5 + 0*n**2 + 0*n**3 + 0 - 1/84*n**7 + 1/24*n**4. Suppose a(l) = 0. Calculate l.
0, 1
Let t = -20 + -11. Let b = t - -33. Find o, given that -3/4*o**b - 3/4*o + 0 = 0.
-1, 0
Suppose -1/4 + 1/4*y**3 + 1/4*y**2 - 1/4*y = 0. What is y?
-1, 1
Let g be 1576/780 - 4/2. Let p = 172/65 + g. Factor -4/3 - p*i**2 - 6*i.
-2*(i + 2)*(4*i + 1)/3
Let w(h) = -h**3 + 5*h**2 + 6*h + 1. Let o be w(6). Suppose o = 3*b - 8. Determine u so that -2/3*u**b + 0*u**2 + 2/3*u + 0 = 0.
-1, 0, 1
Suppose -14 = -4*h - 2. Suppose 14 = h*m - 10. Let 2*c + 6*c**4 + 10*c**3 - 8*c**4 - m*c**2 - 2*c**4 = 0. What is c?
0, 1/2, 1
Suppose 2*c - 3*c = 2, -46 = -5*v + 3*c. Factor v*b**2 - 3*b - b + b**3 - 8*b**3 + 3*b**3.
-4*b*(b - 1)**2
Let f(y) = -y**3 + y**2 + 3. Let b be f(0). Factor b + 4*m**4 + 0*m**4 - m**2 + 1 - 7*m**2.
4*(m - 1)**2*(m + 1)**2
Let a(f) = -f**3 - f**2 - 2. Suppose -17 = -7*s + 3*s - 5*q, 0 = -4*q + 20. Let y be a(s). Factor -y*u**2 + 4*u**3 + 7*u - 7*u - 2*u**4.
-2*u**2*(u - 1)**2
Let s(a) be the first derivative of 2*a**5/15 + 11*a**4/18 + 8*a**3/9 + 4*a**2/9 - 36. Let s(z) = 0. What is z?
-2, -1, -2/3, 0
Suppose 2*p - 2 - 2 = 0. Let q = 17 - 15. Determine w, given that -w**2 - q*w**2 + 2*w**p = 0.
0
Let w(u) be the second derivative of u**7/28 - u**6/20 - 3*u**5/20 + u**4/4 + u**3/4 - 3*u**2/4 - 8*u. Factor w(h).
3*(h - 1)**3*(h + 1)**2/2
Let r(u) be the second derivative of 4*u - 1/30*u**4 + 1/50*u**5 - 1/15*u**3 + 0*u**2 + 1/75*u**6 + 0. Factor r(l).
2*l*(l - 1)*(l + 1)**2/5
Suppose -n - 5*d + 28 = 0, 0*n = n + 3*d - 18. Let l(a) be the second derivative of 1/30*a**4 + 0*a**n - 1/5*a**2 + 0 - 2*a. Suppose l(q) = 0. What is q?
-1, 1
Let h(a) be the third derivative of -a**8/20160 + a**7/2520 - a**6/720 - a**5/30 - 2*a**2. Let x(z) be the third derivative of h(z). Factor x(c).
-(c - 1)**2
Let r(j) = -j - 4. Let t be r(-6). Let x(u) = u**3 - u**2 + u - 1. Let d be x(1). Factor -8*v**5 + d*v + 0*v - t*v**4 + 6*v**5.
-2*v**4*(v + 1)
Let z(o) = 3*o**3 + o**2 - 5*o + 5. Let h(v) = 4*v**3 - 2 - 4*v**3 - 2*v**3 + 2*v + v**3. Let f(w) = -5*h(w) - 2*z(w). Find l such that f(l) = 0.
-2, 0
Suppose 0 = 5*w, 4*w + 2 = 2*u - 6. Factor -r**2 + 2*r**3 - u + 7*r**2 - 2 - 2.
2*(r - 1)*(r + 2)**2
Let p = 18 + -28. Let k(f) = -7*f**4 + f**3 - 7*f**2 + 5*f. Let d(v) = -3*v**4 - 3*v**2 + 2*v. Let q(c) = p*d(c) + 4*k(c). Factor q(h).
2*h**2*(h + 1)**2
Let p(n) be the first derivative of n**6/120 - n**5/40 - n**4/48 + n**3/12 - 2*n - 6. Let l(k) be the first derivative of p(k). Factor l(w).
w*(w - 2)*(w - 1)*(w + 1)/4
Factor 3*p**2 + p**2 + 5*p + 5*p**3 - 6*p**2 - 8*p**2.
5*p*(p - 1)**2
Let m = 180 - 124. Let k be (m/98)/(2/14). Factor 0 - 3*l**3 - 2*l**2 - 2*l**k - 1/2*l - 1/2*l**5.
