4*x + 14*x**3 + s*x**2 - 12*x**2 + 0*x = 0.
-2/7, 0, 1
Let k be 2/(-16) - (438/(-48) - 2). Suppose 2*a = -6*o + 3*o + k, 9 = 2*o + 3*a. Factor -27/2*l**2 + 6 - 18*l + 21/2*l**o.
3*(l - 2)*(l + 1)*(7*l - 2)/2
Let m(j) be the third derivative of -2*j**3 - 8/35*j**7 + 0*j - 7/5*j**6 + 7/2*j**4 - 33/20*j**5 + 0 + j**2. Suppose m(y) = 0. What is y?
-2, 1/4
Let o(b) be the third derivative of -b**8/3360 + b**7/1050 - b**6/1200 - 7*b**2 + 1. Factor o(s).
-s**3*(s - 1)**2/10
Determine w, given that 5/8*w**3 + 3/4 + 1/8*w**4 - 7/8*w**2 - 5/8*w = 0.
-6, -1, 1
Suppose 0 = 11*m - 36 + 20 + 16. Factor m + 4*t**2 + 8/3*t + 4/3*t**3.
4*t*(t + 1)*(t + 2)/3
Let w(u) be the second derivative of -u**6/90 + 3*u**5/10 - 15*u - 2. Factor w(k).
-k**3*(k - 18)/3
Factor 5041*p**2 + 1/6*p**4 - 715822/3*p + 25411681/6 - 142/3*p**3.
(p - 71)**4/6
Let g(t) be the second derivative of 0*t**2 - 1/6*t**3 + 0 + 1/48*t**4 - 7*t. What is l in g(l) = 0?
0, 4
Let l(w) = -6*w**2 - 103*w + 27. Let c(n) = -3*n**2 - n. Let m(z) = -2*c(z) - l(z). Factor m(i).
3*(i + 9)*(4*i - 1)
Let s(m) be the first derivative of -17 - 1/16*m**2 - 1/24*m**3 + 0*m. Factor s(d).
-d*(d + 1)/8
Suppose -6 = -3*k - 3*m, 0 = -4*k - m + 5*m - 8. Suppose -2*i + k*d + 30 = -5*d, 4*d = i - 21. Factor l**4 - i*l**4 + 8*l - 67*l**3 + 4 + 59*l**3.
-4*(l - 1)*(l + 1)**3
Let b be (-2)/12 + 34/(-48). Let w = b - -9/8. What is y in 1/4*y**4 - 3/4*y**3 + w*y + 0 - 1/4*y**2 + 1/2*y**5 = 0?
-1, 0, 1/2, 1
Let f be 7/(126/32) + 2/9. Determine c, given that 43*c**f + 3*c - 38*c**2 + 2*c = 0.
-1, 0
Let j(w) = 6*w**2 - w**3 + 0 - 9 + 3*w - 2*w**2. Let m be j(4). Suppose -8*u**3 + 0 + 0 + u**2 + 10*u**m = 0. What is u?
-1/2, 0
Let c = -1711 + 1714. Let g(i) be the second derivative of -1/4*i**4 - 2*i - 1/2*i**c + 0 + 3/20*i**5 + 1/10*i**6 + 0*i**2. Let g(k) = 0. Calculate k.
-1, 0, 1
Let s(w) = w**2 - 4*w - 2. Let r be (-24)/(-9)*(-3)/2. Let j be (-2)/r - 70/28. Let g(x) = -3*x**2 + 15*x + 9. Let u(c) = j*g(c) - 9*s(c). Factor u(n).
-3*n*(n - 2)
Suppose -15 = 4*x - 7*x. Solve 46*n - 15*n**3 - 18*n + 5*n**4 - 13*n - x*n**2 = 0.
-1, 0, 1, 3
Let f(k) be the second derivative of k**6/120 - 7*k**5/20 + 49*k**4/8 + 3*k**3 - 29*k. Let a(m) be the second derivative of f(m). Factor a(v).
3*(v - 7)**2
Let u(g) be the first derivative of 1/3*g**3 + 0*g - 17 + 9/2*g**2. Factor u(h).
h*(h + 9)
Let k be 0/(5/(-30)*6). Factor 2/5*p**3 + 0*p - 2/5*p**2 + k.
2*p**2*(p - 1)/5
Factor 16/3*h**2 - 4/3*h - 16/3 + 4/3*h**3.
4*(h - 1)*(h + 1)*(h + 4)/3
Let w(n) be the third derivative of -n**8/1008 + n**6/360 + 2*n**2 + 2. What is r in w(r) = 0?
-1, 0, 1
Let o(s) be the first derivative of -s**5/30 + 5*s**4/6 - 25*s**3/3 + 13*s**2 + 9. Let c(a) be the second derivative of o(a). Factor c(j).
