)**2*(s + 1)/5
Let i(g) = g**4 + 3*g**3 + 2*g**2 - 4*g + 2. Let w(v) = -v**4 - v**2 - 1. Let u(d) = i(d) + 2*w(d). Factor u(j).
-j*(j - 2)**2*(j + 1)
Let h = -2218 - -2221. Find a such that 0 + 3/8*a + 3/8*a**h + 3/4*a**2 = 0.
-1, 0
Suppose j - 4 = -k, -4*j + 6 = -0*k + 2*k. Let -22*h**2 - h**2 + 25*h + 8*h**2 - 5 - 5 + 5*h**4 - k*h**3 = 0. Calculate h.
-2, 1
Let m = 31363 - 31363. Factor -2/3*o**3 + 0*o + 2/3*o**5 + m*o**2 + 0 + 0*o**4.
2*o**3*(o - 1)*(o + 1)/3
Let s(r) = -3*r**3 + 45*r**2 + 4*r - 4. Let h(l) = -21*l**3 + 315*l**2 + 27*l - 27. Let f(b) = -4*h(b) + 27*s(b). Factor f(k).
3*k**2*(k - 15)
Factor -164/7 - 78/7*p + 2/7*p**2.
2*(p - 41)*(p + 2)/7
Let u(w) = w**2 + w. Let c(g) = 5*g**2 + 6*g + 6. Let y(q) = -q. Let d(v) = -c(v) + 5*y(v). Let z(l) = -3*d(l) - 12*u(l). Factor z(m).
3*(m + 1)*(m + 6)
Suppose 4 = 10*y - 46. Let q(o) be the first derivative of 52/15*o**3 + 0*o + 4/5*o**2 + 11/2*o**4 + 3*o**y + 2. Factor q(x).
x*(3*x + 2)*(5*x + 2)**2/5
Let a(k) = -7*k - 40. Let u be a(-6). Let y(z) = z**2 + z - 1. Let q be y(u). What is s in 0 + 0*s**3 - 4/5*s**4 + 2/5*s + 4/5*s**2 - 2/5*s**q = 0?
-1, 0, 1
Let o = 241 - 229. Let j be (-8)/o - 5672/(-156). Determine s, given that 204/13*s**2 + 2/13 + 64/13*s**4 + 34/13*s - 768/13*s**5 + j*s**3 = 0.
-1/4, -1/6, 1
Let m be (-112)/(-42) + -2 + 1. Let -3*k**3 + 2/3 - m*k - 16/3*k**2 = 0. Calculate k.
-1, 2/9
Let f be (0 + 3/9)*6. Let u(i) = i**3 - i**2 - i + 1. Let j be u(f). Factor 2*a**3 - 3*a**5 - 3*a**4 - 6*a**5 + 3*a**5 + a**j.
-3*a**3*(a + 1)*(2*a - 1)
Let p be (-47)/(-1269)*(-2)/(-2)*3. Let y(t) be the first derivative of -4/3*t**2 + p*t**3 - 6 + 16/3*t. Suppose y(a) = 0. What is a?
4
Let b(a) = 2*a**2 - 4*a - 2. Let n be b(-3). Suppose 0 = 8*o - o - n. Let 191*p**3 - 190*p**3 - 2*p**4 + 2*p**2 + p**o = 0. What is p?
-1, 0, 2
Let n(l) = 3*l**3 - 23*l**2 - 65*l - 54. Let m(d) = -2*d**3 + 11*d**2 + 32*d + 28. Let h(c) = -10*m(c) - 6*n(c). Suppose h(g) = 0. Calculate g.
-11, -2, -1
Let u(w) = 5*w**2 + 9*w + 6. Let h(m) = 4*m**2 - 10*m + 17 + 36*m + 10*m**2. Let b(j) = 6*h(j) - 17*u(j). Factor b(r).
-r*(r - 3)
Let w = -99 + 32. Let y = w + 83. Factor -y*c - 28/5*c**3 - 92/5*c**2 - 16/5.
-4*(c + 1)*(c + 2)*(7*c + 2)/5
Factor 45*c - 5*c**2 + 78*c - 28*c.
-5*c*(c - 19)
Let i = 2441 + -2417. Let n(h) be the first derivative of 32*h - 8/3*h**3 + 11*h**4 - i*h**2 - 24/5*h**5 + 1 + 2/3*h**6. Find j such that n(j) = 0.
-1, 1, 2
Let a(t) be the second derivative of t**4/32 - 9*t**3/4 + 243*t**2/4 - 493*t. Factor a(s).
3*(s - 18)**2/8
Let z be 1/2 + 10/4 + -3. Suppose w + 4 = 3*q, z = 3*q - 0*q - 5*w - 20. Determine v so that -1/5*v**3 + 1/5*v**5 + 4/5 - 7/5*v**2 + q*v + 3/5*v**4 = 0.
-2, -1, 1
Suppose 2*o + 13 = -11. Let j be (9/o)/(14/(-56)). Factor 0 + 0*i**j + 4/3*i**2 + 0*i - 1/3*i**4.
-i**2*(i - 2)*(i + 2)/3
Let c(h) be the second derivative of -h**6/216 - 13*h**5/540 - h**4/54 + 2*h**3/27 + 3*h**2 - 39*h. Let b(r) be the first derivative of c(r). Factor b(n).
