) be the first derivative of 2/27*u**3 + 2/9*u**2 + 0*u + 12. Suppose l(x) = 0. Calculate x.
-2, 0
Let l(y) = y**3 + 2*y**2 + 2*y + 1. Let o(r) = 30*r**3 + 150*r**2 - 350*r + 755. Let h(v) = 35*l(v) - o(v). Factor h(t).
5*(t - 6)**2*(t - 4)
Let h be 4/13 + (-1540)/(-572). Let n(i) be the first derivative of 6 - 4*i**2 + 0*i - 4/3*i**h. Factor n(x).
-4*x*(x + 2)
Let b = -33 - -35. Let f be b/(-6) + 49/84. Factor 0*v**3 + 0 + 1/2*v**4 + 1/4*v - 1/2*v**2 - f*v**5.
-v*(v - 1)**3*(v + 1)/4
Solve -v**5 - 2*v**5 + 2*v**3 + 5*v**4 + 430*v - 430*v = 0 for v.
-1/3, 0, 2
Let v(o) be the third derivative of 1/132*o**4 + 0 + 0*o + 1/1848*o**8 + 0*o**3 + 1/110*o**6 + 2/165*o**5 + 4/1155*o**7 - 18*o**2. Find y, given that v(y) = 0.
-1, 0
Let c(z) be the first derivative of -z**8/3360 - z**7/420 - z**6/180 + 4*z**3/3 + 2. Let m(t) be the third derivative of c(t). Factor m(q).
-q**2*(q + 2)**2/2
Let b(t) = -t**3 + t**2 - 3*t. Let c(n) = -n**4 + 124*n**3 - 3602*n**2 + 6746*n. Let k(s) = 6*b(s) + c(s). Factor k(z).
-z*(z - 58)**2*(z - 2)
Let j(y) = 2 + 0*y + 8*y**2 - 12*y - 10*y**2. Let v(x) = 2*x**2 + 13*x - 3. Let f(g) = -3*j(g) - 2*v(g). Factor f(k).
2*k*(k + 5)
Let o(a) be the second derivative of a**7/63 - 2*a**5/15 - a**4/9 + a**3/3 + 2*a**2/3 - a + 27. Factor o(b).
2*(b - 2)*(b - 1)*(b + 1)**3/3
Let u be ((-6)/10)/(-28*8/160). Let -u - 6/7*l - 3/7*l**2 = 0. What is l?
-1
Suppose 0 = -5*z - z. Let 64 - 40*m**3 - 160*m + 71*m**2 + 3*m**4 + z*m**4 + 61*m**2 + m**4 = 0. What is m?
1, 4
Let z = 128 + -129. Let n(q) = -6*q - 3. Let p be n(z). Find s, given that -5/4*s**p - 25/4*s**2 - 35/4*s - 15/4 = 0.
-3, -1
Suppose v = -1 + 127. Determine u so that 59*u**2 + 69*u**4 + 1 - 20*u**2 - 12*u**5 - 6*u - 10 + 45*u**2 - v*u**3 = 0.
-1/4, 1, 3
Let l(n) = n**2 - 4*n - 18. Let u be l(6). Let y be 1 + -2 + (-87)/u. What is k in 9/2*k**2 - 1/2*k**3 + 27/2 - y*k = 0?
3
Let b(j) be the second derivative of -2/75*j**5 + 0 + 0*j**3 + 1/60*j**4 - 2*j - 5/2*j**2. Let g(d) be the first derivative of b(d). What is r in g(r) = 0?
0, 1/4
Let o(b) = -2*b**5 - b**2 - b + 1. Let q(t) = 3*t**5 - 18*t**4 - 39*t**3 - 33*t**2 - 9*t - 3. Let h(c) = 3*o(c) + q(c). Factor h(s).
-3*s*(s + 1)**2*(s + 2)**2
Let q = -16973/5 + 3395. Factor 2/5*j**3 + q - 2/5*j**2 - 2/5*j.
2*(j - 1)**2*(j + 1)/5
Let z(r) be the second derivative of 0 - 3/20*r**5 + 3/2*r**4 + 18*r - 9/2*r**3 + 6*r**2. Let z(t) = 0. What is t?
1, 4
Suppose 5/11*p - 4/11*p**2 - 2/11 + 1/11*p**3 = 0. Calculate p.
1, 2
Let j = 88 + -84. Let y(l) = l**2 - l + 1. Let q(a) = -a**3 + 11*a**2 - 29*a + 29. Let x(p) = j*y(p) - 2*q(p). Factor x(f).
2*(f - 3)**3
Let s be -40*(-22)/(-968)*-4. Let 2/11*b**4 + s*b**3 + 162/11 + 236/11*b**2 + 360/11*b = 0. Calculate b.
