 + 1)/3
Let n = 313/634 + 2/317. Factor -1/2*t**3 + 1/4 - 3/4*t**4 + 3/4*t - 1/4*t**5 + n*t**2.
-(t - 1)*(t + 1)**4/4
Let q = 21 - 19. Solve 5*z**3 + z**4 + 12*z**2 - 3*z**3 + q*z**4 + 10*z**3 = 0.
-2, 0
Let c be ((-32)/(-12))/((-742)/(-111)). Let h = c - 6/53. Find k such that 0*k + 0 + h*k**3 + 4/7*k**2 = 0.
-2, 0
Let y(q) be the first derivative of -2*q**5/15 + 7*q**4/15 - 8*q**3/15 + 2*q**2/15 + 2*q/15 + 1. Factor y(d).
-2*(d - 1)**3*(5*d + 1)/15
Suppose 4*u - 5*n + n - 4 = 0, 0 = -u + 3*n + 3. Suppose u*w = 2*w. Factor w + 2/5*l + 2/5*l**2.
2*l*(l + 1)/5
Let b(l) = l**2 - 5*l - 3. Let k be b(6). Suppose 3*f - f - k*h = 13, 4*h = -4. Solve -4*r - 4*r**5 - 2 + 20*r**2 + 4 + 10*r**4 - 20*r**3 - 6*r + 2*r**f = 0.
1
Suppose 4*v - 75 = v. Let w = -49/2 + v. Factor 0 + w*b**2 - 1/2*b.
b*(b - 1)/2
Find p such that 8/3*p + 20/3 - 4*p**2 = 0.
-1, 5/3
Let k(v) be the third derivative of -v**8/168 + v**6/60 - 7*v**2. Determine b so that k(b) = 0.
-1, 0, 1
Suppose 0 = -3*w + 6. Let j = -2/21 - -3/7. Let j*m**w - m + 2/3 = 0. Calculate m.
1, 2
Let p(h) = -3*h**2 + 30*h + 48. Let u(x) = x**2 - x. Let b(j) = -p(j) - 6*u(j). Solve b(t) = 0 for t.
-4
Let i = 320 + -2236/7. Let v(r) be the first derivative of i*r - 2/21*r**3 + 1/7*r**2 + 2. Factor v(z).
-2*(z - 2)*(z + 1)/7
Let q(s) = 2*s**4 + 30*s**3 - 12*s**2 + 4*s - 22. Let n(b) = -b**3 + b**2 + 1. Let v(p) = 44*n(p) + 2*q(p). Factor v(l).
4*l*(l + 1)**2*(l + 2)
Let x(n) = -n**3 - 1 - 6 - 4*n + 9 - 5*n**2. Let f be x(-4). Find u such that 2 + 1/2*u**3 + 4*u + 5/2*u**f = 0.
-2, -1
Let r(g) be the second derivative of g**4/6 + g**2/2 - 3*g. Let b be r(1). Determine f, given that 2 + f - b*f + f**2 - 1 = 0.
1
Suppose -9/2*b**2 + 3/2*b + 3*b**4 + 3/2 - 3/2*b**3 = 0. What is b?
-1, -1/2, 1
Let j be 2/8 - (-60)/16. Suppose -v + 1 = -2*v - 4*d, -3*v - 5*d = -j. Factor 0 + 0*i + 0*i**2 + 2/7*i**v.
2*i**3/7
Let w(h) be the second derivative of h**5/100 - h**4/20 + h**3/10 - h**2/10 - 4*h. Factor w(k).
(k - 1)**3/5
Find d, given that -15*d + 96*d - 27*d + 3*d**2 + 243 = 0.
-9
Solve -26*k**5 - 3*k**3 + 0*k**4 + 29*k**5 + 0*k**4 = 0 for k.
-1, 0, 1
Let r be 9/(-18)*(-1 - -1). Let v(j) be the third derivative of 0*j**6 + j**2 + 0*j**4 + 0 + 1/70*j**7 + 0*j**3 + 0*j + r*j**5. Suppose v(n) = 0. What is n?
0
Let v(a) be the first derivative of a**3/3 + 3*a**2/5 + a/5 + 2. Factor v(m).
(m + 1)*(5*m + 1)/5
Let w(t) be the first derivative of -t - 1/3*t**3 + 1/18*t**4 + 2/3*t**2 - 1. Let c(p) be the first derivative of w(p). Determine m, given that c(m) = 0.
1, 2
Let b(j) be the first derivative of 3 + 0*j**2 + 1/3*j**3 - j. Determine p so that b(p) = 0.
-1, 1
Let p(o) be the second derivative of -o**5/30 + o**4/18 + o**3/9 - o**2/3 - 5*o. Factor p(h).