-(n + 1)*(n + 2)*(5*n - 2)/9
Suppose 3*x + 0*x = -f + 29, -59 = -3*f - 2*x. Let j = f + -13. Factor 2*n**2 + 3*n - 6 - 4*n**3 + 5*n**3 - j*n**3 + 4*n**2.
-3*(n - 2)*(n - 1)*(n + 1)
Let n(a) = a**2 + 16*a + 44. Let j be n(-13). Let w be (-40)/100*(j/(-4) + 0). Let 5*m + 25/2 + w*m**2 = 0. What is m?
-5
Let q(r) be the third derivative of -r**8/2520 + r**7/315 + r**6/450 - r**5/45 - r**4/180 + r**3/9 - 25*r**2. Determine d so that q(d) = 0.
-1, 1, 5
Let c be -3 - (735/(-441) - (-4)/(-3)). Find r, given that -8*r**2 + c + 8*r - 1/2*r**5 + 2*r**4 + 0*r**3 = 0.
-2, 0, 2
Let n be 27/198*3/6. Let z = 103/220 - n. Factor 0 + 0*b + 2/15*b**2 - 2/15*b**5 + 2/5*b**4 - z*b**3.
-2*b**2*(b - 1)**3/15
Suppose -4*q = -4*b - 5*q + 171, 2*q = -b + 34. Let 22*i**2 - 60*i**4 + 10*i**2 - 1453*i + b*i**3 + 1437*i = 0. What is i?
-2/3, 0, 2/5, 1
Factor -1/5*a**4 - 4/5*a**2 - a**3 + 0 + 0*a.
-a**2*(a + 1)*(a + 4)/5
Let a(y) = y**2 + y. Let m(p) = 7*p**2 + 5*p - 8. Let j = -8 - -16. Let g(h) = h - 9. Let w be g(j). Let f(u) = w*m(u) + 5*a(u). Suppose f(o) = 0. Calculate o.
-2, 2
Let z(u) be the second derivative of -u**7/7980 + u**5/285 + 8*u**3/3 - 5*u. Let x(v) be the second derivative of z(v). Solve x(a) = 0 for a.
-2, 0, 2
Let j = 17/224 - -15/224. Let y(c) be the first derivative of 1/35*c**5 + 10 + 1/7*c**2 + 0*c + 0*c**4 - j*c**3. Solve y(w) = 0.
-2, 0, 1
Factor -50 - 6*c**2 + 4*c**2 - 50 + 20*c + 85*c - 3*c**2.
-5*(c - 20)*(c - 1)
Factor -15/4*x - 1/4*x**2 - 7/2.
-(x + 1)*(x + 14)/4
Let g(p) be the second derivative of 7*p**5/60 - 13*p**4/12 - 4*p**3/3 - 39*p**2/2 - 21*p. Let w(s) be the first derivative of g(s). Let w(f) = 0. What is f?
-2/7, 4
Let y(z) be the second derivative of -z**5/70 + z**4/6 + 8*z**3/21 - 118*z. What is m in y(m) = 0?
-1, 0, 8
Let t(o) = 2*o**3 + 12*o**2 + 4*o. Let n(x) = -x**2 - x - 1. Let q(u) = -6*n(u) - t(u). Suppose q(w) = 0. What is w?
-3, -1, 1
Let -8/5 - 34/5*x**3 - 6*x**2 + 72/5*x = 0. Calculate x.
-2, 2/17, 1
Let l(b) = 14*b**4 - 38*b**3 + 32*b**2 - 8*b - 2. Let p(t) = t**5 + 55*t**4 - 153*t**3 + 128*t**2 - 31*t - 9. Let a(k) = 9*l(k) - 2*p(k). Factor a(w).
-2*w*(w - 5)*(w - 1)**3
Let r(q) = q**2 + q. Let s(t) = 3*t**3 - 12*t**2 - 18*t + 24. Suppose -2*l + 3*w + 39 = -7*l, 2*l + 5*w = -27. Let z(c) = l*r(c) - s(c). Factor z(v).
-3*(v - 2)**2*(v + 2)
Let m(s) = -4*s**3 + 23*s**2 - 64*s + 27. Let c(j) = j**3 - j**2 + 2*j - 1. Let y(i) = -6*c(i) - 3*m(i). Factor y(a).
3*(a - 5)**2*(2*a - 1)
Let m = 30 - 32. Let q be (24/(-16))/(m*(-6)/(-16)). Suppose 0 + 1/2*f + 0*f**4 - f**3 + 1/2*f**5 + 0*f**q = 0. Calculate f.
-1, 0, 1
Let q(w) be the first derivative of -2*w**4 + 4*w**3/3 + 3*w**2/2 - 14*w + 15. Let l(g) = -g**3 - g**2 - 1. Let z(v) = -5*l(v) + q(v). What is p in z(p) = 0?
-1, 1, 3
Let b be -12 - 9825/(-630) - 4/24. Factor -12/7*g**2 - b*g - 2/7*g**3 - 16/7.
-2*(g + 2)**3/7
Let u(w) be the third derivative of -w**9/10080 + w**8/4480 + 2*w**4/3 + 18*w**2. Let h(l) be the second derivative of u(l). Factor h(f).
-3*f**3*(f - 1)/2
Let d(g) be the first derivative of -29 - 28/15*g**3 + 16/5*g - 24/5*g**2. Fac