 Let s(k) = -4*c(k) - f(k). Factor s(z).
2*(z + 1)**3*(z + 2)
Let h be (1 + 1)/((1/(-9))/((-228)/5643)). Suppose -h*a - 2/11 - 2/11*a**4 - 12/11*a**2 - 8/11*a**3 = 0. Calculate a.
-1
Let m(z) be the first derivative of -z**3/9 + 3*z**2 + 19*z/3 + 86. Let m(s) = 0. What is s?
-1, 19
Factor -288/5*f**2 + 48*f - 10.
-2*(12*f - 5)**2/5
Let a be 800/(-60)*6/(-4). Solve 2*f**2 + a*f + 12558 - 12558 = 0.
-10, 0
Suppose 22/3*w - 2/3*w**3 + 20/3*w**2 + 0 = 0. What is w?
-1, 0, 11
Let j(g) be the third derivative of g**8/40 - 31*g**7/350 - 47*g**6/100 - 31*g**5/100 + 13*g**4/20 + 4*g**3/5 + 452*g**2. What is a in j(a) = 0?
-1, -2/7, 1/2, 4
Factor -102*w**3 - 1 + 12*w**2 - 3*w**4 + 114*w**3 - 48*w + 1.
-3*w*(w - 4)*(w - 2)*(w + 2)
Let r(d) = -3*d + d**2 + 3*d + 3*d + 3*d - 7. Let p(x) = 2*x**2 + 11*x - 13. Let h(m) = -4*p(m) + 7*r(m). Let h(b) = 0. What is b?
-3, 1
Let y(q) = -22*q**2 + 418*q - 32. Let g(x) = -7*x**2 + 139*x - 10. Let h(w) = -16*g(w) + 5*y(w). Factor h(a).
2*a*(a - 67)
Let u(m) be the first derivative of -m**6/27 + 2*m**5/15 + 5*m**4/6 + 34*m**3/27 + 2*m**2/3 + 127. Solve u(j) = 0 for j.
-1, 0, 6
Let z(u) be the third derivative of 0*u + 1/9*u**3 + 1/54*u**4 + 0 + 26*u**2 - 1/270*u**5. Factor z(q).
-2*(q - 3)*(q + 1)/9
Let r(x) be the first derivative of -x**7/525 - x**6/300 + x**5/150 + x**4/60 + 6*x**2 + 6. Let s(n) be the second derivative of r(n). Factor s(m).
-2*m*(m - 1)*(m + 1)**2/5
Let c(s) be the third derivative of -49*s**2 + 0*s**3 + 1/45*s**5 - 1/180*s**6 - 1/36*s**4 + 0 + 0*s. Factor c(x).
-2*x*(x - 1)**2/3
Let a(y) be the first derivative of y**6/2 + 267*y**5/5 - 135*y**4/2 + 913. Let a(u) = 0. What is u?
-90, 0, 1
Let z(m) be the third derivative of 35*m**2 - 3/28*m**7 + 0*m + 5/6*m**4 + 0*m**3 + 19/24*m**6 + 0 - 11/6*m**5. Factor z(s).
-5*s*(s - 2)**2*(9*s - 2)/2
Let g(v) = v**3 + 6*v**2 + 6*v + 7. Let b be g(-5). Let k be ((-58)/2233)/(4/(-44)). Factor k*y**3 + 0 + 0*y + 0*y**b.
2*y**3/7
Let b = -25 - -48. Suppose -3*d - 4*w = -2*w - 5, 0 = -5*d + 4*w + b. Suppose 7/3*k**d - 19/3*k**2 + 4/3 + 8/3*k = 0. What is k?
-2/7, 1, 2
Factor -48*i + 98*i - 50*i**2 + 48*i**2.
-2*i*(i - 25)
Suppose -5*x + 7 = -l, 2*x + 5 = l + 6. Suppose -4*c = z + 3*z, 0 = -5*z + l*c. Factor 2/5*a**5 + 0 - 8/5*a**4 + 8/5*a**3 + 0*a + z*a**2.
2*a**3*(a - 2)**2/5
Suppose 5*f - 4 = 3*f, 2*l = f + 622. Let s = -1245/4 + l. Determine z, given that -s*z**2 + 1/4*z**4 + 1/2*z + 0 + 0*z**3 = 0.
-2, 0, 1
Let i be (-75)/(-2)*42/210. Solve 5/2*k**4 + 0 - i*k**2 + 0*k**3 - 5*k = 0 for k.
-1, 0, 2
Let p(b) be the first derivative of -b**4/6 - 4*b**3/3 + 5*b**2 + 16*b + 4. Let d(a) be the first derivative of p(a). Find u, given that d(u) = 0.
