+ 2)**3/3
Let k(q) = 26*q**2 - 2*q - 1. Suppose -2 = 2*u + 4*f - 0, 0 = 3*f. Let n be k(u). Suppose -n + 6 - 3 + 84*i**3 + 64*i**2 - 44*i = 0. Calculate i.
-1, -3/7, 2/3
Let l be ((-112)/4)/4*-2. Let a = -11 + l. What is g in -a + 57*g**4 + 2*g + 2*g**5 - 4*g**3 + 0*g**5 - 59*g**4 + 1 + 4*g**2 = 0?
-1, 1
Let j = 45 - 49. Let v be (-2)/j*(180/21 - 6). Factor v*p + 6/7 - 6/7*p**2.
-3*(p - 2)*(2*p + 1)/7
Suppose -5*b + 5*x + 40 = 0, 4*b - 8*b + 2*x = -28. Let i(c) be the third derivative of 0 + 0*c**3 + 1/70*c**5 + 0*c**4 + 1/56*c**b - 2*c**2 + 0*c. Factor i(l).
3*l**2*(5*l + 2)/7
Let g be (3 - (322/(-18))/(-7))/((-8)/(-36)). Suppose -1/4*f**3 + 0 + 1/4*f**g + 1/4*f - 1/4*f**4 = 0. Calculate f.
-1, 0, 1
Let a(l) be the third derivative of 1/2160*l**6 + 0*l**4 + 0*l**5 - 6*l**2 - 1/2*l**3 + 0 + 0*l. Let z(c) be the first derivative of a(c). Factor z(x).
x**2/6
Solve 0 - 352/3*k**2 + 94/9*k**3 - 128*k - 2/9*k**4 = 0 for k.
-1, 0, 24
Suppose -3*x + 12 = x. Let h(r) = -5*r**3 + 2*r**2. Let l(z) = -9*z**3 + 4*z**2. Let f(a) = x*l(a) - 5*h(a). Solve f(p) = 0.
0, 1
Let q(x) be the first derivative of 0*x + 2/33*x**3 + 1/11*x**2 - 13. Let q(g) = 0. What is g?
-1, 0
Let i(k) be the first derivative of -k**5/20 + 21*k**4/16 - 77. Factor i(g).
-g**3*(g - 21)/4
Let y(q) be the third derivative of -1/36*q**4 + 0*q + 0 + 1/12*q**3 + 1/360*q**5 + 11*q**2. Factor y(o).
(o - 3)*(o - 1)/6
Let x(b) be the first derivative of -b**6/240 + b**5/40 - b**4/16 - 8*b**3/3 - 4. Let t(j) be the third derivative of x(j). Find s, given that t(s) = 0.
1
Suppose 0 = g + 3*w - 1, 3*g + 3*w + 0*w - 33 = 0. Let m be 12/27*3 + g/(-15). Find r, given that -2/15*r**3 + 8/15*r**2 - 2/3*r + m = 0.
1, 2
Let k(a) be the second derivative of a**5/5 + 17*a**4/3 - 116*a**3/3 + 80*a**2 + a + 72. Let k(b) = 0. What is b?
-20, 1, 2
Let b = 17783 + -17783. Factor 12/5*v + b + 3/5*v**2.
3*v*(v + 4)/5
Let h be 2*(3 + (-7)/2). Let n = 3 + h. Factor -4*z + 38 - 34 - 2*z + n*z**2.
2*(z - 2)*(z - 1)
Let d(v) be the second derivative of 0 - 1/42*v**4 + 0*v**2 + 2*v + 2/21*v**3. Factor d(j).
-2*j*(j - 2)/7
Let v = -20/959 - -42/137. Factor 2/7*t**3 + v*t**2 + 0 - 2/7*t - 2/7*t**4.
-2*t*(t - 1)**2*(t + 1)/7
Let n(p) = 10*p**4 + 11*p**3 + 3*p**2 + 13*p - 1. Let z(f) = -9*f**4 - 11*f**3 - 4*f**2 - 11*f + 1. Let k(q) = -5*n(q) - 6*z(q). Find w such that k(w) = 0.
-1, 1/4
Let n be (-6 - (-180)/35)/((-2)/(-14)). Let r be 0 - n - (6 + 4/(-2)). Let 0*g**r + 2/5 + 4/5*g**3 - 2/5*g**4 - 4/5*g = 0. What is g?
-1, 1
Let z(w) be the third derivative of w**7/70 + w**6/5 + w**5/4 - 25*w**4/4 + 103*w**2. Factor z(q).
3*q*(q - 2)*(q + 5)**2
Let j(l) be the second derivative of 13/3*l**3 + 0 + 10*l**2 - 1/2*l**4 - 1/2*l**5 + 1/15*l**6 - 30*l. Factor j(t).