-9, -1
Suppose 17 = -2*i + 25. Determine v so that -6*v + 1078*v**3 - 1354*v - 320 + 43*v**3 + 104*v**3 + 1715*v**i - 1260*v**2 = 0.
-4/7, 1
Suppose 4*k - 5*k + 7 = 0. Factor -a**3 + 0*a**4 + 5*a**4 - 13*a**4 + 2*a**2 + k*a**4.
-a**2*(a - 1)*(a + 2)
Let o be (3 - -3) + (-32)/4 + 2. Let p(d) be the third derivative of 0*d**3 + 7*d**2 + 0*d - 1/9*d**4 + 1/180*d**6 + 0*d**5 + o. Factor p(i).
2*i*(i - 2)*(i + 2)/3
Let r be (20/(-20))/((-83)/(-23) - 1). Let j = r + 17/15. Factor 1/4*a**2 - j*a + 1/2.
(a - 2)*(a - 1)/4
Let x(o) be the first derivative of o**4/2 - 70*o**3/3 + 67*o**2 - 66*o - 370. Factor x(i).
2*(i - 33)*(i - 1)**2
Let u be 7*(2/(-4) + -1 + 17/10). Suppose 0 - 1/5*n**2 - u*n = 0. Calculate n.
-7, 0
Let a(u) = -3 - 13*u + 17 + 4*u**2 + 0*u**2 - 5*u**2. Let k be a(-14). Factor 0*q + 6/5*q**3 + 8/5*q**4 + k - 2/5*q**2.
2*q**2*(q + 1)*(4*q - 1)/5
Let s(u) be the third derivative of u**6/360 + u**5/120 + 7*u**3/6 + 14*u**2. Let c(i) be the first derivative of s(i). Let c(k) = 0. Calculate k.
-1, 0
Let g = -2/1697 - -13586/8485. Let q = 0 - -3. Find n, given that -g*n**2 + 24/5*n**q + 18/5*n**4 + 0*n + 0 - 14/5*n**5 = 0.
-1, 0, 2/7, 2
Suppose 4*y = -0*y + s + 155, -2*s = 6. Factor 2 - y + 20*h + 12 + 0*h**2 - 4*h**2.
-4*(h - 3)*(h - 2)
Suppose -113*h + 105*h + 40 = 0. Suppose 4*i - h*n = 2, 5*n + 3 - 4 = 3*i. Factor -6/7*l**2 + 2/7*l**4 + 2/7*l**i + 4/7 - 2/7*l.
2*(l - 1)**2*(l + 1)*(l + 2)/7
Let k(p) = -p**3 + 6*p**2 - 4*p + 1. Let f be k(5). Let q be -6*(-2)/9*f/14. Suppose 2*l**5 + 0 + 54/7*l**3 + q*l + 26/7*l**2 + 46/7*l**4 = 0. Calculate l.
-1, -2/7, 0
Let p(g) be the third derivative of -g**5/120 + 281*g**4/24 - 78961*g**3/12 - 945*g**2. Factor p(r).
-(r - 281)**2/2
Let v(j) be the second derivative of -7*j**6/30 + 53*j**4/84 - 2*j**2/7 + 28*j. Let v(h) = 0. Calculate h.
-1, -2/7, 2/7, 1
Suppose -w - 4*w = -25. Suppose -p + w*c = 3, p + 0*p - 7 = -5*c. Determine a so that p + 4*a**4 - 6*a**4 - 2 + 2*a**3 = 0.
0, 1
Let w = -235 + 332. Let -13 + 25*y**2 - 23 - w*y + 55*y**2 - 14*y**3 - 5*y = 0. What is y?
-2/7, 3
Let m(v) be the third derivative of -1/180*v**5 + 0 + 0*v - 1/180*v**6 + 0*v**3 - 18*v**2 - 1/630*v**7 + 0*v**4. What is x in m(x) = 0?
-1, 0
Solve 335*k - 11163 - 3*k**2 + 60*k - 29*k = 0 for k.
61
Let s(x) be the first derivative of -3/7*x + 5 + 0*x**2 + 1/7*x**3. Determine u so that s(u) = 0.
-1, 1
Let d(s) be the third derivative of -s**8/588 - 128*s**7/735 - 33*s**6/5 - 504*s**5/5 - 441*s**4/2 - 61*s**2. Factor d(h).
-4*h*(h + 1)*(h + 21)**3/7
Let a(l) = -l + 2. Let b be a(-1). Suppose -7*n + b*n + 40 = 0. Determine o so that 11*o**2 + o**3 - 5*o**2 - n*o**2 = 0.
0, 4
Let g(t) be the third derivative of -t**7/630 + t**5/90 + 19*t**3/3 - 26*t**2. Let m(z) be the first derivative of g(z). Factor m(l).
