be n(5). Factor -6/7*s - q - 2/7*s**a.
-2*(s + 1)*(s + 2)/7
Let -93 - 2*j - j**2 + 43 - 25*j = 0. Calculate j.
-25, -2
Suppose f - 19 = 4*x, -4*f + 32 = -0*f - 5*x. Suppose f*w + 3 = 3*q, -3*q - 3*w = -12 - 9. Factor -2*l**4 - 4*l**2 + 2*l**q - 9*l - 3*l**4 + 6 + 9*l**3 + l**2.
-3*(l - 2)*(l - 1)**2*(l + 1)
Let i(g) = 4*g**2 + 4*g + 4. Let n(w) = -2*w + 38. Let r be n(17). Let o(l) = l**2 + 1. Let k(q) = r*o(q) - 2*i(q). Find s such that k(s) = 0.
-1
Let r(g) = -10*g**4 + 25*g**3 + 10*g**2 - 40*g. Let b(p) = -15*p**4 + 38*p**3 + 14*p**2 - 60*p. Let h(w) = 5*b(w) - 7*r(w). Factor h(c).
-5*c*(c - 2)**2*(c + 1)
Let z(h) be the first derivative of -h**3/3 - 13*h**2/2 - 12*h + 50. Factor z(s).
-(s + 1)*(s + 12)
Let q = -9 - -14. Suppose 2*k + 28 = 3*s, 16 = -4*k - 4. Factor 4*j + s*j**4 + 8*j**q - 11*j**3 - 15*j**2 + j**5 + 11*j**2.
j*(j + 1)**2*(3*j - 2)**2
Determine d, given that 409 - 835 + 35*d - 10*d**2 + 396 = 0.
3/2, 2
Let o be 2868/18*(-15)/10. Let a = o - -242. Suppose 3/2*t**a + 0 + 3*t**2 + 0*t = 0. What is t?
-2, 0
Factor -29*f**2 - 22*f**2 + 53*f**2 - 8*f.
2*f*(f - 4)
Let y = 309/10 + -293/10. Find v, given that y*v**2 + 16/5*v + 0 + 1/5*v**3 = 0.
-4, 0
Let a be (4/12)/(7/21). Let q(v) = -2*v**2 - 14*v + 1. Let b(z) = z**2 + z + 1. Let t(g) = a*q(g) + 5*b(g). Factor t(u).
3*(u - 2)*(u - 1)
Let t be (-48 - 6)*(-4)/6. Let c be 26/28 - (-18)/t. Suppose 2/7*z**4 - 8/7*z + 0 - c*z**3 + 16/7*z**2 = 0. What is z?
0, 1, 2
Suppose -2*b = -10, -a + 2*b = -4 + 3. Find m such that -a*m**2 - 2*m**3 - 2 + 2 + 13*m**2 + 2*m**5 - 2*m**4 = 0.
-1, 0, 1
Let -3*v**3 - 18 - 2777*v - 24*v**2 + 6*v**3 + 2816*v = 0. Calculate v.
1, 6
Let j(w) = w**3 - 9*w**2 - 49*w + 10. Let a be j(13). Let k be (5 - -2)*2/a. Factor 0*t**2 + 0 + k*t**3 - 2/7*t.
2*t*(t - 1)*(t + 1)/7
Find p, given that -20/7*p - 2*p**4 + 2/7*p**5 + 2*p**2 + 18/7*p**3 + 0 = 0.
-1, 0, 1, 2, 5
Let w(r) = -4*r**5 - 62*r**4 + 64*r**3 - 34*r**2 - 24*r - 12. Let g(j) = j**5 + 2*j**3 + j**2 + j + 1. Let m(l) = 12*g(l) + w(l). Solve m(u) = 0 for u.
-1/4, 0, 1, 6
Solve 25/3*q**5 - 1/3 - 34/3*q**3 + 5*q**4 + 3*q - 14/3*q**2 = 0.
-1, 1/5, 1
Let p be (-90)/(-8) - (-2)/(-8). Suppose -1 = -6*z + p. Factor f**3 + 2/3*f + 4/3*f**4 + 0 - 3*f**z.
f*(f - 1)*(f + 2)*(4*f - 1)/3
Let s(j) be the second derivative of -j**5/90 + 5*j**4/27 + 23*j**3/27 + 4*j**2/3 + 2*j + 178. Factor s(t).
-2*(t - 12)*(t + 1)**2/9
Let r(f) be the second derivative of -f**7/2940 - f**6/420 + f**5/105 - 13*f**3/3 + 9*f. Let x(w) be the second derivative of r(w). Solve x(a) = 0.
-4, 0, 1
Let g be (-28)/(-6) + 2/6. Suppose -15*y = 4 - 64. Factor -2*d**5 + d**5 - 15*d**3 + 6*d**2 - 2*d**g + 12*d**y.