2*(t - 5)*(t - 2)*(t + 1)**2
Suppose -3*a = 4*u - 6, 5*u + 2*a - a = 13. Factor -55*i**u + 55*i**3 + 10*i**2 - 2*i - 10*i**4 - 3*i + 5*i**5.
5*i*(i - 1)**3*(i + 1)
Let o(f) = 4*f**3 + 4*f**2 - 4*f + 1. Let y(l) = l**3 + l**2 - l + 1. Let w(a) = -o(a) + 3*y(a). Let d be w(0). Factor 4 + d*q**2 - 7*q**2 + 3*q**2 + q**2.
-(q - 2)*(q + 2)
Let p(i) = -10*i + 7 - i**3 + 5 + 11*i**2 - 8. Let b be p(10). Factor 2*z**b + z**2 + 0*z**2 - 5*z**2 + 2*z**2.
2*z**2*(z - 1)*(z + 1)
Let p(q) be the first derivative of q**5/5 - 5*q**4/2 - 28*q**3 - 92*q**2 - 128*q + 311. Determine l, given that p(l) = 0.
-2, 16
Let u(m) be the third derivative of -15*m**2 + 1/90*m**5 + 0*m**3 + 0*m + 0 + 1/36*m**4. Factor u(l).
2*l*(l + 1)/3
Let z = 123 - 121. Let m(q) be the first derivative of -q**z - 9 + 8/15*q**3 + 2/5*q. Suppose m(h) = 0. Calculate h.
1/4, 1
Let r(j) = -10*j**2 + 6*j + 4. Let t(l) = 10*l**2 - 8*l - 6. Let v(i) = 3*r(i) + 4*t(i). What is w in v(w) = 0?
-3/5, 2
Suppose 0 = 2*t - 8*t. Suppose 0 = 3*v - t*v - 12. Factor -y**2 - y**2 + v*y**2 - 3*y**2.
-y**2
Let y(j) = -j**2 + 4*j + 8. Let c be y(-3). Let d = c - -41/3. Factor -2/3 - 2*u**2 - 2*u - d*u**3.
-2*(u + 1)**3/3
Let t(o) be the second derivative of 5*o**6/12 - 23*o**5/3 - 49*o**4/3 - 40*o**3/3 - 51*o**2/2 + 41*o. Let y(p) be the first derivative of t(p). Factor y(q).
2*(q - 10)*(5*q + 2)**2
Suppose 2*u - 3/4*u**4 + 3*u**2 + 1/8*u**3 + 0 + 1/8*u**5 = 0. What is u?
-1, 0, 4
Let g = 2209 - 2207. Suppose 12/5*d**3 + 4/5*d - 12/5*d**g - 4/5*d**4 + 0 = 0. What is d?
0, 1
Let y(v) be the second derivative of -v**4/18 + 5*v**3/9 + 778*v. Factor y(n).
-2*n*(n - 5)/3
Let -4/5*v**3 + 0*v - 4/5*v**4 + 0 + 24/5*v**2 = 0. Calculate v.
-3, 0, 2
Let y(f) = -4*f**5 - 6*f**3 + 6. Let t(i) = -5*i**5 - i**4 - 7*i**3 + 7. Let c(n) = 6*t(n) - 7*y(n). Factor c(s).
-2*s**4*(s + 3)
Let s(q) be the second derivative of -q**7/315 - q**6/180 + q**5/30 + q**4/3 - 2*q. Let x(y) be the third derivative of s(y). Factor x(z).
-4*(z + 1)*(2*z - 1)
Find h, given that 18/13*h**5 - 2*h**2 + 112/13*h - 10*h**3 - 40/13 + 66/13*h**4 = 0.
-5, -1, 2/3, 1
Suppose -2*j - 61 = -4*c - 3*j, 0 = 3*c + j - 47. Determine z so that -3*z**3 + c*z**3 - 5*z**3 - 6*z**2 + 2*z - 2*z**4 = 0.
0, 1
Let g(t) be the first derivative of -4*t**5/5 - 2*t**4 + 87. Factor g(f).
-4*f**3*(f + 2)
Let i be (4 + (-7 - -5))/(8/12). Let u(x) be the first derivative of 0*x + 2/5*x**5 + 2/9*x**6 + 0*x**2 + 0*x**i - 9 + 1/6*x**4. Factor u(h).
2*h**3*(h + 1)*(2*h + 1)/3
Let r(q) be the first derivative of -q**6/420 - q**5/280 + q**4/56 + 7*q**3/3 + 8. Let g(p) be the third derivative of r(p). Factor g(h).
-3*(h + 1)*(2*h - 1)/7
Factor -3/2*c**2 + 3/2*c**3 + 0 + 3/2*c**4 - 3/2*c.
