
-1, 0
Factor -2349*a**2 + 4695*a**2 - 2*a**4 - a**5 + a - 2344*a**2.
-a*(a - 1)*(a + 1)**3
Suppose -8*p - 4*p + 72 = 0. Let x(w) = -w**4 + 6*w**3 + 6*w**2 + 6*w. Let b(s) = s**3 + s**2 + s. Let a(g) = p*b(g) - x(g). Let a(u) = 0. Calculate u.
0
Let g(u) be the second derivative of -7*u**5/120 - 17*u**4/18 - 155*u**3/36 + 25*u**2/6 - 566*u. Factor g(o).
-(o + 5)**2*(7*o - 2)/6
Solve -4/3*h - 6*h**2 + 52/3*h**3 + 0 = 0.
-2/13, 0, 1/2
Let g be (-1)/(-2) - (-45)/10. Factor -44*t**3 + 33*t**5 - 16*t**4 - 24*t**2 - 17*t**5 - 12*t**g.
4*t**2*(t - 6)*(t + 1)**2
Let j(r) be the third derivative of r**7/280 - r**6/72 - r**5/30 + r**4/6 + 4*r**3 - 32*r**2. Let d(h) be the first derivative of j(h). Factor d(y).
(y - 2)*(y + 1)*(3*y - 2)
Let l(u) be the second derivative of u**8/26880 - u**7/3360 - u**6/720 + 7*u**4/3 - 18*u. Let m(b) be the third derivative of l(b). Find z, given that m(z) = 0.
-1, 0, 4
Factor 7/8*n**2 + 0*n - 1/8*n**4 + 0 - 3/4*n**3.
-n**2*(n - 1)*(n + 7)/8
Let d(w) be the second derivative of -w**6/60 + 7*w**5/40 - w**4/4 - 32*w. Factor d(q).
-q**2*(q - 6)*(q - 1)/2
Let r(t) = -t**3 + 4*t**2 + 9. Let u be r(4). Suppose 4*z = u - 1. Factor -4/5*a + 2/5*a**z + 2/5.
2*(a - 1)**2/5
Let o(l) = 3*l - 6. Let u = -1 - -4. Let x be o(u). Determine j so that -2*j**x - 10*j + 11 - 9 - 8*j**2 - 6 = 0.
-2, -1
Factor -60*w**3 - 2*w - 266*w**2 - 25*w - 27*w - 3*w**4 + 155*w**2.
-3*w*(w + 1)**2*(w + 18)
Let u(s) be the first derivative of 1/10*s**2 + 11 + 0*s - 1/15*s**3. Find h such that u(h) = 0.
0, 1
Let d(s) be the second derivative of s**4/60 - s**3/6 + s - 67. Suppose d(t) = 0. Calculate t.
0, 5
Determine j so that 1/6*j**2 + 2*j - 1/6*j**3 + 0 = 0.
-3, 0, 4
Let q(n) be the third derivative of 1/30*n**4 + 0 - 1/300*n**6 - 1/175*n**7 + 0*n + 23*n**2 + 0*n**3 - 1/840*n**8 + 1/50*n**5. Determine w so that q(w) = 0.
-2, -1, 0, 1
Suppose 2*f - 4*c + 1 = -3*c, f + 13 = 3*c. Let d = -13 + 16. Factor -7*s**3 + 15*s**2 - f*s**4 - 5*s**2 - 6*s + d*s**3 + 2*s**3.
-2*s*(s - 1)**2*(s + 3)
Let j = 42 + -36. Factor -3*h**2 + 4*h**2 + j*h**2 - 4 - 3*h**2.
4*(h - 1)*(h + 1)
Suppose -4*w = -5*w - 6. Let a(v) = 2*v**2 + 6*v - 8. Let i(n) = 6*n**2 + 17*n - 24. Let z(o) = w*i(o) + 17*a(o). Factor z(h).
-2*(h - 2)*(h + 2)
Let f be (-20)/(-15)*6/4. Factor 2/7*m**f + 0 + 2/7*m**3 + 0*m.
2*m**2*(m + 1)/7
Let x(w) be the first derivative of 2/3*w**3 + 6*w**2 + 10*w - 32. Factor x(c).
2*(c + 1)*(c + 5)
Let v(d) = -3*d**3 - 25*d**2 - 155*d - 1174. Let s be v(-8). Determine u, given that 0 + 14/13*u**s + 0*u + 2/13*u**3 = 0.
-7, 0
Let w be (-35)/14 - (-340)/8. Let n be -3 + 276/w + 8/(-20). Factor -1 + n*h - h**2 - 3/2*h**3.
-(h - 1)*(h + 2)*(3*h - 1)/2
Factor 4*y - 4*y**2 + 4*y - 11*y - 15*y - 10*y + 32.