-3*d**2*(d - 2)*(d - 1)**2
Factor 24/5 + 32/5*w + 2/5*w**3 + 14/5*w**2.
2*(w + 2)**2*(w + 3)/5
Suppose 0 = 3*b - 2*t - 9, 2*b - 2*t = -2*b + 14. Factor 6*f**3 + f**4 - b*f**5 + 4*f**5 + 2*f**4 - 2*f**5.
-3*f**3*(f - 2)*(f + 1)
Let c be ((-22)/3)/(8/(-12)). Factor 3*s**5 - 14*s**4 - 2 + 18*s**3 + 8*s**3 + 42*s**2 - 66*s**2 + c*s.
(s - 1)**4*(3*s - 2)
Let k(n) be the second derivative of -55*n**4/36 - 46*n**3/9 - 14*n**2/3 - 3*n + 8. Find q, given that k(q) = 0.
-14/11, -2/5
Suppose -679*c + 693*c = 0. Let z(b) be the second derivative of 1/2*b**2 + 11*b + b**3 + c + 3/4*b**4 + 1/5*b**5. Let z(u) = 0. Calculate u.
-1, -1/4
Let k be ((-6)/(-12) + (-9)/6)/(-3). Factor 0 + 4/3*l**2 + k*l**3 + 0*l.
l**2*(l + 4)/3
Let y(n) be the second derivative of 0 + 16*n + 4/13*n**2 - 1/78*n**4 + 0*n**3. Suppose y(a) = 0. Calculate a.
-2, 2
Let f(h) = 10*h**4 - 40*h**3 + 54*h**2 - 14. Let b(n) = 2*n**4 - 8*n**3 + 11*n**2 - 3. Let d(s) = 14*b(s) - 3*f(s). Suppose d(q) = 0. Calculate q.
0, 2
Factor 37 - 15*y - 64 + 9*y**2 + 3*y**3 - 3*y**4 + 33.
-3*(y - 1)**3*(y + 2)
Let h be 40/12 + 3/1 - 1. Factor 16/3 - h*y**2 - 4/3*y**3 + 4/3*y.
-4*(y - 1)*(y + 1)*(y + 4)/3
Let s(t) = -t**3 - t**2 + 6*t + 4. Let p be s(-3). Solve 0*d + 2 - p*d + 5*d**2 - 3*d + 0*d = 0.
2/5, 1
Let f(v) be the second derivative of -1 - 8*v + 1/3*v**3 - 1/6*v**4 + 0*v**2 + 1/40*v**5. Determine m so that f(m) = 0.
0, 2
Solve -144 + 105*t**2 - 300*t**2 + 103*t**2 + 96*t**2 - 36*t = 0.
-3, 12
Let j = 4241/1892 - -4/473. Solve -15/4*m**2 + 0 - j*m = 0.
-3/5, 0
Suppose -p + 2*p - 5 = 0. Let k be 72/28*56/6. Let a(q) = -9*q**2 + 35*q - 14. Let w(t) = 45*t**2 - 174*t + 69. Let m(x) = k*a(x) + p*w(x). Factor m(y).
3*(y - 3)*(3*y - 1)
Let l(s) be the first derivative of -27*s**6/2 + 1494*s**5/5 - 163*s**4 + 24*s**3 + 774. Let l(h) = 0. What is h?
0, 2/9, 18
Let k = 10/247 - -1195/988. Factor 3/2*n - 1/4*n**2 - k.
-(n - 5)*(n - 1)/4
Let s = -871 - -878. Let c(u) be the third derivative of 0 - 1/210*u**s - 1/60*u**6 + 0*u**3 - 2*u**2 + 0*u + 0*u**4 + 0*u**5. Let c(a) = 0. Calculate a.
-2, 0
Let k(r) be the third derivative of r**7/504 - r**6/144 - r**5/12 + r**4/2 + 9*r**2. Let s(o) be the second derivative of k(o). Factor s(q).
5*(q - 2)*(q + 1)
Suppose 3*u - 45 = -6*u. Let -u*t + 3*t**5 + 2*t + 6*t**3 + 7*t**5 - 13*t**5 = 0. What is t?
-1, 0, 1
Factor 1138 + 1708 + 1800*v - 185*v**2 - 4466 + 5*v**3.
5*(v - 18)**2*(v - 1)
Factor -3/4*d**2 - 9/4*d + 15/2.
-3*(d - 2)*(d + 5)/4
Let p be 4/(-70)*270/(-54). What is c in p*c**3 + 10/7*c**2 + 8/7 + 16/7*c = 0?
-2, -1
Let c be (8/(-24))/((-2)/510). Let q(v) = -155*v**2 + 125*v - 140. Let y(k) = -11*k**2 + 9*k - 10. Let b(a) = c*y(a) - 6*q(a). Factor b(s).
