*c.
2*(c + 1)**3*(c + 5)/11
Suppose -306 = -18*o - 0*o. Let r be -12*((-5)/(-4) - 2). Determine h, given that h**4 + 6*h**4 + r*h**3 - 4*h**4 - 11*h**2 + o*h**2 = 0.
-2, -1, 0
Let b be (-12)/(-21) + (-28960)/210. Let t = b - -140. Solve -8/3 - 2/3*n**4 + 2*n**2 + 4/3*n**3 - t*n = 0.
-1, 2
Let x be ((-50)/(-5) - 11)/(-3 - (-32)/12). Let 0 + h**2 - h**4 + 1/4*h - 1/4*h**x = 0. Calculate h.
-1, -1/4, 0, 1
Let c(f) be the third derivative of -8/3*f**3 - 1/6*f**6 + 5*f**2 + 0*f + 0 - 17/15*f**5 - 8/3*f**4. Factor c(d).
-4*(d + 1)*(d + 2)*(5*d + 2)
Suppose -3*i + 9/2 + 1/2*i**2 = 0. What is i?
3
Factor -p**3 + 11*p - 9*p**2 - 4*p**4 - 11*p + 3*p**4 + 11*p**2.
-p**2*(p - 1)*(p + 2)
Factor -32/3*q**2 + 0*q - 4*q**3 + 2/3*q**4 + 0.
2*q**2*(q - 8)*(q + 2)/3
Find k, given that 5/4*k**2 - 1/4*k**3 - 2*k + 1 = 0.
1, 2
Factor 1/4*b**3 + 3/4*b**2 + 0 - 5/2*b.
b*(b - 2)*(b + 5)/4
Suppose -12*c + 5*a = -13*c - 12, 5*a + 4 = -2*c. Suppose -2*l - r + 5*r + c = 0, -2*l + 2*r = -4. Factor 16/17*o**2 + 2/17*o**4 + 8/17*o + l + 10/17*o**3.
2*o*(o + 1)*(o + 2)**2/17
Let w(y) = y**3 - 9*y**2 - 3*y + 4. Let l be w(8). Let v be (-2)/(-4)*(-48)/l. Solve 0 + v*p**2 - 4/7*p = 0 for p.
0, 2
Let y = -11632/3 - -3884. Factor -4/3*z**2 + 8 + y*z.
-4*(z - 6)*(z + 1)/3
Let o be (6 - 7485/1250)/(18/5). Let j(g) be the third derivative of 0 - g**2 + o*g**5 + 1/30*g**3 - 1/60*g**4 + 0*g. Find a such that j(a) = 0.
1
Let h = -249 - -751/3. Let w(n) be the first derivative of h*n**2 + 4/3*n + 2 - 11/9*n**3 + 1/4*n**4. Determine l, given that w(l) = 0.
-1/3, 2
Let x(t) = 6*t**4 + 12*t**3 + 28*t**2 + 18*t - 2. Let j(s) = 2*s**4 - s**3 + s - 1. Let y(l) = 2*j(l) - x(l). Factor y(n).
-2*n*(n + 1)*(n + 2)*(n + 4)
Let q be (-9)/(-15)*16/3. Let w be (-56)/30*((-360)/42 + 6). Determine y so that 12/5*y**2 - w*y - 2/5*y**3 + q = 0.
2
Let b be 1*(-10)/(1 - 3). Solve 9*s**4 - 5*s**5 + b*s**5 - 9*s**3 - 3*s**5 + 3*s**2 = 0.
0, 1
Suppose 468 = -105*o + 108*o. Let q = -460/3 + o. Factor 1/3*f**2 - q*f + 16/3.
(f - 4)**2/3
Let a = 4/555 - -1649/2220. Let g(i) be the first derivative of 5 + 0*i - a*i**4 + 5/4*i**3 + 3/20*i**5 - 3/4*i**2. Suppose g(d) = 0. What is d?
0, 1, 2
Factor -303 + 2*r + 625 - 310 - 14*r**2.
-2*(r - 1)*(7*r + 6)
Factor -1/3*p**3 + 2 + 5/3*p - 2/3*p**2.
-(p - 2)*(p + 1)*(p + 3)/3
Let k be (-4)/(-1) - (64989/7380 + -5). Let h = 1/164 + k. Factor -4/5*v - h*v**2 - 3/5.
-(v + 1)*(v + 3)/5
Find u such that -3/2*u**4 + 30*u + 0 - 33/2*u**3 - 12*u**2 = 0.
-10, -2, 0, 1
Let o(m) = 3*m**2 + 18*m - 6. Let j(t) = 7*t**2 + 36*t - 13. Let z(a) = -6*j(a) + 13*o(a). Determine c so that z(c) = 0.
0, 6
Solve 3/4*j**4 - j - 3*j**2 - j**5 + 0 + 17/4*j**3 = 0.
