1
Suppose -4*w + 4 = 16. Let s be (w/9)/(6/(-12)). Factor 8/3 - 8/3*n + s*n**2.
2*(n - 2)**2/3
Factor 2/9 + 4/3*y**2 + 2/9*y**4 + 8/9*y + 8/9*y**3.
2*(y + 1)**4/9
Factor -3/2 + 3/4*t**2 - 3/4*t.
3*(t - 2)*(t + 1)/4
Let r = 177 - 174. Factor 1/8 - 1/8*g**r - 1/8*g**2 + 1/8*g.
-(g - 1)*(g + 1)**2/8
Suppose 0 = 5*p + 14 + 6. Let l be p*((-10)/8 - 0). Let l*w**5 + 3*w**2 - 7*w**3 + 0*w**4 - 2*w**4 + 2*w - w**4 = 0. Calculate w.
-1, -2/5, 0, 1
Let l(z) = -8*z**4 + 10*z**3 - 5*z**2 - 12*z + 1. Let s(c) = c**4 - c**3 + c**2 + 1. Let b(i) = 5*l(i) + 35*s(i). Let b(g) = 0. Calculate g.
-2, 1, 2
Let h(f) = -4*f**3 + 31*f**2 - 41*f + 39. Let s(c) = 2*c**3 - 16*c**2 + 20*c - 20. Let r(t) = -4*h(t) - 7*s(t). Factor r(l).
2*(l - 2)**3
Let w(k) = -k**2 - 4*k - 2. Let h be w(-3). Suppose -29*s + 30*s - 3*f - 14 = 0, s + f + 2 = 0. Factor -p**s - 7/2*p**3 + 7/2*p + h.
-(p - 1)*(p + 1)*(7*p + 2)/2
Let g be ((-3)/4)/((-27)/72). Factor 0 - 3*s**3 + s**2 + 3 - 9*s + 8*s**g.
-3*(s - 1)**3
Let l(u) = -u**3 - 30*u**2 - 55*u + 33. Let s be l(-28). Find m, given that -12/7*m**2 + 0 - 16/7*m**3 + 12/7*m**4 - 2/7*m + 18/7*m**s = 0.
-1, -1/3, 0, 1
Let a(o) be the third derivative of 0*o**5 + 0*o - 1/60*o**6 + 0 + 1/24*o**4 + 0*o**3 + 1/336*o**8 + 0*o**7 - 4*o**2. Find p such that a(p) = 0.
-1, 0, 1
Let h(g) = g**2 + 2*g - 6. Let w(y) = -1. Let m(b) = h(b) - 6*w(b). Let m(c) = 0. What is c?
-2, 0
Let p(f) be the second derivative of -f**6/50 - 9*f**5/50 - f**4/4 - 17*f. Factor p(b).
-3*b**2*(b + 1)*(b + 5)/5
Let t = 454 + -1355/3. Find l such that 2/3*l**4 + t*l - 8/3*l**2 + 2/3*l**3 - 2/3 - 1/3*l**5 = 0.
-2, 1
Let b = 143/522 - 3/58. Factor 0 - b*o**3 + 0*o + 0*o**2.
-2*o**3/9
Determine c, given that 0 + 0*c**2 + 0*c + c**4 + 1/6*c**3 + 3/2*c**5 = 0.
-1/3, 0
Let q be 0 + 2 - -2 - 1. Solve -5*i**3 - 8*i - 5*i**q - 14*i**2 + 4*i = 0.
-1, -2/5, 0
Suppose 2*l = -2 + 6. Let q(i) = -i**3 + 2. Let k be q(0). Determine f so that -4*f - 3*f**2 - 2*f**l + 0*f**k + 7*f**2 = 0.
0, 2
Suppose 16 = 13*f - 23. Let x(b) be the first derivative of -3 + 8/3*b**3 + 0*b + 0*b**2 + f*b**6 + 8*b**4 + 42/5*b**5. Factor x(g).
2*g**2*(g + 1)*(3*g + 2)**2
Let n = 41 - 41. Let l(b) be the third derivative of -1/420*b**6 - 1/735*b**7 + n + 0*b**5 + 0*b**4 - 3*b**2 + 0*b + 0*b**3. Find d such that l(d) = 0.
-1, 0
Let m(k) be the first derivative of 3*k**5 - 3*k**2 + 0*k - 7/2*k**6 - 5*k**3 + 27/4*k**4 + 3. Let m(z) = 0. What is z?
-1, -2/7, 0, 1
Let d be 3/2*40/30. Determine s so that -2/5 - 2/5*s**3 - 6/5*s**d - 6/5*s = 0.
-1
Let h(x) be the third derivative of -x**5/240 - 11*x**2. Factor h(b).
-b**2/4
Let k(c) = -c**3 + 8*c**2 - 6*c - 7. Let p be k(7). Let 2 + p*n**2 - 3*n - 2*n**2 + 3*n**2 = 0. Calculate n.
