4, -1, 0, 2
Suppose 63 = -4*l + 167. Factor l*m**3 - 22*m**4 + 14*m - 4*m**2 - 39*m + 25*m.
-2*m**2*(m - 1)*(11*m - 2)
Suppose 0 = 7*y + 7*y - 140. Let g be (-12)/10*y*1/(-8). Determine n, given that 0 - 1/2*n - g*n**2 + 2*n**3 = 0.
-1/4, 0, 1
Factor 31*a**3 - 225*a**2 + 126*a + 64*a + a**3 + 13*a**3 - 40.
5*(a - 4)*(3*a - 2)*(3*a - 1)
Let c = -2845 + 14228/5. Factor -3/5*b**3 + 0 - c*b**2 + 0*b.
-3*b**2*(b + 1)/5
Suppose 4 + 7 = 2*u + q, -4*u = 3*q - 17. Find m such that -4*m**5 + 25*m**4 + 15*m**2 + 28*m**2 + m**2 - u*m + 0*m**2 - 54*m**3 = 0.
0, 1/4, 2
Factor 6 + 9*a + 1/3*a**3 + 10/3*a**2.
(a + 1)*(a + 3)*(a + 6)/3
Factor -45 + 8*m**2 + 25*m**2 - 73*m + 8*m**2 - m**2 - 32*m.
5*(m - 3)*(8*m + 3)
Let u(k) be the first derivative of 3*k**2 + 2 - k**4 + 0*k + 2/3*k**3. Let o(i) = i**2 - i. Let w(x) = 6*o(x) + u(x). Factor w(r).
-4*r**2*(r - 2)
Let j(z) = 5*z**2 - 3*z - 3. Let s be j(-2). Find y such that 2*y**2 + 19 + 0*y**2 + 8 + s - 20*y = 0.
5
Let w = 20 + -17. Let f(y) be the third derivative of 0 + 1/22*y**4 - 3/11*y**w + 0*y - 1/330*y**5 + 3*y**2. What is g in f(g) = 0?
3
Let l(a) be the first derivative of 2*a**3/9 - 4*a**2/3 + 8*a/3 + 44. Determine w, given that l(w) = 0.
2
Let s(b) be the second derivative of -b**8/420 + b**7/210 - 3*b**3/2 - 9*b. Let l(x) be the second derivative of s(x). Factor l(j).
-4*j**3*(j - 1)
Let q = -34828/15983 - 4/1453. Let d = q - -59/22. Determine m, given that 0*m + d*m**3 + 0*m**2 - 1/2*m**4 + 0 = 0.
0, 1
Let c(v) = -2*v**2 + 19*v + 12. Let w be c(10). Factor 8*n**4 - 2*n**5 - 12*n**3 - 2*n + 81*n**2 - 153*n**w + 80*n**2.
-2*n*(n - 1)**4
Let r(f) be the first derivative of f**6/540 - 7*f**5/270 + 11*f**4/108 - 5*f**3/27 + f**2 - 32. Let x(m) be the second derivative of r(m). Factor x(a).
2*(a - 5)*(a - 1)**2/9
Let n be (-25)/15*(-36)/10. What is s in 6 - 50*s - 4 - 3 + n + 125*s**2 = 0?
1/5
Let f(a) be the third derivative of -a**8/504 - 2*a**7/315 + a**5/45 + a**4/36 - 243*a**2. Factor f(w).
-2*w*(w - 1)*(w + 1)**3/3
Let r(z) be the first derivative of -2*z**3/3 + 62*z**2 - 457. Solve r(c) = 0.
0, 62
Let x(f) = f**2 - 3*f. Suppose m = -2, 5*k + 3*m - 10 = -2*m. Let l be x(k). Factor -6*o**2 - 5*o**4 + l*o**2 - 2*o - o**4 + 10*o**3.
-2*o*(o - 1)**2*(3*o + 1)
Let k(h) be the third derivative of 1/112*h**8 + 0 - 16*h**3 - 4*h**5 - 1/7*h**7 + 0*h + 15*h**2 + 10*h**4 + h**6. Factor k(p).
3*(p - 2)**5
Let w be 930/189 + (-20)/(-90). Determine m, given that 0*m - 18/7*m**4 + 0 - w*m**3 - 3/7*m**5 - 24/7*m**2 = 0.
-2, 0
Suppose -5*a - 17*u = -19*u - 6, 0 = -3*a - 5*u + 47. Solve 0 + 1/10*h**2 + 29/10*h**a - h**3 + 0*h - 2*h**5 = 0.
0, 1/5, 1/4, 1
Let k(h) be the first derivative of -3*h - 6 - 9/8*h**4 - 9/2*h**2 - 13/4*h**3 - 3/20*h**5. Determine q so that k(q) = 0.