-4*(y - 1)*(y + 8)
Factor 0 - 3*t**3 - 27/4*t**2 + 27/4*t.
-3*t*(t + 3)*(4*t - 3)/4
Let j(n) be the third derivative of 2/15*n**4 - 1/75*n**5 + 0*n**3 - 27*n**2 + 0*n + 0. Solve j(s) = 0.
0, 4
Solve -20/9*g - 2*g**3 + 0 + 94/9*g**2 = 0.
0, 2/9, 5
Let t(z) be the first derivative of -z**2 + 2/9*z**3 + 15 + 10/9*z + 1/18*z**4. Let t(d) = 0. What is d?
-5, 1
Let c(v) = 2*v**2 - 2*v. Let i(b) = -55*b**2 + 240*b - 65. Let j(t) = -20*c(t) - i(t). Solve j(n) = 0 for n.
1/3, 13
Let b(i) = 7*i**5 + 36*i**4 + 108*i**3 + 4*i**2 - 4*i. Let c(j) = j**5 + j**2 - j. Let a(m) = -b(m) + 4*c(m). Factor a(x).
-3*x**3*(x + 6)**2
Let n be 19/4*12/9 - (815 + -810). Factor -8/3*w**3 + n*w**4 - w**2 + 7/3*w - 2/3.
(w - 2)*(w + 1)*(2*w - 1)**2/3
Let x(a) be the third derivative of 21*a**2 + 0 - 4/3*a**4 - 5/12*a**6 + 0*a + 0*a**3 + 4/3*a**5. Factor x(y).
-2*y*(5*y - 4)**2
Let n(m) = -33*m**2 + 27*m - 69. Suppose -23 - 61 = -4*a. Let c(g) = -8*g**2 + 7*g - 17. Suppose 15 = 7*r - 10*r. Let y(k) = a*c(k) + r*n(k). Factor y(x).
-3*(x - 2)**2
Let x = 143 - 104. Find l, given that -24*l**3 - 63*l**2 + x*l + 3 - l**3 + 81*l**4 - 2*l**3 - 9 = 0.
-1, 1/3, 2/3
Suppose -p + 6*p = -2*f - 7, 0 = 4*f - 2*p - 22. Let q(b) be the first derivative of -2 + 5/3*b**3 + f*b - 1/4*b**4 - 4*b**2. Factor q(s).
-(s - 2)**2*(s - 1)
Determine f so that -4/5*f**2 - 32/5*f - 64/5 = 0.
-4
Factor 250 - 48/5*r**2 + 1/5*r**3 + 105*r.
(r - 25)**2*(r + 2)/5
Suppose 5*b = 4*l - l + 1, -2*b + 19 = 5*l. Let -3/2*u**b + 6*u - 6 = 0. What is u?
2
Let l be ((-16)/64)/(-1*1). Let i(n) be the third derivative of -l*n**4 - n**2 + 0 + 1/60*n**6 - 2/3*n**3 + 0*n**5 + 0*n. What is b in i(b) = 0?
-1, 2
Suppose 0 = -3*k - g - 268, 0 = 2*k + g + 134 + 44. Let w be (-38)/(-10) - 18/k. Solve -w*n**2 - 8*n + 17 + 11 - 16 = 0 for n.
-3, 1
Let t(i) be the second derivative of 0*i**2 + 4/9*i**4 - 1/6*i**5 - 17*i + 0 + 1/45*i**6 - 4/9*i**3. Factor t(f).
2*f*(f - 2)**2*(f - 1)/3
Let k(y) be the second derivative of y**6/30 - y**4/2 + 4*y**3/3 - 3*y**2/2 + 269*y. Determine l so that k(l) = 0.
-3, 1
Solve 30*j + 4*j**2 - 3*j**2 + 124*j + 31*j + 4*j**2 = 0.
-37, 0
Let k = -64 - -70. Let j be (-22)/77 + 2 + k/(-28). Solve -1/2*p**2 + 0 + j*p = 0.
0, 3
Let f = 10008/55165 + 2/5015. Factor 2/11*g**3 + 0*g - 2/11*g**2 + 0 - 2/11*g**5 + f*g**4.
-2*g**2*(g - 1)**2*(g + 1)/11
Let g(y) be the second derivative of -y**4/4 + 3*y**3/8 + 145*y. Let g(a) = 0. Calculate a.
0, 3/4
Let d(t) = 20*t**4 - 71*t**3 + 99*t**2 - 65*t + 17. Let q(c) = 61*c**4 - 214*c**3 + 297*c**2 - 196*c + 52. Let h(b) = -7*d(b) + 2*q(b). Factor h(i).
-3*(i - 1)**3*(6*i - 5)
Let n = 23 + -12. Factor -8*u**3 - 13*u**2 - n + 3*u**3 - 23*u + 2*u**3 + 2*u**3.