-5, 1
Let i(r) = r**2 - 36*r - 67. Let m(g) = 3*g**2 - 72*g - 135. Let u(y) = 14*i(y) - 6*m(y). Factor u(j).
-4*(j + 2)*(j + 16)
Let x = 2293 - 11459/5. Let n be (-2 + 0)*(-9)/10. Find y such that 3/5*y**5 + x*y**2 - 9/5*y - n*y**4 + 6/5*y**3 + 3/5 = 0.
-1, 1
Factor -1/3*c**3 - 8/3 - 7/3*c**2 - 14/3*c.
-(c + 1)*(c + 2)*(c + 4)/3
Suppose -2*z + 2/9*z**2 + 28/9 = 0. What is z?
2, 7
Suppose -15*i + 6*i = -18. What is r in 4*r**4 - i*r**2 + 258*r - 2 + 254*r - 503*r - 9*r**3 = 0?
-1, 1/4, 1, 2
Determine d, given that 2*d**4 + 11*d**3 - 17*d**3 - 3*d**5 + 7*d**4 = 0.
0, 1, 2
Let y = 632 - 1263/2. Solve y*x**3 + x**2 - 3/2*x + 0 = 0.
-3, 0, 1
Suppose a - 9 = -2*a, -2*a + 4 = -k. Suppose 0 = -k*l + 7*l - 15. Factor -4*z**4 - z**l - z + 0*z**3 + 4*z**2 + 2*z**3.
-z*(z - 1)*(z + 1)*(4*z - 1)
Determine a, given that 3*a**2 + 6*a**2 - 10*a - 5*a - 12*a**2 = 0.
-5, 0
Factor 3*f**3 + 7 + 21 - 9*f**2 - 19 - 3*f.
3*(f - 3)*(f - 1)*(f + 1)
Let o(z) be the third derivative of z**6/630 - z**5/168 + z**4/168 + 23*z**3/6 - 10*z**2. Let v(l) be the first derivative of o(l). Factor v(m).
(m - 1)*(4*m - 1)/7
Suppose -3*j = -5*j + 5*h, 0 = -3*h. Let t(y) be the third derivative of 0 + 1/6*y**3 + 1/36*y**4 + 3*y**2 + j*y - 1/180*y**5. Determine l so that t(l) = 0.
-1, 3
Solve -9/5*s + 2*s**2 - 1/5 = 0 for s.
-1/10, 1
Factor -2*q**2 + 13*q**2 + 14*q - 18 - 2*q**3 - 12*q + 7*q**2.
-2*(q - 9)*(q - 1)*(q + 1)
Let r(t) be the second derivative of t**6/12 - 39*t**5/40 - t**4/3 + 2*t - 23. Factor r(c).
c**2*(c - 8)*(5*c + 1)/2
Let d(p) be the second derivative of 0 + 3*p - 1/21*p**4 + 1/21*p**3 + 2/7*p**2 - 1/70*p**5. Factor d(t).
-2*(t - 1)*(t + 1)*(t + 2)/7
Factor 2/3*c**5 + 10*c**4 + 150*c - 380/3*c**2 + 20*c**3 - 54.
2*(c - 1)**3*(c + 9)**2/3
Let b(j) = 2*j**4 + 15*j**3 + 27*j**2 + 13*j - 6. Let i(t) = 4*t**4 + 31*t**3 + 55*t**2 + 25*t - 14. Let n(s) = 7*b(s) - 3*i(s). Factor n(g).
2*g*(g + 2)**3
Suppose -10*n**3 - 24*n**2 - 144 + 28*n**3 - 36*n**2 - 7*n**3 - 8*n**3 + 201*n = 0. What is n?
1, 3, 16
Factor 143*q + 255*q + 63*q + 93*q + 91*q + 3*q**2.
3*q*(q + 215)
Let l(j) be the first derivative of j**5/100 - 7*j**4/120 - j**3/5 - 9*j**2/2 + 11. Let c(x) be the second derivative of l(x). Factor c(o).
(o - 3)*(3*o + 2)/5
Let g(a) = -2*a**2 - 156*a - 3044. Let v(z) = 2. Let q(w) = 2*g(w) + 2*v(w). Factor q(n).
-4*(n + 39)**2
Let l(o) be the first derivative of o**3/3 - 39*o**2/4 + 19*o/2 + 369. Factor l(w).
(w - 19)*(2*w - 1)/2
Let a(b) be the first derivative of b**6/30 + b**5/5 + b**4/3 - 9*b - 2. Let k(d) be the first derivative of a(d). Let k(g) = 0. What is g?
-2, 0
Let d(k) be the second derivative of k**7/98 + 11*k**6/70 + 99*k**5/140 + 9*k**4/28 - 27*k**3/7 + 528*k + 1. Let d(g) = 0. Calculate g.
