2*l - 131 - l**2 + t = 0.
-2, 0
Suppose 11*g - 15*g = 72. Let n be (g/40)/((-27)/45). Factor -1/4*o**2 - n + 5/4*o - 1/4*o**3.
-(o - 1)**2*(o + 3)/4
Let p be -5 - -5*(5 - 1)/4. Let o(c) be the second derivative of p + c + 1/12*c**4 + c**2 - 1/2*c**3. Determine u so that o(u) = 0.
1, 2
Let z(c) = 14*c**2 - 77*c - 115. Let i(n) = 5*n**2 - 27*n - 38. Let q(p) = 11*i(p) - 4*z(p). Determine w so that q(w) = 0.
-3, 14
Suppose -5*x = -4*n + 70, -6*n + 3*x + 51 = -3*n. Suppose -n*s = -19*s. Factor 2/7*g**2 + s - 1/7*g**3 - 1/7*g.
-g*(g - 1)**2/7
Suppose 2*f + 39 = -211. Let j = 877/7 + f. Determine c so that 0*c + j*c**4 - 2/7*c**2 + 0*c**3 + 0 = 0.
-1, 0, 1
Let b be 1/2 - (-42)/4. Let h be 2 + b/(-4) - 63/(-28). Let 3/2*u**2 + 0 - h*u = 0. What is u?
0, 1
Let t(w) be the third derivative of w**6/96 - 103*w**5/240 - 19*w**4/12 - 11*w**3/6 - 342*w**2. Suppose t(l) = 0. What is l?
-1, -2/5, 22
Let -4/9*m**2 + 16/9 - 8/9*m + 2/9*m**3 = 0. What is m?
-2, 2
Let v(f) be the third derivative of 3/20*f**5 - 1/20*f**6 + 0*f**3 + 0*f**4 - 1/70*f**7 + 0*f + 0 - 4*f**2. Factor v(k).
-3*k**2*(k - 1)*(k + 3)
Let f(k) = -7*k**2 + 160*k - 5932. Let d(w) = 2*w**2 - 2*w + 1. Let s(n) = -15*d(n) - 5*f(n). Factor s(l).
5*(l - 77)**2
Let b be 1/10 + (-4161)/(-2190). Factor -2/15*n**4 - 8/15*n - 8/15*n**3 - 4/5*n**b - 2/15.
-2*(n + 1)**4/15
Let t(k) be the second derivative of -2*k**6/15 + 6*k**5/5 - 3*k**4 + 8*k**3/3 + 23*k. Factor t(a).
-4*a*(a - 4)*(a - 1)**2
Let p(n) = n**2 + n - 1. Let k(r) = 9 - 2 + 3*r**2 - 3*r - r. Let o(c) = -c**3 + 6*c**2 + c - 8. Let m be o(6). Let s(l) = m*p(l) + k(l). Factor s(v).
(v - 3)**2
Let b(r) = -1 - 9*r**2 + 4*r - 4*r. Let z(v) be the second derivative of 2*v**4/3 - 17*v. Let i(t) = -4*b(t) - 5*z(t). Let i(m) = 0. What is m?
-1, 1
Let j(h) = h**2 - 12*h + 25. Let m be j(10). Suppose b - 2*n - 13 + 1 = 0, -m*b + 25 = -3*n. Factor 12*l**3 - 9*l**3 + l + 2*l - 6*l**b.
3*l*(l - 1)**2
Let m(j) = -7*j**2 + 440*j - 12097. Let u(p) = 15*p**2 - 880*p + 24193. Let x(d) = -7*m(d) - 3*u(d). Factor x(k).
4*(k - 55)**2
Let z(y) = 3*y**2 + y - 2. Let b(u) = 2*u**2 + 94*u + 92. Let n(k) = -b(k) + 2*z(k). Factor n(v).
4*(v - 24)*(v + 1)
Let 18/5*g**3 + 8/5*g**4 - 148/5*g**2 - 8 - 198/5*g = 0. Calculate g.
-5, -1, -1/4, 4
Suppose -4*r + 4/5*r**2 - 24/5 = 0. What is r?
-1, 6
Let w(o) = 8*o**3 - 8*o**2 - 12*o. Let i(p) = 7*p**3 - 7*p**2 - 12*p. Let a(x) = 8*x - 18. Let s be a(3). Let l(c) = s*i(c) - 5*w(c). Factor l(u).
2*u*(u - 3)*(u + 2)
Let r = 73 - 49. Suppose r*g - 13*g - 22 = 0. Determine p so that 0 + 7/4*p**5 + 23/4*p**4 + 5*p**3 + 0*p + p**g = 0.
-2, -1, -2/7, 0
Let n(r) = 58 - 100*r - 12 + 96*r. Let g be n(11). Solve 2/3*i**g - 5/3*i + 1 = 0.
1, 3/2
Find k, given that -82/21*k**3 + 30/7*k - 8/21*k**5 + 74/21*k**2 + 22/21 - 32/7*k**4 = 0.