-2*(h - 1)**2*(h + 1)/3
Factor 1/4*r**2 - r + 1.
(r - 2)**2/4
Let a(y) be the third derivative of 0*y**3 + 4*y**2 - 1/30*y**5 + 0 + 0*y + 1/24*y**6 + 0*y**4. Suppose a(v) = 0. What is v?
0, 2/5
Let h(j) be the third derivative of -1/720*j**6 + 0*j + 0*j**4 + 0 + 1/120*j**5 + 4*j**2 - 1/9*j**3. Factor h(u).
-(u - 2)**2*(u + 1)/6
Let t = 22/17 - 86/119. Let n(p) be the first derivative of -1 + 3/7*p**2 + t*p - 10/21*p**3. Factor n(j).
-2*(j - 1)*(5*j + 2)/7
Let x(q) = 2*q**2 + 3*q + 3. Let n be x(-2). Factor -2/3*b**3 + 0 + 0*b**2 + 0*b - 2/3*b**n - 4/3*b**4.
-2*b**3*(b + 1)**2/3
Determine v so that 0 + 6/5*v**2 - 9/5*v - 1/5*v**3 = 0.
0, 3
Let v(a) be the second derivative of -a**6/15 + 3*a**5/5 - 2*a**4/3 - 2*a**3 + 5*a**2 - 10*a. Factor v(g).
-2*(g - 5)*(g - 1)**2*(g + 1)
Let p(o) be the third derivative of -1/18*o**4 - 1/18*o**5 + o**2 + 0*o**3 + 0 + 0*o. Factor p(a).
-2*a*(5*a + 2)/3
Suppose 6*f - 15 = f. Let s = f + -4. Let j(p) = 2*p**4 + 2*p**3 - 2*p - 2. Let c(x) = -x**4 + x**2 - x - 1. Let h(z) = s*j(z) + 2*c(z). Factor h(r).
-2*r**2*(r + 1)*(2*r - 1)
Let v(y) = 8*y**2 + 11*y + 3. Let j(n) = -n**2 - n. Let p(g) = -5*j(g) - v(g). Solve p(h) = 0 for h.
-1
Let o(g) = 2*g - 10. Let w be o(7). Factor -4*p**4 - 2*p**4 + 3*p**2 - 2*p + 4*p**w + p**4.
-p*(p - 1)**2*(p + 2)
Factor 0 - 2/9*d**2 - 2/9*d.
-2*d*(d + 1)/9
Let x be -1 + (-78)/(-45) - 4/10. Factor -2/3*p + x*p**2 + 1/3.
(p - 1)**2/3
Let v(p) be the first derivative of p**4/2 + 4*p**3/3 + 5*p**2 - 2. Let r(m) = m**2 + m. Let u(w) = 8*r(w) - v(w). Factor u(o).
-2*o*(o - 1)**2
Let d(f) = f**3 - 6*f**2 + 5*f + 5. Let o be d(5). Suppose -23 = -5*c - 2*m, -3*m - 7 + 19 = 0. Factor 1/2*t**4 + 0 - 1/2*t**c + 1/2*t**o + 0*t - 1/2*t**2.
t**2*(t - 1)*(t + 1)**2/2
Factor 140*w**3 - 145*w**2 - 14310 + 2305 - 1325*w**2 - 5*w**4 + 6860*w.
-5*(w - 7)**4
Let w(i) = i**3 + i**2 + 1. Let o(r) = 4*r**3 + 14*r**2 - 27*r + 32. Let u = -20 + 10. Let q(c) = u*w(c) + 2*o(c). Suppose q(d) = 0. Calculate d.
3
Let p(c) be the second derivative of 0 + 1/15*c**6 - 1/6*c**4 - 1/10*c**5 - c + 1/3*c**3 + 0*c**2. Factor p(t).
2*t*(t - 1)**2*(t + 1)
Let u(a) be the second derivative of 2*a**6/15 - 4*a**5/5 + 32*a**3/3 - 32*a**2 + 47*a. Factor u(p).
4*(p - 2)**3*(p + 2)
Factor 2/5*z**2 - 8/5 + 6/5*z.
2*(z - 1)*(z + 4)/5
Let n(d) be the first derivative of -7*d**5/25 + d**4/4 + 2*d**3/15 + 38. Factor n(v).
-v**2*(v - 1)*(7*v + 2)/5
Let u(j) be the third derivative of 5*j**2 + 1/4*j**5 + 0*j**3 + 1/8*j**4 + 1/10*j**6 + 0*j + 0. Factor u(x).
3*x*(x + 1)*(4*x + 1)
Let q(v) = 11*v**3 + 39*v**2 - 14*v - 4. Let o(m) = -12*m**3 - 39*m**2 + 15*m + 3. Let s(p) = -4*o(p) - 3*q(p). Factor s(i).