-l*(l + 1)**4/2
Let l(s) be the second derivative of s**7/4200 - s**6/1800 - s**5/600 + s**4/120 + s**3/6 + 3*s. Let d(m) be the second derivative of l(m). Factor d(g).
(g - 1)**2*(g + 1)/5
Suppose 18*y = 12 + 60. Solve 0*w + 10/9*w**y + 0 + 0*w**2 - 4/9*w**3 = 0.
0, 2/5
Determine o so that -8/3 + 20/3*o - 4*o**2 = 0.
2/3, 1
Let o(n) = n + 13. Let r be o(-8). Suppose 3*j + 11 = 3*v + j, -r*j = 2*v - 1. Factor 10/7*c + 2/7 + 6/7*c**v + 2*c**2.
2*(c + 1)**2*(3*c + 1)/7
Suppose 11 = -f - 4*r, 5*f - 5*r + 2*r - 37 = 0. Let -7*s**5 - 3*s**5 + 3*s**3 + 7*s**f - 3*s**2 + 3*s**4 = 0. What is s?
-1, 0, 1
Let k = 3425/16 + -214. Let o(s) be the third derivative of 0*s - k*s**4 - 3*s**2 - 1/6*s**3 + 0 - 1/120*s**5. Let o(f) = 0. What is f?
-2, -1
Let g(i) be the third derivative of 0 + 1/72*i**4 - 1/9*i**3 - i**2 + 0*i + 1/180*i**5. Factor g(r).
(r - 1)*(r + 2)/3
Suppose -2*d = -3 - 9. Let l = 10 - d. Determine u so that -8*u + l - 6*u**2 + 5*u + 13*u = 0.
-1/3, 2
Let h be (-6 - -1)*(-18)/(-5). Let b be (6/(-9))/(4/h). Factor -7*o**3 - 2*o**2 + b*o**3 + 6*o**2 - 4 + 6*o - 2*o**3.
-2*(o - 1)*(o + 1)*(3*o - 2)
Let v(d) be the first derivative of -2*d**3/5 - 8*d**2/5 - 8*d/5 - 1. Suppose v(w) = 0. Calculate w.
-2, -2/3
Let m(y) be the second derivative of y**9/12600 - y**8/2400 + y**7/1260 - y**6/1800 - y**4/4 - 3*y. Let c(f) be the third derivative of m(f). Solve c(t) = 0.
0, 1/3, 1
Let v(j) be the third derivative of -j**6/280 - j**5/70 + j**4/56 + j**3/7 - 15*j**2. Determine o so that v(o) = 0.
-2, -1, 1
Let w be (-290)/120*4 + 10. Factor 0 + 5/3*h**2 - 4/3*h**3 + w*h**4 - 2/3*h.
h*(h - 2)*(h - 1)**2/3
Let f be (-4)/18*(46 + -49). Factor 0 + f*z**3 - z**2 + 1/3*z.
z*(z - 1)*(2*z - 1)/3
Suppose -3*y - 2 - 10 = 0. Let r be y/(-16) + (-22)/(-8). Factor 0*h**4 + 0*h**r - h**3 - h**4.
-h**3*(h + 1)
Let z = 253 + -251. Let t(n) = -n**3 + 4*n**2 - 3*n + 3. Let q be t(2). Factor 0 - 2*l**q + 0*l + 0*l**z + 14/5*l**4 - 4/5*l**3.
-2*l**3*(l - 1)*(5*l - 2)/5
Let g(d) = d**2 + 8*d - 20. Let w be g(-10). Find z such that -53/4*z**3 + 0*z**4 + z + 0 + 49/4*z**5 + w*z**2 = 0.
-1, -2/7, 0, 2/7, 1
Suppose -2*m + 0*m = -6*m. Let 1/4*r**2 - 1/2*r + m = 0. Calculate r.
0, 2
Suppose 3*u + u - 20 = 0. Find x, given that -4 + 2*x**3 - x - x**3 - x**2 + u = 0.
-1, 1
Solve -1/2 + 1/8*u**2 + 0*u = 0.
-2, 2
Let w = 3 - 5. Let f be (9/(-2) + 3)*w. Let 0 - 1/3*q**2 - 2/3*q**f + 0*q - 1/3*q**4 = 0. Calculate q.
-1, 0
Let m(h) = -4*h**5 + 9*h**4 - 8*h**3 + 3*h. Let x(i) = i**5 - i**4 + i**3 - i. Let k(b) = -m(b) - 3*x(b). Suppose k(q) = 0. Calculate q.
0, 1, 5
Let z be 14/60 + (-13)/(-78). Find k, given that 4/5*k**2 + 0 + 2/5*k**3 + z*k = 0.