-11, -1, -1/2, 1
Factor 2601*h**2 + 3*h + h - 2625*h**2 + 12*h**5 - 40*h**4 + 48*h**3.
4*h*(h - 1)**3*(3*h - 1)
Suppose 7*l = 9 - 9. Let g(w) be the third derivative of -1/300*w**5 - 4*w**2 + 0*w + 1/60*w**4 - 1/30*w**3 + l. What is t in g(t) = 0?
1
Suppose -5*n + 21 = 3*v - 10, -24 = -2*v - 4*n. Suppose -5*b + 19 = j + 2*j, 0 = 2*j - v*b - 2. Factor 2/7*s**2 + 0*s + 0 - 2/7*s**j.
-2*s**2*(s - 1)/7
Suppose 5*j - 23*j + 36 = 0. Let s(o) be the third derivative of -4/33*o**3 + 0*o + 1/33*o**4 + 3*o**j - 1/330*o**5 + 0. Factor s(d).
-2*(d - 2)**2/11
Suppose 4*i - 13 = 3*f, i - 4*i = 3*f + 6. Let y be 7/7*3/i. Factor 2*h - 89*h**2 - 3*h + 86*h**2 - h**4 - y*h**3.
-h*(h + 1)**3
Let x(c) be the first derivative of c**7/1400 - c**6/300 - 3*c**5/200 + 16*c**3/3 + 37. Let j(g) be the third derivative of x(g). Find k such that j(k) = 0.
-1, 0, 3
Let t(f) = 127*f + 1147. Let b be t(-9). Suppose b + 2*a + 1/4*a**2 = 0. Calculate a.
-4
Let w(g) = 5*g**4 - 4*g**3 - 8*g**2 - 2*g - 3. Let k(i) = 6*i**4 - 5*i**3 - 9*i**2 - 2*i - 4. Let c(a) = -3*k(a) + 4*w(a). Factor c(t).
t*(t - 2)*(t + 1)*(2*t + 1)
Let z(d) = -d**3 - 3*d**2 + 39*d - 8. Let l be z(-8). What is w in l + 4/15*w**2 + 0*w - 2/5*w**3 + 2/15*w**4 = 0?
0, 1, 2
Let o = -102 + 106. Factor -4*b**o + 12*b**2 + 381 - 373 + 4*b**3 - 20*b + 0*b**4.
-4*(b - 1)**3*(b + 2)
Let h(n) be the second derivative of 0 + 1/2*n**4 + 18*n - 4*n**2 + 1/5*n**5 - 1/15*n**6 - 4/3*n**3. Factor h(f).
-2*(f - 2)**2*(f + 1)**2
Factor -18/5*m - 1/5*m**2 + 19/5.
-(m - 1)*(m + 19)/5
Let p = -2648 + 2650. Factor 1/2*v**5 - 5*v**p - 5/2*v**4 + 5*v**3 + 5/2*v - 1/2.
(v - 1)**5/2
Let m(n) be the second derivative of -5/38*n**4 - 20*n - 1/190*n**5 - 125/19*n**2 + 0 - 25/19*n**3. Suppose m(k) = 0. Calculate k.
-5
Let f(t) = -2*t**2 - 9*t + 1. Let a be f(-4). Factor 183*p**4 - 203*p**4 + 20*p - 5*p**3 + 50*p**2 - 40 - a*p**5 + 0.
-5*(p - 1)**2*(p + 2)**3
Suppose 1/2*z**4 + 7/2*z**3 + 13/2*z**2 - 9 - 3/2*z = 0. What is z?
-3, -2, 1
Factor -319 - a**2 - 356 - 2*a**2 + 90*a.
-3*(a - 15)**2
Suppose -9*f + 3274 = -2810. Let -143*q + 4*q**2 + 0*q**2 + f + 39*q = 0. Calculate q.
13
Suppose -11*p - 5*p = -416. Suppose -213 - 219 - 8*k + p*k**2 + 424 - 10*k**3 = 0. What is k?
-2/5, 1, 2
Let k = -39597 + 752349/19. Factor -2/19 + k*l + 8/19*l**2.
2*(l + 1)*(4*l - 1)/19
Solve -14*i**2 + 56*i + 9 + 12*i**4 - 7*i**4 + 2*i**3 + 3*i**5 - 4*i**5 + 2*i**5 - 59*i = 0 for i.
-3, -1, 1
Suppose 0 - 18*l**2 + 39/2*l**3 - 9*l**4 + 6*l + 3/2*l**5 = 0. Calculate l.
0, 1, 2
Let k(g) be the first derivative of -2/25*g**5 + 1/10*g**2 - 9 + 0*g + 0*g**4 - 1/30*g**6 + 2/15*g**3. Factor k(r).