1, 2
Find q such that 163*q**3 + 32*q**3 + 8*q**5 - 215*q**4 + 67*q**5 - 10*q - 45*q**2 = 0.
-2/15, 0, 1
Let g(q) be the third derivative of 1/105*q**5 + 0*q**3 + 0*q + 0 - 2*q**2 + 1/84*q**6 + 0*q**4 + 2/735*q**7. Factor g(h).
2*h**2*(h + 2)*(2*h + 1)/7
Let d(m) be the second derivative of m**4/16 - m**3/2 + 3*m**2/2 - 7*m. Let d(y) = 0. Calculate y.
2
Let z(f) = f**2 + 8*f - 6. Let n be z(-9). Suppose 2*t**2 - 2*t**5 + 4*t**n - 2*t**2 - 4*t**4 + 2*t**4 = 0. What is t?
-2, 0, 1
Let j(a) = 8*a**3 + 30*a**2 + 24*a - 5. Let z(q) = -24*q**3 - 90*q**2 - 72*q + 14. Let s = 2 + -5. Let g(m) = s*z(m) - 10*j(m). Factor g(v).
-2*(v + 2)**2*(4*v - 1)
Let a = -11/4 - -37/12. Let q = 7/5 - 1/15. Factor -q + 4/3*z - a*z**2.
-(z - 2)**2/3
Let w(z) be the first derivative of -2*z**6/3 - 8*z**5/5 - 7. Suppose w(x) = 0. What is x?
-2, 0
Let f(q) = 5*q**4 + 20*q**3 + 10*q**2 + 10*q + 5. Let s(t) = -5*t**4 - 19*t**3 - 11*t**2 - 9*t - 4. Let h(j) = -4*f(j) - 5*s(j). Suppose h(p) = 0. Calculate p.
-1, 0
Let v(z) = -2*z**2 - z + 1 + 0*z - 3 + z**3. Let l be v(3). Factor -3*o**2 + o**l - o**2 + 3*o**2.
o**2*(o - 1)*(o + 1)
Let h be (-6)/(-9) - (-15)/(-9). Let r be (-9)/(-12) + h/2. Determine z so that -r*z**2 + 0 + 0*z = 0.
0
Suppose -5*x - 41 = -4*o, -x + 5*x = -o - 16. Let t(a) = 4*a - 12. Let f be t(o). Factor 0*b**2 + 0 + 0*b - b**5 - 3/5*b**f + 2/5*b**3.
-b**3*(b + 1)*(5*b - 2)/5
Let q be 1/(2/60) + 2. Let c = q + -30. Factor -3/2*i - 1/2*i**5 - 7/2*i**c - 4*i**3 - 1/4 - 9/4*i**4.
-(i + 1)**4*(2*i + 1)/4
Factor a - 4 - a**2 + 1 + 9 - 4.
-(a - 2)*(a + 1)
Let p(o) be the third derivative of 0*o + 0 - 2*o**2 - 1/6*o**4 - 1/30*o**5 - 1/3*o**3. Suppose p(n) = 0. Calculate n.
-1
Let p = 3/170 + -6381/340. Let h = 19 + p. Find c, given that -1/4*c**3 - h*c + 0 + 1/2*c**2 = 0.
0, 1
Suppose -3*n**5 + 0*n**4 + 148*n - 149*n + 4*n**3 + 2*n**2 - 2*n**4 = 0. What is n?
-1, 0, 1/3, 1
Let r(s) = -s**2 - 6*s + 3. Let i be r(-6). Factor 0*l - 3/7*l**i + 0 - 3/7*l**2.
-3*l**2*(l + 1)/7
Let c be (2/(-4))/(10/(-40)). Find a, given that 0*a + 0 - c*a**4 + 1/2*a**2 - 3/2*a**3 = 0.
-1, 0, 1/4
Let n(q) be the first derivative of -8*q**6/5 + 216*q**5/25 - 267*q**4/20 + q**3 + 36*q**2/5 + 12*q/5 + 20. Determine k so that n(k) = 0.
-1/4, 1, 2
Suppose 2*y + 2 + 2 = 0, -w + 10 = -4*y. Let i(m) be the second derivative of 0 - 1/6*m**4 + w*m**3 - 9*m**2 + 3*m. Find z, given that i(z) = 0.
3
Let f(o) = -o**2 + 4*o - 3. Let v(c) be the first derivative of -c**2/2 + c - 3. Let l(z) = f(z) + 2*v(z). Factor l(i).
-(i - 1)**2
Let o be (-1)/(-2) + (-5)/(-2). Let r be o/((-1)/(-2)*3). Factor 0*g**2 + 6*g**2 + 1 - 2*g**r + 5*g.
(g + 1)*(4*g + 1)
Let d(l) be the first derivative of 5*l**4/4 + 5*l**3/3 - 10*l**2 - 20*l + 9. Find o, given that d(o) = 0.