-2, -1
Let g(m) = m**3 + 46*m**2 - 35*m + 566. Let n be g(-47). Find k, given that -27 - 1/3*k**n - 6*k = 0.
-9
Let z = -3011/3 - -987. Let g = -13 - z. Let g*n + 3*n**2 + 2/3 = 0. What is n?
-1, -2/9
Let y(a) = 11*a**2 - 2*a - 2. Let c be y(-1). Let 4 - 9*g + 4*g - c*g**2 + 12*g**3 - 7*g + 1337*g**4 - 1330*g**4 = 0. What is g?
-2, -1, 2/7, 1
Let f(t) be the second derivative of -t**5/510 + t**4/102 - t**3/51 + 6*t**2 - 6*t. Let j(u) be the first derivative of f(u). Determine v so that j(v) = 0.
1
Suppose 3*x - c - 34 = 0, 5*x = -2*c + 33 + 20. Find a such that -7*a**2 + 15*a**3 + 5*a + x*a**2 - 14*a**3 + 2 = 0.
-2, -1
Let u = 47 - -13. Let l(f) = 28*f**2 - 2*f - 2 + 35*f**2 - u*f**2. Let j(d) = -10*d**2 + 7*d + 5. Let r(z) = -6*j(z) - 21*l(z). Factor r(n).
-3*(n - 2)*(n + 2)
Let l(m) be the first derivative of -3*m**4/4 - 5*m**3 - 9*m**2 + 37. Factor l(y).
-3*y*(y + 2)*(y + 3)
Suppose 8*x + 3*x**2 + 7*x - 12*x + 1 - 7 = 0. Calculate x.
-2, 1
Let q(b) be the third derivative of b**7/50 - b**6/40 - b**5/50 + 70*b**2. Let q(i) = 0. Calculate i.
-2/7, 0, 1
Suppose -62 = -7*s - 41. Find k, given that 0*k + 1/4*k**s - 3/4*k**2 + 1 = 0.
-1, 2
Let r(u) be the third derivative of -u**8/84 + 34*u**7/105 - 44*u**6/15 + 24*u**5/5 + 72*u**4 - 288*u**3 - 2*u**2 + 8. Find q such that r(q) = 0.
-2, 1, 6
Let t(k) be the second derivative of -k**6/75 - 2*k**5/5 - 19*k**4/30 - 113*k. Find u, given that t(u) = 0.
-19, -1, 0
Let n(q) be the third derivative of -2*q**7/105 - 7*q**6/30 - 13*q**5/15 + q**4/2 + 12*q**3 + 179*q**2 + 2*q. Suppose n(g) = 0. Calculate g.
-3, -2, 1
Let i(s) be the first derivative of 0*s + 11 + 2*s**3 - 7/180*s**5 + 0*s**2 + 1/18*s**4 - 1/135*s**6. Let f(t) be the third derivative of i(t). Factor f(x).
-2*(x + 2)*(4*x - 1)/3
Let b(u) = -u**3 - u**2 - u + 1. Let r(m) = m - 11. Let x be r(10). Let f(p) = -p**4 - 2*p**3 + p**2 - 4*p + 2. Let i(v) = x*f(v) + 2*b(v). Factor i(k).
k*(k - 1)**2*(k + 2)
Let w be (-2 + 0)*(1 + -10). Let t = -16 + w. Factor -t*b**2 + 5 + 2*b**2 + 2*b**2 - 7.
2*(b - 1)*(b + 1)
Let k(s) be the second derivative of 0 - 1/60*s**5 + 17*s + 4/3*s**2 - 1/18*s**4 + 2/9*s**3. Determine y, given that k(y) = 0.
-2, 2
Let z = 6201 - 12399/2. Find m such that -3 + 3/2*m**2 - z*m = 0.
-1, 2
Let i(f) be the first derivative of 2*f**3/9 + 23*f**2/9 + 28*f/9 + 46. Factor i(l).
2*(l + 7)*(3*l + 2)/9
Let r(j) be the first derivative of -j**3/18 + j**2/2 - 4*j/3 + 47. Factor r(d).
-(d - 4)*(d - 2)/6
Let n(y) be the first derivative of -3*y**5/5 + 6*y**4 - 5*y**3 - 21*y**2 - 178. What is q in n(q) = 0?
-1, 0, 2, 7
Factor -23/8*r - 1/8*r**3 - 15/8 - 9/8*r**2.
-(r + 1)*(r + 3)*(r + 5)/8
Let y(o) = o**2 + 10*o + 10. Let f be y(-7). Let q = -9 - f. Factor 3 - 3 - q*n**2 + 3*n - 5*n + 4.
