3*y + 3 = t, 2*l = 3*y + 12. Factor -s**2 + 7*s**2 - 24 - 12*s + 3*s**3 - 2*s**l + 2*s**3.
3*(s - 2)*(s + 2)**2
Let l(b) = b**3 - b**2 + b. Let m be l(1). Let g(f) = 3*f**3 - 2*f**2 + 2*f - 1. Let d be g(m). Find c, given that 4/3*c**3 + 0*c + 0 + 2/3*c**4 + 2/3*c**d = 0.
-1, 0
Let n be (17/102)/((-4)/(-6)). Let x = -247/4 + 62. Find m, given that n*m**2 + 0*m - x = 0.
-1, 1
Let z(c) be the first derivative of 2/7*c - 3 + 2/7*c**2 + 2/21*c**3. Determine w so that z(w) = 0.
-1
Let v = 578 - 575. Factor 4/13*m**2 + 0 - 2/13*m - 2/13*m**v.
-2*m*(m - 1)**2/13
Let d(f) be the first derivative of 0*f**3 - f + 3/2*f**2 + 1 - 1/4*f**4. Let y(a) be the first derivative of d(a). Let y(s) = 0. Calculate s.
-1, 1
Let r(u) be the second derivative of -u**6/50 + 3*u**5/100 + u**4/10 + 11*u. Suppose r(n) = 0. What is n?
-1, 0, 2
Let o(w) = w + 3. Let y be o(-3). Let f(a) be the second derivative of 1/2*a**2 + 2*a - 1/3*a**3 + y + 1/12*a**4. Factor f(r).
(r - 1)**2
Let 2/7*m**4 + 10/7*m**3 + 18/7*m**2 + 4/7 + 2*m = 0. What is m?
-2, -1
Let s(x) be the second derivative of 3*x**5/20 + 3*x**4/4 + x**3 - 40*x. Suppose s(k) = 0. What is k?
-2, -1, 0
Suppose -3*a + 11*a - 16 = 0. Let 8/7*k - 12/7*k**a + 8/7*k**3 - 2/7 - 2/7*k**4 = 0. Calculate k.
1
Let q(h) be the third derivative of -h**6/24 - h**5/6 + 5*h**4/24 + 5*h**3/3 - 14*h**2. Factor q(s).
-5*(s - 1)*(s + 1)*(s + 2)
Let p be 189/15 - (-4)/10. Let y be 18/4*p/39. Let 1/2*l**5 - l**2 + y*l**4 - 1/2 - 3/2*l + l**3 = 0. What is l?
-1, 1
Suppose 0*f - 2*f + 4 = 0. Factor -5/4*t - 1/4*t**3 - t**f - 1/2.
-(t + 1)**2*(t + 2)/4
Let s(u) be the second derivative of 7*u**6/12 - 17*u**5/16 + 5*u**4/48 + 5*u**3/12 - 22*u. Solve s(m) = 0 for m.
-2/7, 0, 1/2, 1
Factor 2/7*m**3 + 2/7*m**4 - 2/7*m - 2/7*m**2 + 0.
2*m*(m - 1)*(m + 1)**2/7
Let t be (-12)/54 - (-350)/90. Factor -1/3*p**2 - 4/3*p**5 - t*p**4 + 1/3*p + 0 - 3*p**3.
-p*(p + 1)**3*(4*p - 1)/3
Let t(s) be the third derivative of s**8/2016 - s**7/1260 - s**6/240 + s**5/72 - s**4/72 - 18*s**2. Factor t(r).
r*(r - 1)**3*(r + 2)/6
What is a in 0 + a**2 + 1/3*a**5 - 2/3*a + 1/3*a**3 - a**4 = 0?
-1, 0, 1, 2
Let m(t) be the second derivative of t**7/2520 - t**5/120 - t**4/36 - 5*t**3/6 - 4*t. Let p(i) be the second derivative of m(i). Factor p(h).
(h - 2)*(h + 1)**2/3
Suppose 31*o - 6*o - 50 = 0. Factor -8/5*d**3 - 2/5*d**4 + 0 - 4/5*d - 2*d**o.
-2*d*(d + 1)**2*(d + 2)/5
Solve 0 - 10/9*o**2 + 4/3*o + 2/9*o**3 = 0.
0, 2, 3
Let f(k) be the third derivative of k**6/200 - k**5/50 + k**2 - 7. Suppose f(z) = 0. Calculate z.
0, 2
Factor 14/15*n**3 + 2/15*n**5 + 0 + 0*n - 2/3*n**4 - 2/5*n**2.
2*n**2*(n - 3)*(n - 1)**2/15
Let s(w) be the first derivative of -27*w**4/4 + 7*w**3 + 3*w**2 + 48. Determine z so that s(z) = 0.