-2, -1/4, 0, 1, 2
Factor 61 + 2*g**3 + 7*g**2 - 106*g**2 - 276*g - 269 - 6*g**3 + 27*g**2.
-4*(g + 1)*(g + 4)*(g + 13)
Let c(m) be the second derivative of m**5/35 - m**4/21 - 4*m**3/7 + 121*m. Factor c(x).
4*x*(x - 3)*(x + 2)/7
Factor -191/3*b**2 + 0 - 2/3*b.
-b*(191*b + 2)/3
Let x(q) = -6*q - 1. Let n be x(-1). Suppose -2*h - n*w - 1 = -27, w = 4. What is d in -4*d**5 - 6*d**2 - 10*d**4 - 2*d**2 + 10*d**5 - 12*d**4 + 24*d**h = 0?
0, 2/3, 1, 2
Let d = 4267 + -4265. Factor 0 + 0*r - 16/3*r**3 + 4/3*r**4 + 4*r**d.
4*r**2*(r - 3)*(r - 1)/3
Suppose x - 20 = -4*x. Factor 0*i + 3*i - i**3 + 2*i**3 - x*i**3.
-3*i*(i - 1)*(i + 1)
Let p(q) be the first derivative of -3*q**4/4 + q**3 + 3*q**2 + 29. Factor p(h).
-3*h*(h - 2)*(h + 1)
Let b(j) = -2*j**2 + 574*j - 40322. Let c(v) = -26*v**2 + 7460*v - 524188. Let d(q) = -76*b(q) + 6*c(q). Find y such that d(y) = 0.
142
Let l(r) = 8*r**2 + 9*r + 5. Let n be l(-1). Let z(q) be the first derivative of 0*q + 0*q**2 + 0*q**3 + 1/2*q**n + 2/5*q**5 + 8. Factor z(t).
2*t**3*(t + 1)
Let j(d) = -2*d**4 + 32*d**3 - 76*d**2 + 68*d - 22. Let w(g) = 2*g**4 - 31*g**3 + 75*g**2 - 68*g + 22. Let n(m) = 3*j(m) + 4*w(m). Factor n(h).
2*(h - 11)*(h - 1)**3
Let h(r) be the second derivative of -2*r**6/15 - 6*r**5/5 - 13*r**4/3 - 8*r**3 - 8*r**2 + 2*r + 55. Suppose h(w) = 0. Calculate w.
-2, -1
Let u(c) = 5*c**2 + 204*c + 145. Let v(b) = 45*b**2 + 1845*b + 1305. Let h(j) = 55*u(j) - 6*v(j). Factor h(l).
5*(l + 1)*(l + 29)
Let t(g) = -512*g**3 - 1147*g**2 - 859*g - 221. Let m(v) = -256*v**3 - 574*v**2 - 430*v - 110. Let j(x) = 5*m(x) - 2*t(x). Factor j(o).
-4*(4*o + 3)**3
Let h(b) be the third derivative of -b**6/240 + 3*b**5/20 - 35*b**4/16 + 49*b**3/3 + 2*b**2 + 182*b. Find j such that h(j) = 0.
4, 7
Factor 70/9*z**3 + 2/9*z + 8*z**2 + 0.
2*z*(z + 1)*(35*z + 1)/9
Let b(w) = -w**2 - 15*w + 16. Let x be b(-7). Suppose 0 = -16*d + x - 8. Factor 2/7*h**2 - 2/7*h - 2/7*h**d + 2/7*h**3 + 0.
-2*h*(h - 1)**2*(h + 1)/7
Let x(n) be the first derivative of 11 + 36*n + 48*n**2 + 4/5*n**5 + 88/3*n**3 + 8*n**4. Solve x(w) = 0 for w.
-3, -1
Let d(g) = g**2 - 13*g + 22. Let b be d(2). Factor b + 2/15*u**2 + 0*u - 2/15*u**3.
-2*u**2*(u - 1)/15
Let p(n) be the first derivative of n**3/6 - 21*n**2/2 + 441*n/2 - 264. Factor p(c).
(c - 21)**2/2
Let v = -2/1467 + 4405/2934. Suppose -3 + 9/2*p - v*p**2 = 0. What is p?
1, 2
Let d = 4 - 10. Let r(f) = f**5 + f**3 - f. Let x(p) = -2*p**5 - 8*p**4 - 6*p**3 + 8*p**2 + 2*p. Let g = -122 + 121. Let y(q) = d*r(q) + g*x(q). Factor y(j).
-4*j*(j - 1)**3*(j + 1)
Suppose -3*a - 6*j + 5*j + 12 = 0, 2*a + 4*j = 18. Solve -2/11*x**a + 0 + 2/11*x + 0*x**2 = 0.
-1, 0, 1
Let g = 4813/21456 + -5/2384. Factor -4/9*z - 2/9*z**2 - g.
-2*(z + 1)**2/9
Let a = 5820 - 5817. Solve 12/13*k**2 - 64/13 - 2/13*k**a + 0*k = 0.