-6, -3, 0, 1
Let u(s) be the third derivative of -s**6/300 + 7*s**5/150 + 17*s**4/60 + 3*s**3/5 - 2*s**2 + 78. Find h, given that u(h) = 0.
-1, 9
Factor 3/4*x**3 - 3/2 - 3/4*x + 3/2*x**2.
3*(x - 1)*(x + 1)*(x + 2)/4
Let w(q) be the third derivative of -q**6/40 + 19*q**5/60 + 17*q**4/6 + 6*q**3 + 479*q**2. Factor w(t).
-(t - 9)*(t + 2)*(3*t + 2)
What is g in 132/5*g - 3/5*g**3 + 16 + 16/5*g**2 = 0?
-4, -2/3, 10
Determine s, given that 43*s**3 + 1120*s + 2*s**4 + 1188*s**2 + 13763 + 27709 + 53*s**3 + 540*s**2 + 12704*s = 0.
-12
Solve 52/5*g - 18/5*g**2 + 2/5*g**3 - 48/5 = 0.
2, 3, 4
Let j = -34 - -64. Let c be 3684/j - (-1)/5. Factor 2*p**2 + c*p - 123*p - 9*p**3.
-p**2*(9*p - 2)
Let u = 4987 + -4984. Find z such that -z**4 + 1/3*z**2 + 4/3*z**5 - 13/3*z**3 + 2/3 + u*z = 0.
-1, -1/4, 1, 2
Let h be 1436/(-960) + (-12)/(-8). Let a(d) be the third derivative of -1/3*d**3 + 5*d**2 - 1/12*d**4 + 1/120*d**5 + 0 + h*d**6 + 0*d. Factor a(z).
(z - 2)*(z + 1)*(z + 2)/2
Let a be (1/4)/(3/256). Let q = 19010/21 + -6262/7. Find c such that -a*c**4 + q*c - 4/3 + 128/3*c**3 - 32*c**2 = 0.
1/2
Let j(c) be the first derivative of c**6/2 - 9*c**5 + 21*c**4/2 + 296. Suppose j(v) = 0. Calculate v.
0, 1, 14
Let -4*k**5 - 152*k**4 - 128*k**2 + 2*k**5 - 304*k**3 + 125 + 932*k**3 - 285 + 638*k - 824*k**2 = 0. What is k?
-80, 1
Let q(t) be the second derivative of t**7/252 - t**6/180 - t**5/15 + t**4/9 + 4*t**3/9 - 4*t**2/3 - 126*t. Determine x so that q(x) = 0.
-2, 1, 2
Let s(x) be the third derivative of x**7/560 - x**6/160 - 13*x**5/160 - 5*x**4/32 - 377*x**2 - 2. Factor s(u).
3*u*(u - 5)*(u + 1)*(u + 2)/8
Let g(s) = 7*s**4 - 16*s**3 - 27*s**2 + 19*s + 20. Let n(u) = -13*u**4 + 32*u**3 + 53*u**2 - 37*u - 40. Let l(w) = -5*g(w) - 3*n(w). Solve l(z) = 0 for z.
-1, 1, 5
Let t(j) be the third derivative of j**7/1890 + j**6/540 + j**5/540 + 58*j**2. Determine l, given that t(l) = 0.
-1, 0
Let h(l) = 3*l - 1. Suppose -q - 2 = 0, 3 = -4*x + 3*q + 13. Let t be h(x). Factor -7*u**5 - t*u**3 + u - u + 9*u**4 + 0*u.
-u**3*(u - 1)*(7*u - 2)
Let r(i) be the third derivative of i**8/1176 - 2*i**7/735 - i**6/60 - 2*i**5/105 - 5*i**2 - 6. Factor r(m).
2*m**2*(m - 4)*(m + 1)**2/7
What is i in 72*i**2 - 500*i**3 + 252*i**3 + 245*i**3 - 432*i = 0?
0, 12
Let m(o) be the third derivative of 0 - 1/16*o**4 + 0*o**3 + 17*o**2 + 1/16*o**5 + 0*o - 3/160*o**6. Factor m(k).
-3*k*(k - 1)*(3*k - 2)/4
Let a(n) be the first derivative of n**6/21 - 6*n**5/35 - 3*n**4/7 + 16*n**3/21 - 148. Let a(z) = 0. Calculate z.
-2, 0, 1, 4
Let d(m) be the second derivative of -1/90*m**6 + 1/20*m**5 + 1/3*m**2 - 1/6*m**3 + 45*m + 0 - 1/36*m**4. Factor d(x).
-(x - 2)*(x - 1)**2*(x + 1)/3
Let h(j) be the third derivative of j**7/70 + 11*j**6/20 + 27*j**5/5 - 243*j**4/4 - 3645*j**3/2 + 56*j**2. Determine z, given that h(