-2/9, 0, 1
Let n(b) be the third derivative of -b**6/240 + b**5/60 - b**2. Factor n(t).
-t**2*(t - 2)/2
What is t in -3/5 - 2/5*t + 1/5*t**2 = 0?
-1, 3
Let a be 8/90*12*9/12. Let -2/5*n - a + 2/5*n**2 = 0. Calculate n.
-1, 2
Let n = 13/41 - 2416/7749. Let k(y) be the second derivative of 1/45*y**6 - 1/27*y**4 - 1/9*y**3 + 0 + 1/45*y**5 + y + n*y**7 - 1/9*y**2. Factor k(m).
2*(m - 1)*(m + 1)**4/9
Let h be (-18)/36 - (-4)/2. Find c such that 3*c + 0 + h*c**2 = 0.
-2, 0
Factor 57*l - 14*l**2 - 3*l**2 - 5*l**4 + 2*l**2 - 15*l**3 - 62*l.
-5*l*(l + 1)**3
Find u, given that 2 - 3*u + u**5 - 6 - 3*u**4 - 4 + 2*u**2 + 9 + 2*u**3 = 0.
-1, 1
Let u(k) be the first derivative of -7*k**4/12 + 2*k**3/9 + 7. What is v in u(v) = 0?
0, 2/7
Let p(r) be the second derivative of r**4/90 - 4*r**2/15 - 30*r. Find d, given that p(d) = 0.
-2, 2
Suppose 2*y - 12 = -4*j, -3*y = 5*j + 2*y - 20. Find l such that 3/5*l**5 + 3/5*l**3 + 0*l**j + 0*l - 6/5*l**4 + 0 = 0.
0, 1
Let q(g) be the third derivative of g**8/6720 - g**7/1260 - g**4/12 + 6*g**2. Let i(f) be the second derivative of q(f). Factor i(v).
v**2*(v - 2)
Factor 5*i - 4 - 3*i**2 - 6 + 1 + 7*i.
-3*(i - 3)*(i - 1)
Let j be 2*2/(6/3). Factor 4*g**3 + g**3 - 3*g**2 - j*g**3 - 6*g.
3*g*(g - 2)*(g + 1)
Find f such that 1/4 + 3/2*f**2 + f + f**3 + 1/4*f**4 = 0.
-1
Let q(k) be the third derivative of k**5/210 - 3*k**4/28 + 2*k**3/3 - 50*k**2. Suppose q(f) = 0. Calculate f.
2, 7
Let b = 6 - 2. Suppose 2*c**3 + 2*c**b - 4*c**3 + 4*c**3 = 0. What is c?
-1, 0
Suppose -1 = -5*f + 19. Let g(r) be the third derivative of 0 + 0*r**3 - 1/60*r**5 + 0*r + 1/24*r**f + r**2 - 1/60*r**6. Factor g(x).
-x*(x + 1)*(2*x - 1)
Let v(p) be the first derivative of -p**6/405 + p**5/180 + p**4/108 - p**3/3 - 2. Let z(i) be the third derivative of v(i). Solve z(j) = 0.
-1/4, 1
Let d(o) be the first derivative of 4*o**6/21 + 12*o**5/35 - 4*o**3/21 - 75. Factor d(s).
4*s**2*(s + 1)**2*(2*s - 1)/7
Let x(y) = y**3 - y**2. Let n(z) = 8*z**3 - 11*z**2 - 9*z. Let m(l) = n(l) - 5*x(l). Find a, given that m(a) = 0.
-1, 0, 3
Let j(i) = i**2 + i + 3. Let w(s) be the first derivative of -5*s + s - 2 - s + 4*s. Let g(k) = -2*j(k) - 6*w(k). Let g(r) = 0. What is r?
-1, 0
Let o = 10791/62120 + 2/1553. Let c(h) be the second derivative of 0 + 1/2*h**4 - 1/4*h**3 - 1/2*h**2 - o*h**5 - 2*h. Factor c(g).
-(g - 1)**2*(7*g + 2)/2
Factor n**3 + n**3 + 3*n**4 + 6*n - 2*n**3 - 9*n**2.
3*n*(n - 1)**2*(n + 2)
Let c(a) be the second derivative of a**8/1344 - a**7/840 - 2*a**2 - 2*a. Let v(u) be the first derivative of c(u). Factor v(w).
w**4*(w - 1)/4
Let t(w) be the third derivative of w**7/1365 - w**6/780 - w**5/390 + w**4/156 + 17*w**2. Suppose t(j) = 0. What is j?
-1, 0, 1
Let u(l) be the third derivative of 0*l + 1/420*l**7 + 0*l**3 + 4*l**2 + 1/120*l**6 + 0 + 1/120*l**5 + 0*l**4. Suppose u(t) = 0. What is t?