-2*(j - 5)**2
Suppose k - 2*v = 6, -5*k - v + 12 + 18 = 0. Let z be ((-24)/22)/(k + -8 - 0). Factor -16/11*x + 8/11 + z*x**2.
2*(x - 2)*(3*x - 2)/11
Let o = 23 + -20. Factor -o*x + 8*x - 6*x**3 + 8*x**2 - 7*x.
-2*x*(x - 1)*(3*x - 1)
Let r = 139 + -137. Suppose -m - r - 5 = -2*f, f + 1 = -4*m. Factor 3/5 + 9/5*a + 3/5*a**f + 9/5*a**2.
3*(a + 1)**3/5
Let l(j) be the first derivative of 1/9*j**3 + 7/3*j**2 + 49/3*j - 32. Find k, given that l(k) = 0.
-7
Suppose -3*g = -4*r - 848, -6*g + 3*r + 1428 = -g. Determine i so that g*i**2 + 162*i**2 + 25*i + 15 - 145*i - 7 = 0.
2/15
Suppose -2*s - 2*s = -5*i + 22, 3*s = -9. Let m be (-2)/(-11) + (238/385 - -2). Find c, given that -2/5*c**4 - 18/5*c**i - 4/5 + m*c + 2*c**3 = 0.
1, 2
Factor 18*h**2 + 0 + 13 - 81*h + 0*h**3 - 13 + 3*h**3.
3*h*(h - 3)*(h + 9)
Let i(b) = -42*b**3 + 34*b**2 - 44*b + 16. Let f(h) = -13*h**3 + 11*h**2 - 15*h + 5. Let z(m) = -16*f(m) + 5*i(m). Determine y so that z(y) = 0.
-5, 0, 2
Let r = -90 - -93. Suppose -2*b = -r - 3. What is w in -2*w**4 + 23/7*w**b + 0 + 3/7*w**5 + 4/7*w - 16/7*w**2 = 0?
0, 2/3, 1, 2
Let y(n) = n**2 + 2*n + 3. Let d(b) = 2*b**2 + 5*b + 3 + 8 + b**2 - 4. Suppose -3 = 3*t - 4*x, 2*t + 6 = -5*x - 19. Let l(o) = t*y(o) + 2*d(o). Factor l(u).
(u - 1)*(u + 1)
Factor -3/2*p - 3/2*p**2 + 9.
-3*(p - 2)*(p + 3)/2
Let u be 8/(-14) + 0 - -1. Suppose -2*j = -4*l - 2, 2*l - 69*j + 3 = -66*j. Factor -3/7*w**2 + 1/7*w + u*w**3 + l - 1/7*w**4.
-w*(w - 1)**3/7
Find s, given that 2*s - 9 - 4*s**4 - 4*s**3 + 5 + 44*s**5 + 8*s**2 - 42*s**5 = 0.
-1, 1, 2
Let p(a) be the second derivative of a**9/1512 - a**8/105 + 4*a**7/105 - 8*a**3 - 37*a. Let u(m) be the second derivative of p(m). Find x, given that u(x) = 0.
0, 4
Let g be 0*(2/4 + -1). Suppose g = 4*l - 59 + 51. Determine c so that c + 1/5*c**l - 2/5*c**3 + 2/5 = 0.
-1, -1/2, 2
Let z(n) be the first derivative of 2*n**6/15 - 2*n**5/5 + n + 17. Let q(b) be the first derivative of z(b). Factor q(c).
4*c**3*(c - 2)
Factor 0 + 2/3*c**3 - 8/3*c**2 + 0*c.
2*c**2*(c - 4)/3
Suppose -r = 29 - 129. Factor -r - 4*g**2 - g - 34*g - 5*g.
-4*(g + 5)**2
What is g in 0 - 3/2*g**4 + 126*g**2 + 27*g**3 + 132*g = 0?
-2, 0, 22
Let x(l) be the third derivative of 121/2*l**3 + 0 + 0*l + 11/4*l**4 + 8*l**2 + 1/20*l**5. Factor x(f).
3*(f + 11)**2
Let c be (1 + 5)/(-1) + (2 - (1 - 5)). Determine k so that 2/13*k**2 + 0*k + c - 2/13*k**3 = 0.
0, 1
Let a(j) = -64*j**3 - 452*j**2 + 214*j + 28. Let h(y) = -13*y**3 - 90*y**2 + 43*y + 6. Let m(u) = -6*a(u) + 28*h(u). Factor m(l).
4*l*(l + 10)*(5*l - 2)
Suppose -y - 3*f - 23 = 0, -3*f - f = -2*y - 26. Let b be (-78)/(-14) - (-85)/y. Factor -4/7*d + 1/7*d**5 + 3/7*d**3 + 4/7*d**4 + 0 - b*d**2.
d*(d - 1)*(d + 1)*(d + 2)**2/7
Suppose 12*n - 34 = -5*n - 0*n. Find v such that -2/5*v**4 + 1/5*v**5 + 0 - 1/5*v + 0*v**3 + 2/5*v**n = 0.