-2, 4
Let l(a) = a**3 - 3*a**2 + 3*a - 5. Let p be l(4). Suppose u - p = -5*x, x = -x + 8. Find k, given that 2*k - 7*k**3 - u + 2*k**3 + 3*k**2 + 2*k**3 + k = 0.
-1, 1
Factor -16/11*x**2 + 2/11*x**3 - 20/11 - 38/11*x.
2*(x - 10)*(x + 1)**2/11
Suppose -3*b + 17 + 29*b - 5*b + 61 + 24*b + 3*b**2 = 0. What is b?
-13, -2
Let y be 134/(-17) - (50/10 - 13). Find r, given that y*r**2 + 2/17 - 4/17*r = 0.
1
Let c = 258 - 255. Suppose 20 = 2*a + c*a - 5*w, 3*w + 2 = -2*a. Let -4/3*y - 8/3 + 4/3*y**a = 0. Calculate y.
-1, 2
Let g(h) be the third derivative of -4*h**2 + 0*h + 0*h**4 + 1/8*h**6 - 7/6*h**3 - 1/12*h**5 + 0. Let n(m) be the first derivative of g(m). Factor n(x).
5*x*(9*x - 2)
Suppose 0 = -3*b + 3*p + 2*p, -5*b = p. Suppose b = -2*q + 38 - 32. Factor 8/3 + 10/3*d**2 - 2/3*d**q - 16/3*d.
-2*(d - 2)**2*(d - 1)/3
Suppose -63*r + 20 + 42 = -127. Factor 2/3 - 8/3*q**r - 8/3*q + 4*q**2 + 2/3*q**4.
2*(q - 1)**4/3
Let k(g) = 2*g**2 + 26*g + 25. Let d be k(-19). Let y = -2777/11 + d. Suppose 0 - y*b**3 + 2/11*b**4 - 2/11*b**2 + 4/11*b**5 + 2/11*b = 0. What is b?
-1, 0, 1/2, 1
Let o(q) = q**2 - 50*q + 80. Let w(l) = l**2. Let v(u) = o(u) + 4*w(u). What is b in v(b) = 0?
2, 8
Suppose 2*n - 5*n = -6. Let c be 1/n + (-3)/(-2). What is s in -s - 7 + s**c - 5*s + 10 + 2*s**2 = 0?
1
Find o, given that -6/7*o**2 + 2/7*o**3 + 0 - 8/7*o = 0.
-1, 0, 4
Suppose -2*u + 4 = -0*u. Suppose w = -4, 3*v + v - u*w - 16 = 0. Factor 0 - 1/2*g**v - 1/2*g.
-g*(g + 1)/2
Factor -6*n**3 - 288*n**2 + 132*n + 23*n**3 + 54*n**3 - 7*n**3 - 16.
4*(n - 4)*(4*n - 1)**2
Let z(k) be the first derivative of -2*k**3 - 2/5*k**5 - 4*k**2 + 8*k + 2*k**4 + 16. Factor z(v).
-2*(v - 2)**2*(v - 1)*(v + 1)
Let n be 0/(1/(1 + 12/(-8))). Suppose z + n = 2. Factor -6/7*x**3 + 3/7*x**z + 0*x + 0 + 3/7*x**4.
3*x**2*(x - 1)**2/7
Let h(n) = 6*n - 3. Let u be h(1). Let u*d**3 - 3*d**4 - 1031 + d**5 + 1031 - d**2 = 0. Calculate d.
0, 1
Let y = 0 + 2. Let r(v) = 17*v + 799. Let f be r(-47). Solve f - 4/5*i**y - 6/5*i - 2/15*i**3 = 0 for i.
-3, 0
Determine g, given that -1/2*g**3 + 3844 - 1798*g - 61*g**2 = 0.
-62, 2
Let n(y) be the first derivative of 5*y**6/36 - y**5/30 - 5*y**4/8 - 7*y**3/18 + y**2/6 + 101. Find z such that n(z) = 0.
-1, 0, 1/5, 2
Let z = -63 - -255. Let r = 192 - z. Factor 1/2*s**3 + s + r + 3/2*s**2.
s*(s + 1)*(s + 2)/2
Let s(j) be the first derivative of -j**5 + 25*j**4/4 - 10*j**3 + 270. Factor s(h).
-5*h**2*(h - 3)*(h - 2)
Let b(p) = 3*p**4 - 22*p**3 - 62*p**2 - 52*p + 5. Let t(g) = -4*g**4 + 33*g**3 + 93*g**2 + 77*g - 7. Let f(w) = 7*b(w) + 5*t(w). Let f(u) = 0. What is u?
-7, -3, -1, 0
Let c(m) be the first derivative of -m**5/100 - m**4/4 - 5*m**3/2 - 8*m**2 + 15. Let k(n) be the second derivative of c(n). Factor k(h).
-3*(h + 5)**2/5