-1, 0
Suppose 2*y - 6*y + 16 = 0. Suppose -y = g - 2*g. Factor 3/2*f**g + 0*f + 1/2*f**2 + 0 + 2*f**3.
f**2*(f + 1)*(3*f + 1)/2
Let k(h) be the third derivative of -h**8/112 + 2*h**7/35 - 3*h**6/20 + h**5/5 - h**4/8 + 12*h**2. Factor k(t).
-3*t*(t - 1)**4
Let w be (-80)/(-44) - 4/(-22). Factor -8*r**4 - 2*r**2 - 10*r**3 + w*r**3 + 2*r - 2*r**3 + 2*r**4.
-2*r*(r + 1)**2*(3*r - 1)
Let a be ((-21)/7)/(6/(-4)). Factor -1 - 1/2*j**a + 3/2*j.
-(j - 2)*(j - 1)/2
Suppose 0*t = -5*t + 10. Let l(s) be the second derivative of 0 - 1/16*s**4 - 2*s - 1/12*s**3 + 1/8*s**t. Factor l(b).
-(b + 1)*(3*b - 1)/4
Let y be 2/(-7) + 62/168. Let x(o) be the second derivative of 1/8*o**4 + 3/40*o**5 + 1/60*o**6 + 0*o**2 + 0 - o + y*o**3. Factor x(w).
w*(w + 1)**3/2
Let v(t) be the second derivative of -t**9/7560 - t**8/1680 + t**6/180 + t**5/60 - 5*t**4/12 - 5*t. Let i(p) be the third derivative of v(p). Factor i(g).
-2*(g - 1)*(g + 1)**3
Let y(w) be the second derivative of -w**7/63 + 4*w**6/45 - 2*w**5/15 - 5*w + 1. Factor y(g).
-2*g**3*(g - 2)**2/3
Let q(a) be the third derivative of -4*a**7/1155 - a**6/165 + 7*a**5/330 - a**4/66 - a**2. Factor q(x).
-2*x*(x + 2)*(2*x - 1)**2/11
Let l = 6 + -6. Let m be 2/(2 + l - 1). Factor 0*c**m + 2/5*c**3 - 2/5*c + 0.
2*c*(c - 1)*(c + 1)/5
Let q(b) be the second derivative of -3*b**7/14 - 7*b**6/10 - b**5/2 + b**4/2 + b**3/2 - b**2/2 - 3*b. Factor q(l).
-(l + 1)**3*(3*l - 1)**2
Factor 4*m**2 + 0*m**2 + 125 - 50*m + 0*m**2 + m**2.
5*(m - 5)**2
Suppose -5*f = 4*w + 13, -2*f - 14 = -3*w - f. Factor 0*r**2 - 4*r**4 - 3*r**2 - w*r**2 - 10*r**3 - 2*r**2 - 2*r.
-2*r*(r + 1)**2*(2*r + 1)
Suppose -3*g = -p - 13, -2*g - g = -15. Let z = -33 + 101/3. Factor 0*f**p + 0*f + 0 - z*f**3.
-2*f**3/3
Let w(x) be the first derivative of -x**4/10 - 4*x**3/5 - 12*x**2/5 - 16*x/5 + 8. Factor w(g).
-2*(g + 2)**3/5
Let m = 1 - -1. Let z(f) be the first derivative of 0*f - m - 1/2*f**2 + 1/3*f**3. Factor z(q).
q*(q - 1)
Factor 972 - 4/3*a**4 - 288*a**2 + 648*a + 104/3*a**3.
-4*(a - 9)**3*(a + 1)/3
Let i(z) be the third derivative of z**5/210 - z**4/28 + 4*z**2. Factor i(u).
2*u*(u - 3)/7
Let s(k) be the first derivative of 2*k**4 - 4*k + 22/3*k**3 + 5*k**2 - 7. Factor s(r).
2*(r + 1)*(r + 2)*(4*r - 1)
Let a be (54/(-15) - -3) + 370/450. What is t in -2/3*t**3 - 2/9*t**4 - a*t**2 + 4/9 + 2/3*t = 0?
-2, -1, 1
Let a = 463/6 + -77. Let s(h) be the third derivative of 0 - 3*h**2 - 1/30*h**5 - a*h**4 - 1/3*h**3 + 0*h. Solve s(x) = 0 for x.
-1
Factor -6 - 3*f - 10*f**2 + 10*f**2 + 9*f**2 + 4*f**4 + 3*f**3 - 7*f**4.
-3*(f - 2)*(f - 1)*(f + 1)**2
Let u(y) = -8*y**2 + 11*y + 2. Let i(a) = -9*a**2 + 12*a + 3. Let z = 24 - 15. Suppose -3*j = -z - 6. Let s(n) = j*i(n) - 6*u(n). Determine g so that s(g) = 0.
1
Let w(l) be the third derivative of -125*l**8/112 + 20*l**7/7 + 4*l**6 - 67*l**5/10 + 29*l**4/8 - l**3 - 24*l**2. D