-16, -1
Let i(y) = -66*y**4 - 556*y**3 + 430*y**2 + 153*y. Let w(s) = 32*s**4 + 277*s**3 - 215*s**2 - 76*s. Let a(u) = 6*i(u) + 13*w(u). Suppose a(g) = 0. Calculate g.
-14, -1/4, 0, 1
Let m(a) be the second derivative of a**5/90 - 13*a**4/54 - 10*a**3/9 - 9*a - 10. Factor m(s).
2*s*(s - 15)*(s + 2)/9
Suppose 32 + 6 = 2*v. What is s in 4*s**2 - s**3 + 2040 - 2032 + 20*s - v*s**3 - 12*s**4 = 0?
-1, -2/3, 1
Let d(q) = q**3 - 4*q**2 - 5*q + 2. Let v be 1/(-2) - 66/(-12). Let t be d(v). Suppose 12*j + 3 - j**t - 4*j**2 + 3*j**2 - 21 = 0. Calculate j.
3
Suppose 86 = 19*g + 67. Let 0*h**3 + 1/4*h**4 + g + 0*h - 5/4*h**2 = 0. Calculate h.
-2, -1, 1, 2
Let i(j) = -65*j**3 + 265*j**2 - 715*j. Let m(v) be the first derivative of 11*v**4/4 - 44*v**3/3 + 119*v**2/2 - 12. Let f(h) = -6*i(h) - 35*m(h). Factor f(u).
5*u*(u - 5)**2
Let i(w) = w**3 + 3*w**2 - 30*w + 42. Let u be i(2). Let -2*a**4 - 2*a + 3/2*a**3 + 1/2*a**5 + 0 + u*a**2 = 0. What is a?
-1, 0, 1, 2
Let c(u) be the second derivative of -u**5/90 - 5*u**4/18 - 25*u**3/9 + 21*u**2/2 + 38*u. Let z(o) be the first derivative of c(o). Find r such that z(r) = 0.
-5
Let x be (-110)/(-8) + 6/(-8). Factor -x*a**2 + 11*a**2 + 2*a - 2*a**3 + 0*a**3 + 2.
-2*(a - 1)*(a + 1)**2
Let t be 48/18 + 29/87. Let v(a) be the first derivative of -2/3*a**3 - 11 + 3/2*a**4 - t*a**2 - 2/5*a**5 + 4*a. Suppose v(x) = 0. Calculate x.
-1, 1, 2
Let l = 192 + -161. Let q be 2/(-7) - l/(-35). Factor 4/5*k - 1/5*k**2 - q.
-(k - 3)*(k - 1)/5
Factor -4/3*x**2 + 1/3*x**3 + 0 + x.
x*(x - 3)*(x - 1)/3
Suppose 29*k - 99*k - 39*k + 218 = 0. Suppose 2/5*l**3 - 7/5*l**4 - 2/5*l + 0 + 7/5*l**k = 0. Calculate l.
-1, 0, 2/7, 1
Let c(o) = -1. Let s(w) = w**3 - w**2 + 3*w - 4. Let y be s(1). Let k(x) = x**3 + 7*x**2 + 6*x - 1. Let i(f) = y*c(f) + k(f). Let i(h) = 0. Calculate h.
-6, -1, 0
Let n(v) = -v**2 + 24*v - 10. Let f be n(23). Factor 18*g - 12 + f*g**2 + 19*g**2 - 6*g - 35*g**2.
-3*(g - 2)**2
Let i be -1 + (-5)/(-20)*0. Let o(z) = 24*z**2 + 51*z - 9. Let w(y) = y**2 - y - 1. Let c(x) = i*o(x) - 3*w(x). Factor c(k).
-3*(k + 2)*(9*k - 2)
Let a(l) = -l - 2*l + 7*l - 3*l - l**2. Let c(v) = 6*v**2 - 8*v. Let d be 1 + 3/((-6)/4). Let z(o) = d*c(o) - 8*a(o). Let z(q) = 0. What is q?
0
Suppose 5*f = 2*i + i - 14, 5*i = 2*f + 17. Determine l so that 2*l**i - 4*l**3 + 7*l**4 - 9*l**4 + 4*l**3 = 0.