3*c*(c - 1)*(c + 1)**2/2
Suppose -10242 = -2*u + 3718. Let t be u/990 + -6 + (-2)/(-9). Suppose -2/11*l**3 + 18/11 - 30/11*l + t*l**2 = 0. Calculate l.
1, 3
Let z(k) = -k**3 + 7*k**2 + 9*k - 3. Let n be z(8). Suppose -7*p = -n*p - 4. Find b such that p*b**3 - b**3 - b**4 + 3*b**4 + 3*b**3 = 0.
-2, 0
Let v(b) = 13*b**3 - 108*b**2 - 32*b + 17. Let o(x) = -5*x**3 + 36*x**2 + 11*x - 6. Let j(m) = -17*o(m) - 6*v(m). Solve j(y) = 0 for y.
-5, -1/7, 0
Suppose 5*c = -5*y + 115 + 390, 0 = 5*c + 15. Factor -y*u**3 + 30*u**5 - 37*u**4 - 80*u - 136*u**2 - 11 - 5 - 35*u**5.
-(u + 1)*(u + 2)**3*(5*u + 2)
Let r = -14232/11 - -1294. Factor r*x**5 - 4/11*x**3 + 0*x**2 + 2/11*x + 0 + 0*x**4.
2*x*(x - 1)**2*(x + 1)**2/11
Suppose 9*f + 76 = 76. Find s such that f*s + 4/11*s**2 + 0 + 14/11*s**3 = 0.
-2/7, 0
Let u = 291 - 297. Let b be (-9)/u*-4*3/(-144). Factor b*f - 1/8 + 1/8*f**2 - 1/8*f**3.
-(f - 1)**2*(f + 1)/8
Let -20*k - 587 + 65*k**3 + 225*k**2 - 663 - 105*k + 5*k**4 = 0. Calculate k.
-5, 2
Find v, given that -8/5*v**3 + 0 - 19/5*v**2 - 2*v + 1/5*v**4 = 0.
-1, 0, 10
Factor 9254 - 4610 + 5*w**3 - 4614 - 30*w**2 - 5*w.
5*(w - 6)*(w - 1)*(w + 1)
Solve -44*g**3 - 28*g**3 + 75*g + 38431*g**5 - 30*g**2 - 38434*g**5 + 30*g**4 = 0 for g.
-1, 0, 1, 5
Let j(f) be the third derivative of f**7/140 - 19*f**6/60 - 53*f**5/120 + 13*f**4/24 - f**2 - 149*f. Determine k so that j(k) = 0.
-1, 0, 1/3, 26
Suppose a - 3*h = 2*a + 10, 5*h = 2*a - 24. Let s = -400 - -2008/5. Find m, given that -s - 138/5*m**2 + a*m**3 - 64/5*m + 40*m**4 = 0.
-2/5, -1/4, 1
Let i(f) be the third derivative of 1/1155*f**7 - 1/330*f**5 - 1/1848*f**8 + 0*f + 0*f**3 + 0 + 1/660*f**6 + 0*f**4 - 11*f**2. Factor i(u).
-2*u**2*(u - 1)**2*(u + 1)/11
Factor -1/9*r**2 + 34/9*r + 37/3.
-(r - 37)*(r + 3)/9
Let p(y) be the third derivative of -2*y**7/105 - y**6/10 - 2*y**5/15 + 5*y**2 - 9. Suppose p(s) = 0. What is s?
-2, -1, 0
Suppose 2*l + 3*k - 18 = 0, 2*l + 18*k - 14*k - 22 = 0. Find c, given that 1/6*c**2 + 0 + 1/6*c**l - 1/6*c**4 - 1/6*c = 0.
-1, 0, 1
Let d = -3139 + 3141. What is t in 4 + 8*t + 2*t**3 + 1/4*t**4 + 6*t**d = 0?
-2
Suppose 3*a - 10 - 25 = -2*y, y + 5*a - 28 = 0. Factor -8*o**4 + o**4 + 3*o**3 + 3*o**5 + y*o**4.
3*o**3*(o + 1)**2
Determine v, given that 0 + 8/9*v**2 - 2/9*v**5 + 8/9*v**3 + 0*v - 2/9*v**4 = 0.
-2, -1, 0, 2
Let q(k) be the second derivative of -k**5/45 + 4*k**4/27 + 2*k**3/27 - 8*k**2/9 + 516*k. Find i such that q(i) = 0.
-1, 1, 4
Let h = 11247 + -11245. Let 3/4 - 15/2*t**3 + 9/4*t**4 + 9*t**h - 9/2*t = 0. Calculate t.
1/3, 1
Let a(m) be the second derivative of m**6/600 - m**5/60 + 7*m**4/120 - m**3/10 - 5*m**2 - 6*m. Let x(k) be the first derivative of a(k). Factor x(g).
(g - 3)*(g - 1)**2/5
Let m(p) be the third derivative of p**5/60 - p**3/6 + 12*p**2. 