-1, 0, 1
Let i(h) be the first derivative of h**3/3 + 79*h**2 - 64. Factor i(j).
j*(j + 158)
Let i(f) be the first derivative of -f**6/360 + f**5/90 - f**4/72 - 2*f**2 + 5. Let n(g) be the second derivative of i(g). Factor n(k).
-k*(k - 1)**2/3
Solve 3 - 49*h**2 + 25*h**2 - 248 + 70*h + 19*h**2 = 0 for h.
7
Let i = -4559/6 + 760. Let l(p) be the second derivative of -8*p + 0 + 0*p**2 - i*p**3 - 1/24*p**4. Factor l(h).
-h*(h + 2)/2
Let x be (-64)/(-60)*78/104. Suppose 0*z**4 - 4/5 + 8/5*z**3 - 2/5*z**5 - 6/5*z + x*z**2 = 0. Calculate z.
-1, 1, 2
Factor 1/4*t**3 + 0*t**2 + 0 + 1/2*t**4 + 0*t.
t**3*(2*t + 1)/4
Suppose -5 + 23/2*b + 5/2*b**2 = 0. What is b?
-5, 2/5
Let a(x) be the third derivative of x**5/180 + 3*x**4/4 + 81*x**3/2 - 101*x**2. Factor a(g).
(g + 27)**2/3
Let g(k) be the first derivative of 21*k**5/20 - 31*k**4/8 + 65*k**3/12 - 7*k**2/2 + k - 41. Find f, given that g(f) = 0.
2/7, 2/3, 1
Let n be 2/7 + (-460)/(-7). Let r(l) = -l**2 + 9*l + 2. Let a be r(9). Solve 65*i**3 + 5*i + 0*i**2 + a*i**2 - n*i**3 - 6*i = 0 for i.
0, 1
Let r be (20*(-6)/4)/(-2). Suppose 0 = 3*x + 2*x - r. Factor y**2 + 3*y + 2*y**2 + 5*y**2 - 2*y**2 - x.
3*(y + 1)*(2*y - 1)
Suppose h - 7*h + 24 = 0. Determine q, given that 4*q**2 + 8*q + 4 - h = 0.
-2, 0
Suppose 100 = -3*l + 145. Suppose 14*d - l = 9*d. Factor -1/3*t**4 + 0 - 5/3*t**d - 4/3*t - 8/3*t**2.
-t*(t + 1)*(t + 2)**2/3
Let h(o) be the first derivative of 4*o**5/15 - 2*o**4 + 16*o**3/3 - 16*o**2/3 + 21. Factor h(p).
4*p*(p - 2)**3/3
Suppose -2 - 33 = -7*s. Find q such that -15*q**3 + 4*q**2 - 3*q**2 + s*q**2 = 0.
0, 2/5
Let o = -182 - -182. Suppose o = 4*u - s - 15, -6*s = u - 11*s - 18. Factor 0*b**u - 2*b**4 - 1/2*b + 3/2*b**2 + 0.
-b*(b + 1)*(2*b - 1)**2/2
Factor -6*g**2 + 21 - 24 + 9*g + g**4 - g.
(g - 1)**3*(g + 3)
Suppose 61/6*i + 59/3 + 1/6*i**2 = 0. What is i?
-59, -2
Suppose 15*z - 14*z = -3. Let d(i) = 2*i**3 + 7*i**2 - 14*i + 8. Let h(w) = -5*w**3 - 14*w**2 + 28*w - 16. Let v(x) = z*h(x) - 7*d(x). Factor v(c).
(c - 4)*(c - 2)*(c - 1)
Let d(a) be the first derivative of 5*a**4/4 - 230*a**3/3 + 2645*a**2/2 + 21. Suppose d(h) = 0. What is h?
0, 23
Factor 0*m + 322/9*m**2 - 2/9*m**3 + 0.
-2*m**2*(m - 161)/9
Let j(m) be the first derivative of m**4/4 + 104*m**3/3 - m**2/2 - 104*m + 512. Find t such that j(t) = 0.
-104, -1, 1
Suppose -2 = 3*r - f - 19, 47 = 5*r + 3*f. Suppose -2*c = 2*g - 21 + 7, 2*c = 5*g - r. Factor -13/4*d**3 - g*d**2 - d + 0 - 1/4*d**5 - 3/2*d**4.
-d*(d + 1)**2*(d + 2)**2/4
Suppose -13*q = -k - 18*q - 41, -4*k - 2 = 2*q. Solve -30*f**2 - 1/2*f**k - 13/2*f**3 - 56*f - 32 = 0 for f.
-4, -1
Let q(r) be the first derivative of -r**7/1680 