-4*l*(l - 1)*(l + 1)/3
Let 12*a**2 + 3*a**3 - 404*a + a**2 + 380*a - 7*a**2 = 0. Calculate a.
-4, 0, 2
Let i be 14/(-12)*(2055/700 - 3). Let w(o) be the second derivative of -1/12*o**3 - i*o**5 - 1/60*o**6 - 3*o + 0*o**2 + 0 - 1/8*o**4. Factor w(b).
-b*(b + 1)**3/2
Let r(s) = -3*s**3 - 10*s - 9. Let u be r(-1). Let y(q) be the first derivative of 0*q**2 + 2 + 1/9*q**3 - 1/12*q**u + 0*q. Factor y(w).
-w**2*(w - 1)/3
Let r(s) = -381*s + 4576. Let f be r(12). Let 64/3*w - 32*w**2 - f*w**4 + 52/3*w**3 + 0 + 1/3*w**5 = 0. What is w?
0, 2, 4
Suppose 5*g - 26 = -4*h - 0*g, 0 = -5*g + 10. Let m(s) be the first derivative of 1/4*s**6 + 3/2*s**h - 15/4*s**2 - s**3 - 3*s + 6/5*s**5 + 4. Factor m(r).
3*(r - 1)*(r + 1)**3*(r + 2)/2
What is n in 1681/4 + 1/4*n**2 + 41/2*n = 0?
-41
Let i(h) be the second derivative of -2*h**6/15 + 6*h**5/5 + 7*h**4/3 + 210*h. Suppose i(b) = 0. Calculate b.
-1, 0, 7
Let z be ((-13)/3)/((-2)/6). Let y be z/12*3 - 6/24. Solve 1/5*x**y + 0 + 0*x**2 + 0*x = 0.
0
Let y(j) be the first derivative of -j**7/5460 - j**6/1170 + j**5/780 + j**4/78 + 19*j**3/3 - 13. Let l(z) be the third derivative of y(z). Factor l(i).
-2*(i - 1)*(i + 1)*(i + 2)/13
Let x(q) be the third derivative of -1/160*q**6 + 0*q**3 + 0*q**4 + 22*q**2 + 0*q + 0 + 1/120*q**5. Factor x(l).
-l**2*(3*l - 2)/4
Let s(a) be the first derivative of a**4/2 + 104*a**3/3 - a**2 - 104*a + 49. Find g, given that s(g) = 0.
-52, -1, 1
Suppose -11*y = 119 - 141. Let 0 - 9/8*r - 3/8*r**y = 0. Calculate r.
-3, 0
Let f = -25 - -16. Let n = -4 - f. Find j, given that -4*j**3 + n*j**3 - 4*j**2 + 10*j - 2 - 5*j = 0.
1, 2
Suppose -2/13*y**4 + 6/13 + 8/13*y**3 - 8/13*y - 4/13*y**2 = 0. What is y?
-1, 1, 3
Let c be ((-13)/26)/(-3*(-26)/(-8)). Let p(a) be the first derivative of -c*a**3 + 2/13*a**2 - 4 + 6/13*a. Find r such that p(r) = 0.
-1, 3
Let g = 59393/51975 - -1/7425. Factor g + 2/7*o**2 - 8/7*o.
2*(o - 2)**2/7
Suppose 0 = -3*n - 2*w + 14, -2*n + 9 = n - 3*w. Let o(k) = 4*k - 122. Let t be o(31). Factor -2*f - 4*f**2 + 4*f**2 + n - 2*f**t.
-2*(f - 1)*(f + 2)
Let l(c) be the second derivative of -3*c**5/5 + 23*c**4/3 + 16*c**3/3 - 660*c. Factor l(d).
-4*d*(d - 8)*(3*d + 1)
Suppose 0 = 3*z + 1240 - 1249. Let a(h) be the first derivative of 2 + 3/2*h**2 + 6/5*h - 2/5*h**z - 3/4*h**4. Factor a(y).
-3*(y - 1)*(y + 1)*(5*y + 2)/5
Determine p so that -16/5*p - 2/5*p**2 - 32/5 = 0.
-4
Let j(p) be the first derivative of 1/2*p**3 - 9/4*p**2 + 3/10*p**5 - 3*p + 9/8*p**4 - 4. Factor j(q).
3*(q - 1)*(q + 1)**2*(q + 2)/2
Let x(i) = -i**3 - 5*i**2 - i. Let o be x(-5). Let -11*q**2 - 24*q**4 + 29*q**4 - 14*q - o*q**3 - 14*q**2 - q = 0. What is q?
-1, 0, 3
Let q(t) = -t**5 - 13*t**4 - 2*t**3 + 12*t**2 + 2. Let i(g) 