-2*(n - 1)*(n + 2)
Suppose 0 = 3*s + 4*l - 14, -s - 8*l + 12 = -3*l. Suppose -u - q + 2 = u, -3*q + 6 = 0. Solve -4/5*n**3 + 2/5*n**5 + 0 + u*n**s + 0*n**4 + 2/5*n = 0 for n.
-1, 0, 1
Let i(p) = -4*p**3 - 4*p**2 + 5*p - 4. Suppose -20*u = -14*u + 84. Let a(n) = n**3 - n**2 + 1. Let g(f) = u*a(f) - 2*i(f). Factor g(s).
-2*(s - 3)*(s - 1)*(3*s + 1)
Let g(f) be the first derivative of 4/9*f**3 + 11 - 2/3*f**2 + 1/4*f**4 + 0*f. Solve g(r) = 0 for r.
-2, 0, 2/3
Let p be 1/(0 + (-15)/18). Let f = -7/10 - p. Determine h so that f*h**5 + 0*h + 1/2*h**3 + 0*h**2 - h**4 + 0 = 0.
0, 1
Let m = 205 + -213. Let g be (-5 + m + 9)*(-2 - -1). Suppose 12/7*t**3 - 9/7*t**g + 12/7 + 33/7*t**2 - 48/7*t = 0. What is t?
-2, 1/3, 1, 2
Let p(c) be the third derivative of 0*c - 1/5*c**3 + 0 - 7*c**2 - 1/40*c**4 + 1/100*c**5. Factor p(w).
3*(w - 2)*(w + 1)/5
Let v = 707 - 707. Factor 1/4 + v*z - 1/4*z**2.
-(z - 1)*(z + 1)/4
Let a = 367/28 + -90/7. Factor 0 - a*k**2 + 3/4*k.
-k*(k - 3)/4
Let g(u) = -7*u**2 - 2*u + 3. Let y be g(1). Let h be 2/(-5)*5/y. Let 2/3*z**2 - 1/3 - 1/6*z**5 + h*z**3 - 1/6*z - 1/3*z**4 = 0. Calculate z.
-2, -1, 1
Let h(q) = -q + 17. Let y be h(10). Factor -2*a**2 + a**5 - 9*a**2 - 2 - a**4 + 3*a**2 - y*a - 2*a**3 + 3*a**4.
(a - 2)*(a + 1)**4
Let q(a) be the third derivative of a**8/1680 - 107*a**7/1050 + 711*a**6/100 - 12393*a**5/50 + 150903*a**4/40 + 177147*a**3/10 - 213*a**2. Factor q(u).
(u - 27)**4*(u + 1)/5
Let v be 0/(12/(0 + -3)). Let k(c) be the third derivative of 1/360*c**6 - c**2 - 1/60*c**5 + 0*c**4 + 0*c**3 + 0*c + v. Solve k(x) = 0 for x.
0, 3
Suppose 0*n - 10 = -5*n. Let m(s) be the first derivative of 0*s + 0*s**3 + 1/4*s**4 + 3/5*s**5 + 0*s**n - 1. Factor m(q).
q**3*(3*q + 1)
Suppose -30 = -6*u + 4*u + 4*a, 0 = -2*u - 4*a - 10. Let y(o) be the first derivative of o**4 - o + o**3 - o**2 + 6 - 4/5*o**u. Factor y(d).
-(d - 1)**2*(2*d + 1)**2
Let v = 57 - 68. Let t(k) = 17*k**2 + 73*k + 294. Let w(j) = -9*j**2 - 36*j - 147. Let d(p) = v*w(p) - 6*t(p). Factor d(u).
-3*(u + 7)**2
Let t = 1453 + -1451. Solve t*n**2 - 6/7*n + 0 - 10/7*n**3 + 2/7*n**4 = 0.
0, 1, 3
Suppose -g - 17 = -5*h, -41*g - 21 = -3*h - 44*g. Suppose -2*t**5 + 0 + 0*t - 6/7*t**h + 2*t**3 + 6/7*t**2 = 0. What is t?
-1, -3/7, 0, 1
Suppose 0 = -3*f - 6, 3*z - f - 2*f - 21 = 0. Suppose 6*g - z*g - 2*g - 2*g**2 - 3*g = 0. Calculate g.
-2, 0
Let v(t) be the third derivative of t**7/70 - 3*t**6/40 + t**4/2 + 4*t**2 - 12*t. Factor v(u).
3*u*(u - 2)**2*(u + 1)
Let u = 3317 + -13259/4. Factor -u*l - 3/4*l**2 - 3/2.
-3*(l + 1)*(l + 2)/4
Let k be (11 - 0) + ((-8)/2 - (218 + -214)). Suppose -16/3*t**k + 0 - 2/3*t**5 + 8/3*t**2 + 0*t + 10/3*t**4 = 0. Calculate t.
0, 1, 2
Factor -1806 - 222*d - 2