-2, -1, 2
Let r = 53 - 51. Let j(i) be the first derivative of -1/4*i**4 + 2 + 2/3*i**3 + 0*i**r + 0*i. Suppose j(d) = 0. What is d?
0, 2
Factor 45*s**4 - 95*s**3 - 10*s**2 + 125*s**5 - 75*s**4 - 170*s**4.
5*s**2*(s - 2)*(5*s + 1)**2
Let w(s) be the third derivative of 1/180*s**5 + 1/2*s**3 - 3*s**2 + 0*s + 0 + 1/12*s**4. Find i such that w(i) = 0.
-3
Let x be 3 - 1/(-2)*-5. Solve -x + h - 1/2*h**2 = 0.
1
Factor -9/2*t - 3/4*t**2 - 27/4.
-3*(t + 3)**2/4
Let w = 12206/3 + -13027/3. Let b = -271 - w. Solve 8/3 - b*h + 2/3*h**2 = 0 for h.
2
Let h(i) = -3*i**3 + i**2 + 3*i + 3. Let o(q) = -7*q**3 + 3*q**2 + 7*q + 7. Let g(k) = -5*h(k) + 2*o(k). Factor g(f).
(f - 1)*(f + 1)**2
Let x(l) = -l**3 + 5*l**2 - 5*l + 9. Let a be x(4). Factor 1 - 4 - s**3 + 3*s + a.
-(s - 2)*(s + 1)**2
Let k be -1 + 5 + 1 + -3. Let g(u) be the third derivative of 1/210*u**5 + u**k + 0*u + 0*u**4 + 0 + 0*u**3. Solve g(f) = 0 for f.
0
Let i(m) = -2 - 8*m - 4 - 2 - m**2. Let w be i(-6). Factor 2*c - 3*c + c**w - 4*c**2 + 3*c**2 + c**3.
c*(c - 1)*(c + 1)**2
Let d(q) = q**3 + 9*q**2 - 9*q + 12. Let t be d(-10). Factor 4*v**2 + 4*v - 16*v**3 - 3*v**5 + 14*v**4 - v**5 + 0*v - t.
-2*(v - 1)**4*(2*v + 1)
Let c be (-8)/(-4) + (-8)/5. Let g be (8/(-5) + 2)*1. What is s in c*s**2 - g*s + 0 = 0?
0, 1
Let d(r) be the third derivative of r**7/70 - r**6/10 + r**5/5 - 15*r**2. Determine b so that d(b) = 0.
0, 2
Let o(b) be the first derivative of 0*b**2 - 2/5*b + 2/15*b**3 - 2. Factor o(p).
2*(p - 1)*(p + 1)/5
Let d(w) be the first derivative of -49*w**3/15 + 42*w**2/5 - 36*w/5 - 4. Determine i, given that d(i) = 0.
6/7
Let o be 0 + 1 + (-6)/8. Determine s, given that 0 - o*s**4 + 1/4*s**2 - 1/4*s + 1/4*s**3 = 0.
-1, 0, 1
Let c = 3 + 0. Factor 10*p**2 + 2*p**2 + 6*p - 3*p**2 + c*p**3.
3*p*(p + 1)*(p + 2)
Let d(x) be the first derivative of -x**5/300 - x**4/120 - x**2 + 5. Let y(z) be the second derivative of d(z). Factor y(p).
-p*(p + 1)/5
Suppose f + 3 - f**2 - 4*f + f = 0. Calculate f.
-3, 1
Let j = 5 - 5. Suppose -c + 2*c + 9*c**3 + 2*c + 15*c**2 - 3 + j = 0. Calculate c.
-1, 1/3
Let f = 7/15 + 1/5. Let 0 + 0*t + t**3 + f*t**2 + 1/3*t**4 = 0. Calculate t.
-2, -1, 0
Solve 4/3*s**3 + 1/3*s**4 + 5/3*s**2 + 0 + 2/3*s = 0.
-2, -1, 0
Let b = -59/5 - -123/10. Factor 2 + b*c**2 + 2*c.
(c + 2)**2/2
Let y(g) be the third derivative of -3*g**5/40 - 7*g**4/48 + g**3/6 + 9*g**2. Factor y(j).
-(j + 1)*(9*j - 2)/2
Let s(j) be the first derivative of -j**4/6 - 4*j**3/9 + 8*j**2/3 + 55. Factor s(b).
-2*b*(b - 2)*(b + 4)/3
Let x(u) be the second derivative of u**9/22680 - u**7/1260 - u**6/540 + u**4/12 - 2*u. Let i(k) be the third derivative of x(k). Solve i(g) = 0.
-1, 0, 2
Let w = 8 - 2. Let j be w/3 + -1 + -1. Factor j - 2/7*b**2 + 2/7*b.
-2*b*(b - 1)/7
Let q