-5*(s - 2)*(s - 1)
Suppose 130*y = 146*y. Find a, given that -2/9*a**5 + 4/9*a - 2/9*a**3 + y - 2/3*a**4 + 2/3*a**2 = 0.
-2, -1, 0, 1
Factor 8/5*j + 7/5 + 1/5*j**2.
(j + 1)*(j + 7)/5
Let k(z) be the first derivative of -z**3/4 - 57*z**2/8 - 342. Factor k(p).
-3*p*(p + 19)/4
Let m(s) = s**3 - s**2. Let b be m(1). Suppose b*t + 2*t = 6. Factor t*d + 3*d**2 - 6 + 0*d**2 + 0*d.
3*(d - 1)*(d + 2)
What is v in v**4 - 4*v + 20*v**3 + 0*v**4 + v**5 - 3*v**4 + 8*v**2 - 23*v**3 = 0?
-2, 0, 1, 2
Let z be -2 - (-1 - 6/2). Solve 7*p**2 - 9*p + 3 + 9*p**2 - 3*p**3 - 3*p**z - 4*p**2 = 0 for p.
1
Let g(l) be the second derivative of l**7/63 - 7*l**6/45 - l**5/15 + 23*l**4/9 + 65*l**3/9 + 25*l**2/3 - l - 11. Factor g(b).
2*(b - 5)**2*(b + 1)**3/3
Determine p, given that -151*p - 4*p**3 - 165*p + 332*p + 12*p**2 = 0.
-1, 0, 4
Let d(a) = -a**2 - 17*a + 45. Let x be d(-20). Let l be (12/x - -1)*(0 + 3). Factor l*m**4 + 0*m - 6/5*m**2 + 3/5 + 0*m**3.
3*(m - 1)**2*(m + 1)**2/5
Let y(o) be the second derivative of -5/72*o**4 + 1/24*o**5 + 0 + 0*o**3 + 13*o + 0*o**2. Factor y(f).
5*f**2*(f - 1)/6
Solve -273/4*x + 69 - 3/4*x**2 = 0.
-92, 1
Let h(c) be the third derivative of c**6/96 + 7*c**5/24 + 175*c**4/96 + 55*c**3/12 + 53*c**2 + 2. Determine y so that h(y) = 0.
-11, -2, -1
Let m(l) be the first derivative of l**2 + 17*l - 6. Let z be m(0). Factor 27 - z + 15*q**3 + 19*q**2 - 59*q**2 + 15*q.
5*(q - 2)*(q - 1)*(3*q + 1)
Let c(b) be the third derivative of b**7/945 - b**6/90 + b**5/30 - 42*b**2 + 2*b. Suppose c(o) = 0. Calculate o.
0, 3
Let k be -7 - -7 - (0 + 1/(-4)). Let o(l) be the second derivative of 0 - 3/16*l**4 - 1/8*l**2 + 12*l + k*l**3. Find w, given that o(w) = 0.
1/3
Let m(g) be the third derivative of g**7/280 + g**6/48 + g**5/20 - 7*g**4/12 + 25*g**2. Let j(o) be the second derivative of m(o). Factor j(a).
3*(a + 1)*(3*a + 2)
Suppose -2*t + 8 = b - t, 2*b + t - 11 = 0. Let o(a) = a**2 - 3*a + 3. Let m(d) = -d**2 + 3*d - 4. Let f(u) = b*m(u) + 4*o(u). Let f(s) = 0. Calculate s.
0, 3
Let k(a) be the third derivative of a**5/450 - a**4/90 - a**3/3 + 286*a**2. Factor k(h).
2*(h - 5)*(h + 3)/15
Let x = -1969 + 1969. Suppose 20*i**3 - 88/7*i**2 + 16/7*i + x - 50/7*i**4 = 0. What is i?
0, 2/5, 2
Let f(u) = 10*u + 100. Let i be f(-10). Solve 1/5*r**2 + 1/5*r + i = 0 for r.
-1, 0
Let u(x) be the second derivative of -x + 1/15*x**3 - 1/225*x**6 - 1/90*x**4 + 2/15*x**2 - 1/50*x**5 + 0. What is n in u(n) = 0?
-2, -1, 1
Find z, given that 56*z**2 - 3*z**5 + 3*z**3 - 2*z**4 - z**4 - 53*z**2 = 0.
-1, 0, 1
Let p be -9*(-5 - -4) + -5. Suppose 5*k - 5*w = 5, -4 = -4*w + p. Factor -6/7 + 10/7*n**2 - 8/7*n**k + 4/7*n.
-2*(n - 1)**2*(4*n + 3)/7
Let n = -2/2005 - -24074/14035. Let y = n - 32/35. Factor 0*i**4 + 0 + 6/5*i**3 - 2/5*i**5 + 0*i + y*i**2.
-2*i**2*(i - 2)*(i + 1)**2/5
Let g(r) be the first derivative of -r**6/6 - 6*r**5/5 - 11*r**4