3*i*(i + 3)*(5*i - 2)
Suppose -4*o - 66 = 14. Let i = o - -24. Solve 0*c + 0 - 1/4*c**3 + 1/4*c**i + 0*c**2 = 0.
0, 1
Let l(x) be the first derivative of x**2/2 + 10*x - 1. Let f be l(-7). Factor 2*b**4 - 2*b**2 - b**f + 2*b**2 - b**5.
-b**3*(b - 1)**2
Let c(m) be the first derivative of -m**6/900 + m**4/15 - 2*m**3/3 + 7. Let v(i) be the third derivative of c(i). Factor v(f).
-2*(f - 2)*(f + 2)/5
Let b be (1 - (-8)/(-10))/21. Let a(h) be the second derivative of -b*h**6 + 0 + 0*h**2 + 1/70*h**5 - 2*h + 0*h**3 + 0*h**4. Find u such that a(u) = 0.
0, 1
Let g = 0 + 0. Suppose g = 3*p - 4*r - 32, 4*p - 15 + 4 = -r. Factor -2*x**3 + x**3 - 2*x - 8*x**2 + 3*x**3 + 8*x**p.
2*x*(x - 1)*(x + 1)*(4*x + 1)
Let y(v) be the second derivative of -v**7/280 - v**6/40 - v**5/20 + v**3/3 - 3*v. Let h(x) be the second derivative of y(x). Factor h(k).
-3*k*(k + 1)*(k + 2)
Let j(h) be the third derivative of h**8/3920 - h**7/980 + h**5/140 - h**4/56 + h**3 + 5*h**2. Let m(a) be the first derivative of j(a). What is v in m(v) = 0?
-1, 1
Let g(k) be the first derivative of 0*k + 3/10*k**6 + 0*k**2 + 24/25*k**5 + 2/5*k**3 + 21/20*k**4 - 3. Factor g(m).
3*m**2*(m + 1)**2*(3*m + 2)/5
Let -5*t**5 - 10*t**4 + 4*t**2 + 5*t + 10*t**2 - 4*t**2 = 0. Calculate t.
-1, 0, 1
Let n(y) be the second derivative of 3*y**7/280 + y**6/24 + y**5/20 + y**3/6 - 5*y. Let s(o) be the second derivative of n(o). Factor s(x).
3*x*(x + 1)*(3*x + 2)
Let f(r) = 4*r**4 - r**3 + 3*r**2 + 3. Let u(w) = -4*w**4 - 4*w**2 - 4. Let l be 5*(-1 + 32/20). Let t(o) = l*u(o) + 4*f(o). Factor t(b).
4*b**3*(b - 1)
Let b be (-957)/174*4/(-14). Suppose -1/7*z + 4/7*z**4 + 9/7*z**2 - b*z**3 - 1/7 = 0. What is z?
-1/4, 1
Let q(h) be the third derivative of -h**6/30 - 2*h**5/15 - h**4/6 + 9*h**2. Suppose q(b) = 0. What is b?
-1, 0
Let h(g) = -6*g**2 + 6. Let l(p) = -p**2 + 1. Suppose -5*y + 3 = -2. Let w(o) = y*h(o) - 4*l(o). Solve w(q) = 0.
-1, 1
Let h(f) be the first derivative of f**5/10 + f**4/2 + f**3 + f**2 + f/2 + 13. Factor h(y).
(y + 1)**4/2
Determine h so that -36/19*h**2 + 14/19*h + 10/19*h**3 + 12/19 = 0.
-2/5, 1, 3
Find j, given that 58 - 44*j + 0*j**2 - 64*j**2 - 28*j**3 - 66 = 0.
-1, -2/7
Let j be -39*126/(-1911)*1/2. Factor -3/7*d**2 - 6/7 + j*d.
-3*(d - 2)*(d - 1)/7
Let w(y) be the first derivative of -y**9/10584 - y**8/1176 - 2*y**7/735 - y**6/315 - 5*y**3/3 + 2. Let g(b) be the third derivative of w(b). Factor g(v).
-2*v**2*(v + 1)*(v + 2)**2/7
Let m(h) be the third derivative of -h**9/1890 - h**8/600 - h**7/1050 + h**6/900 + h**3/2 - 3*h**2. Let z(u) be the first derivative of m(u). Factor z(j).
-2*j**2*(j + 1)**2*(4*j - 1)/5
Suppose -u**4 - u**3 + 10*u - 3 + u**3 + 6*u**3 + 6*u**2 - 18*u**2 = 0. What is u?
1, 3
Let n(c) = -c**3 - 4*c**2 + 6*c + 6. Let q be n(-5). What is r in 8*r + 5*r**2 + 3 - r**3 + r**3 + q + r**3