-r*(r - 1)*(r + 1)**3/5
Suppose 11 = -4*b - 1. Let c be (1/12)/((-1)/b). Factor 19/4*z**4 + 7/4*z**5 + 15/4*z**3 + c*z**2 + 0 - 1/2*z.
z*(z + 1)**3*(7*z - 2)/4
Factor 0*c + 1/4*c**5 + 9*c**2 + 13/4*c**4 + 0 + 12*c**3.
c**2*(c + 1)*(c + 6)**2/4
Let i(v) be the second derivative of -2/15*v**3 - 7/50*v**5 - 3/10*v**4 + 0*v**2 + 0 + 13*v. Factor i(o).
-2*o*(o + 1)*(7*o + 2)/5
Let t(a) = 2*a**3 + 3*a**2 - 2*a. Let h be t(1). Suppose 3*w = 2*w - 2*s - 5, -h*s - 3 = 3*w. Find z such that -3/5*z + 0*z**2 + 0 + 3/5*z**w = 0.
-1, 0, 1
Let k(x) = -x**3 - 12*x**2 - 13*x - 17. Let f be k(-11). Let m(v) be the first derivative of -4/3*v**3 + f + 4*v - v**2 + 1/2*v**4. Solve m(z) = 0.
-1, 1, 2
Let 2/9*m**4 - 7/9*m**5 + 0 + 7/3*m**3 - 4/9*m + 8/9*m**2 = 0. What is m?
-1, 0, 2/7, 2
Let u(l) be the third derivative of 4*l**2 - 4/45*l**5 + 19/36*l**4 + 0 + 0*l - 10/9*l**3 - 1/180*l**6. Factor u(m).
-2*(m - 1)**2*(m + 10)/3
Let k(t) = 9*t - 1 - 2 - t**2 - 2. Let u be k(8). Factor 5*a**2 - 6*a**2 + 3*a + u*a**3 - 5*a**2.
3*a*(a - 1)**2
Let n(o) = -2*o**4 + 2*o**3 - 4*o**2 - 20*o - 12. Let l(g) = g**4 + g**3 - g - 1. Let f(w) = 4*l(w) + n(w). Factor f(a).
2*(a - 2)*(a + 1)*(a + 2)**2
Let u(r) = 26*r**4 - 33*r**3 - 70*r**2 - 5*r + 10. Let a(p) = 53*p**4 - 64*p**3 - 140*p**2 - 10*p + 20. Let d(v) = -4*a(v) + 7*u(v). Let d(z) = 0. Calculate z.
-1, -1/2, 1/3, 2
Let m(v) be the second derivative of v**8/10752 + v**7/1680 + v**6/640 + v**5/480 - 2*v**4/3 + 16*v. Let k(l) be the third derivative of m(l). Factor k(h).
(h + 1)**2*(5*h + 2)/8
Suppose -3/2*n**2 - 3 + 9/2*n = 0. Calculate n.
1, 2
Let t be (6/(-7))/((-895)/(-70) + -13). Find i such that 4/17*i**3 - 2/17 - 4/17*i + 0*i**2 + 2/17*i**t = 0.
-1, 1
Solve -25*r**4 + 32*r**2 + 43*r**4 - 8*r**3 + 6*r + 8 - 26*r**4 - 34*r + 4*r**5 = 0 for r.
-2, 1
Let k(r) = -8*r**5 - 26*r**4 + 36*r**3 - 12*r**2 + 10. Let c(q) = q**5 + q**4 - q**3 - 1. Let o(i) = 20*c(i) + 2*k(i). Factor o(u).
4*u**2*(u - 6)*(u - 1)**2
Suppose -c = 3*c - 12. Let y be c/15*45/18. Factor v - 1/4*v**3 + y*v**2 - 2.
-(v - 2)**2*(v + 2)/4
Let q(j) be the first derivative of -3/4*j**2 - 17 + 9/8*j + 1/8*j**3. Factor q(l).
3*(l - 3)*(l - 1)/8
Let w(s) be the first derivative of -2*s**3/15 + 7*s**2/5 + 12*s + 25. Factor w(t).
-2*(t - 10)*(t + 3)/5
Let l(c) be the second derivative of -c**6/6 + 3*c**5/4 - 10*c**3/3 + 6*c - 11. Factor l(i).
-5*i*(i - 2)**2*(i + 1)
Let j(g) be the second derivative of -g**5/30 + 4*g**4/9 - 16*g**3/9 + 2*g + 18. Suppose j(q) = 0. What is q?
0, 4
Let o be (36/27)/(-1)*-18. Suppose 0 = 4*t - 25 - 11. Factor -11*v**2 + 8*v**2 - 4*v - t*v**2 + 8 + o*v.
-4*(v - 2)*(3*v + 1)
Determine f, given that -93312/23 + 7776/23*f + 2/23*f**3 - 216/23*f**2 = 0.
36
Factor 3*f**3 + 62*f**2 + 49*f**2 + 1312*f + 280 + 692 - 232*f.
3*(f + 1)*(f + 18)**