-1, 0
Let s(z) = z - 20. Let k be s(22). Factor 1/2*f**2 + k*f + 3/2.
(f + 1)*(f + 3)/2
Let n be (-1 - 0) + -1 + (-15)/(-6). Factor -n*a + 0 + 1/2*a**5 - a**4 + 0*a**3 + a**2.
a*(a - 1)**3*(a + 1)/2
Let w(d) be the second derivative of -d**5/10 + d**4/6 + 2*d**3/3 + 6*d. Determine m so that w(m) = 0.
-1, 0, 2
Let n(i) be the third derivative of 5*i**8/168 - 8*i**7/105 + i**6/60 + i**5/15 - 2*i**2. Factor n(u).
2*u**2*(u - 1)**2*(5*u + 2)
Let x(k) be the first derivative of -k**4 - 8*k**3/3 + 6*k**2 - 18. Factor x(i).
-4*i*(i - 1)*(i + 3)
Let s = -11 + 15. Suppose -s*i + 3*i + 2 = 0. Factor -3*n**2 + n**i - n**3 - n**3.
-2*n**2*(n + 1)
Factor d - 1/3*d**2 + 0.
-d*(d - 3)/3
Let u = -622/3 + 210. Let q(y) be the first derivative of -2 + 1/2*y**4 + u*y**3 + 2/3*y**6 - 3*y**2 + y - 9/5*y**5. Factor q(v).
(v - 1)**3*(v + 1)*(4*v - 1)
Let m be 3 + 5/(-1) - -6. Let d(y) be the second derivative of 0 + 0*y**2 + 1/24*y**3 + 2*y - 1/48*y**m. Factor d(w).
-w*(w - 1)/4
Let a be (-9)/(-6)*(-8)/(-3). Factor -t**3 + 3*t**2 - t**3 - 2*t - a*t**2 + 5*t**2.
-2*t*(t - 1)**2
Factor -8/7*g + 4/7 + 4/7*g**2.
4*(g - 1)**2/7
Suppose -4*w + 1 + 7 = 0. Solve 2*r + 16*r**4 - 18*r**4 + r**3 + 2*r**w - 3*r**3 = 0.
-1, 0, 1
Let c be (27/(-36))/(2/(-8)). Find s such that 15*s**2 - 12*s**3 + c*s**4 - s + 0*s - 4*s - s = 0.
0, 1, 2
Let v(p) be the first derivative of -p**6/16 + 3*p**5/40 + 3*p**4/16 - p**3/4 - 3*p**2/16 + 3*p/8 - 1. Factor v(m).
-3*(m - 1)**3*(m + 1)**2/8
Factor 7*g + 5*g**3 - 7*g + 0*g - 5*g**4.
-5*g**3*(g - 1)
Suppose p + k = -4*k - 9, -5*k = 20. Suppose 0 = w + 9 - p. Find o, given that 1/2*o**2 + 2*o + w = 0.
-2
Let x(f) be the second derivative of 5/12*f**4 - 1/14*f**7 + 0 - f - 1/9*f**3 + 29/90*f**6 - 11/20*f**5 + 0*f**2. Factor x(j).
-j*(j - 1)**3*(9*j - 2)/3
Let m = -97 + 393/4. What is f in -5/4*f**4 + 3/4*f**3 + m*f**2 - f**5 + 0 + 1/4*f = 0?
-1, -1/4, 0, 1
Let h(p) = -6*p**4 - 4*p**3 + 12*p**2 + 10*p + 6. Let t(d) = d**4 + d + 1. Let y(l) = h(l) - 6*t(l). Solve y(k) = 0.
-1, -1/3, 0, 1
Let n = -2903/7 - -415. Determine m, given that -n*m**2 + 4/7*m**3 - 8/7*m + 6/7 = 0.
-3/2, 1
Let x(n) be the third derivative of n**5/2 - 25*n**4/24 - 10*n**3/3 - 37*n**2. Factor x(i).
5*(2*i + 1)*(3*i - 4)
Let t(z) = -14*z**2 - 56*z + 56. Let w(j) = j**3 - 2*j**2 - 3*j + 3. Let v be w(3). Let g(i) = 3*i**2 + 11*i - 11. Let l(y) = v*t(y) + 16*g(y). Factor l(h).
2*(h + 2)*(3*h - 2)
Factor -m**5 + 3*m**3 - 4*m - 28*m**2 - 2*m**4 + 11*m**2 + 21*m**2.
-m*(m - 1)**2*(m + 2)**2
Let j = -539 + 543. Factor 0*a - 2/9*a**j + 4/9*a**2 + 0*a**3 - 2/9.
-2*(a - 1)**2*(a + 1)**2/9
Let z be 2/(-2) - (9 + -10). Let n