0, 1
Let r(k) be the third derivative of -k**7/42 + 5*k**6/24 + k**5/2 + k**2 - 9. Suppose r(y) = 0. What is y?
-1, 0, 6
Let d(a) = a**3 + 11*a**2 - 13*a - 9. Let n be d(-12). Let -3*o**4 + 18*o**n + 6*o**2 + 19*o**3 - 34*o**3 = 0. Calculate o.
-1, 0, 2
Suppose 8 = -2*g + 6, 4*g = -w - 2. Solve 6 + 0*i - 9/2*i**w + 3/2*i**3 = 0 for i.
-1, 2
Find s, given that -76/3*s**2 - 8/3*s**4 + 32/3*s + 18*s**3 - 2/3*s**5 + 0 = 0.
-8, 0, 1, 2
Let x = 64 - 71. Let v = x + 7. Factor 2/7*f**5 + 4/7*f**4 + 0 + 0*f**3 + 0*f**2 + v*f.
2*f**4*(f + 2)/7
Let j be (-6 + (-92)/(-14))/((-286)/(-77)). Factor 0 - 128/13*o**2 - j*o**4 + 0*o - 32/13*o**3.
-2*o**2*(o + 8)**2/13
Suppose n - 4*n - 2*b = -63, 4*n + 2*b = 84. Let y = -19 + n. Factor 0*m + 0 - 18/5*m**3 + 4/5*m**y.
-2*m**2*(9*m - 2)/5
Let p(c) be the third derivative of 1/480*c**6 - 1/1344*c**8 - 1/840*c**7 + 1/240*c**5 + 0*c**4 - 4*c**2 + 0*c + 0*c**3 + 0. Factor p(b).
-b**2*(b - 1)*(b + 1)**2/4
Let f be (378/68 + -6)*(-154)/27. Let i = f - 11/153. Suppose -i*t + 8/3*t**2 + 4/9 + 2*t**3 = 0. Calculate t.
-2, 1/3
Let u(q) be the second derivative of 2*q**7/21 - q**6/10 - 9*q**5/20 - q**4/6 + 226*q. Let u(i) = 0. What is i?
-1, -1/4, 0, 2
Suppose -1129 = 5*o - 1144. Solve 9/2*h**4 + 6*h - 6*h**o - 3/2 - 3*h**2 = 0 for h.
-1, 1/3, 1
Let i(h) be the second derivative of -h**7/42 - h**6/6 + h**5/20 + 5*h**4/12 - 2*h - 10. Let i(p) = 0. What is p?
-5, -1, 0, 1
Let a(q) be the second derivative of -q**5/30 + 5*q**4/18 - 4*q**3/9 + 130*q. Determine t so that a(t) = 0.
0, 1, 4
Factor 171*l**3 + 159*l**3 - 507 + 75*l**2 - 327*l**3 + 429*l.
3*(l - 1)*(l + 13)**2
Let s = 362 - 362. Let x(w) be the second derivative of 0 + s*w**2 + 1/6*w**4 - 2/3*w**3 + 3*w. Factor x(r).
2*r*(r - 2)
Factor 2/5*q**3 + 12/5 + 0*q**2 - 14/5*q.
2*(q - 2)*(q - 1)*(q + 3)/5
Let w(j) be the first derivative of -6/13*j - 9 - 4/13*j**2 - 2/39*j**3. Let w(u) = 0. What is u?
-3, -1
Let r(o) be the third derivative of o**8/672 - o**7/168 + o**6/144 + 7*o**4/24 - 7*o**2. Let d(q) be the second derivative of r(q). What is p in d(p) = 0?
0, 1/2, 1
Let s(q) = -q**3 - 2*q**2 + 3*q - 1. Let v be s(-3). Let c be v + -2 + 6 - (-34)/(-14). Factor c*p + 0 + 2/7*p**2.
2*p*(p + 2)/7
Let u be ((-195)/13 - -14)/((-9)/27). Factor 1/2*l**u + 2*l - 2*l**2 + 0.
l*(l - 2)**2/2
Let w(n) = 5*n**4 + 155*n**3 + 1275*n**2 + 1126*n + 1. Let s(z) = z + 1. Let v(y) = s(y) - w(y). Factor v(u).