-(u + 1)**2*(u + 11)
Let l(r) be the first derivative of r**6/45 + r**5/30 - 23*r**3/3 - 22. Let a(j) be the third derivative of l(j). Solve a(w) = 0 for w.
-1/2, 0
Let k be 1/(-3)*-15*1. Suppose -10*p = -k*p - 55. Find o, given that 15*o**5 + 8*o**4 + 2*o**3 - p*o**5 + 2*o**3 = 0.
-1, 0
Let y be (9 - (-5 - 174/(-24))*4)/(-1). Factor -2/7*a**3 + y*a + 6/7*a**2 + 0.
-2*a**2*(a - 3)/7
Let i be (15/(-24))/(22/(-132)). Factor i*t - 3/4*t**2 - 3.
-3*(t - 4)*(t - 1)/4
Let a = -33003 + 99011/3. Factor a*g**2 + 8/3*g + 8/3.
2*(g + 2)**2/3
Find d, given that -6*d**2 + 31*d - 25*d**3 + 9*d + 5*d**4 + 3*d**2 + 13*d**2 = 0.
-1, 0, 2, 4
Let u(r) = -6*r**2 - 98*r - 30. Let t be u(-16). Let j(f) be the first derivative of 2/3*f**3 - 4 + 4*f - 3*f**t. Solve j(k) = 0 for k.
1, 2
Suppose -h + 1 = 2*o - 9, -2*h - 4 = -2*o. Suppose 9 = h*u + u, -4*i - u = -15. Factor -5*b**3 - 2*b**5 + 3*b**4 + 8*b**i + b**2 + 3*b**5.
b**2*(b + 1)**3
Let m(c) be the third derivative of c**9/5040 + c**8/1120 - c**6/120 - c**5/40 + 3*c**4/8 - 2*c**2. Let b(t) be the second derivative of m(t). Factor b(o).
3*(o - 1)*(o + 1)**3
Let a(c) be the third derivative of -c**9/15120 - c**8/1680 - c**7/504 - c**6/360 + c**4/6 + 12*c**2. Let x(t) be the second derivative of a(t). Factor x(j).
-j*(j + 1)**2*(j + 2)
Let a(s) be the first derivative of 2*s**3/9 - 2*s**2 - 18*s - 79. Let a(f) = 0. What is f?
-3, 9
Let l(y) be the second derivative of -y**7/1050 + y**6/400 - y**4/240 - 9*y**2/2 - 17*y. Let j(t) be the first derivative of l(t). Find d, given that j(d) = 0.
-1/2, 0, 1
Let s(c) be the second derivative of 0 - 1/36*c**4 + 1/3*c**2 + 1/18*c**3 + 34*c. Find r, given that s(r) = 0.
-1, 2
Let a(j) be the first derivative of 3*j**5/20 + 9*j**4/8 + 9*j**3/4 + 3*j**2/2 - 313. Factor a(o).
3*o*(o + 1)**2*(o + 4)/4
Let b = -1559/7 - -1565/7. Let b - 12/7*x**3 - 6/7*x**2 + 3/7*x**5 + 9/7*x + 0*x**4 = 0. Calculate x.
-1, 1, 2
Let k = -1282658 + 83370106/65. Let v = k + 208/5. Factor -2/13*t**2 + v*t - 8/13.
-2*(t - 2)**2/13
Solve 233*q - 8*q**2 + 33*q**2 - 253*q - 5*q**3 = 0.
0, 1, 4
Suppose z = -18 + 22 - 1. Factor -z + 3/2*s**4 - 9/2*s**2 - 3/2*s**3 + 15/2*s.
3*(s - 1)**3*(s + 2)/2
Let r(d) be the second derivative of -d**7/56 + 43*d**6/120 - 61*d**5/40 + 23*d**4/8 - 67*d**3/24 + 11*d**2/8 - 335*d + 2. Let r(h) = 0. Calculate h.
1/3, 1, 11
Let j(z) be the second derivative of -5*z**4 - 25/2*z**2 + 1/2*z**5 + 1/6*z**6 + 35/3*z**3 - 23*z + 0. Factor j(g).
5*(g - 1)**3*(g + 5)
Let g(u) = -14*u**4 + 11*u**3 + 3*u**2 + 2*u - 2. Let y = 10 + -11. Let w(k) = k**4 - k**3 - k + 1. Let t(p) = y*g(p) - 2*w(p). Suppose t(m) = 0. Calculate m.
-1/4, 0, 1
What is a in 15/4*a**2 - 3/4*a**3 + 0 - 3*a = 0?
0, 1, 4
Let i(t) = t**2 - 1. Let j be ((-5)/2 - -3)/((-1)/(-2)). Let p(l) = -18*l**2 - 33*l - 15. Let k(