-5*u*(u + 1)*(u + 15)**2
Let j(g) be the third derivative of 0*g**4 + 15*g**2 - 2/3*g**3 + 0*g + 1/60*g**5 + 0. Factor j(b).
(b - 2)*(b + 2)
Let b(r) be the second derivative of -r**5/50 - r**4/2 - 16*r**3/5 + 64*r**2/5 + 2*r - 12. What is t in b(t) = 0?
-8, 1
What is z in 26/5*z + 4 + 2/5*z**4 - 6/5*z**2 - 2*z**3 = 0?
-1, 2, 5
Solve 191*t**2 - 2*t + 6*t + 21*t - 192*t**2 + 8*t = 0.
0, 33
Let u(c) be the second derivative of c**7/168 - 7*c**6/15 + 783*c**5/80 + 7*c**4/6 - 98*c**3/3 - 152*c. Let u(a) = 0. Calculate a.
-1, 0, 1, 28
Let z(k) = -k**2 - k. Let j(f) = -f**3 - 3*f**2 - 11*f. Suppose -2*y = 7 + 53. Let l = -51 - y. Let h(g) = l*z(g) + 3*j(g). Find s, given that h(s) = 0.
0, 2
Suppose 5*h + 4*u - 27 = 0, -2*h + 4*u - 3*u = -16. Suppose -9*m**3 - 7*m**2 + 4*m + 10*m**2 + h*m - 5*m = 0. Calculate m.
-2/3, 0, 1
Let n(k) = 2*k - 2 - 4 + 1 - 2*k**3. Let d(r) = -9*r**3 + 9*r - 24. Let j(i) = 5*i - 16. Let s be j(8). Let l(h) = s*n(h) - 5*d(h). Factor l(b).
-3*b*(b - 1)*(b + 1)
Let m(b) be the second derivative of -b**9/22680 + b**8/3360 - b**7/1890 - 5*b**4/6 - 12*b. Let i(n) be the third derivative of m(n). Factor i(p).
-2*p**2*(p - 2)*(p - 1)/3
Let v(s) be the first derivative of s**6/8 + s**5/60 - s**4/2 - 2*s**3/3 - 3*s**2 + 9. Let m(w) be the second derivative of v(w). Factor m(p).
(p - 1)*(3*p + 2)*(5*p + 2)
Let j(u) be the third derivative of 1/120*u**5 - 22*u**2 - 1/2*u**3 + 0*u + 0 - 5/48*u**4. Factor j(f).
(f - 6)*(f + 1)/2
Let z(r) = -16*r**3 + 225*r**2 - 1512*r + 1275. Let n(j) = 5*j**3 - 75*j**2 + 504*j - 426. Let k(h) = 7*n(h) + 2*z(h). Find u, given that k(u) = 0.
1, 12
Suppose 30 = 3*n - 3*j, -24 - 18 = -n + 5*j. Find b such that -6*b - 1 + 9/4*b**4 - 35/4*b**n + b**5 - 5/2*b**3 = 0.
-2, -1, -1/4, 2
Suppose -2*v - 7 = -11. Determine j so that -j - j**2 - j - j**3 - j**4 + 3*j**3 + v*j**2 = 0.
-1, 0, 1, 2
Let o(p) be the second derivative of -p**8/112 - p**7/42 - p**6/60 + 16*p**2 + 8*p. Let m(z) be the first derivative of o(z). Factor m(y).
-y**3*(y + 1)*(3*y + 2)
Suppose 0 = -5*p + 3 + 7. Suppose 0*f**4 + 4*f**p - f**2 - f - 3*f**3 + f**4 = 0. Calculate f.
0, 1
Let c(v) be the second derivative of -v**5/270 + v**4/54 - v**3/27 + 11*v**2/2 + 11*v. Let s(g) be the first derivative of c(g). Factor s(t).
-2*(t - 1)**2/9
Let l = 1011 + -494. Factor -l*o - 29160*o**3 - 32805*o**4 + 11 - 923*o - 91 - 9720*o**2.
-5*(9*o + 2)**4
Solve -56*r**3 + 16*r - 14*r**2 - 5*r**5 - 18*r**4 - 15*r**4 + 2*r**2 = 0.
-4, -2, -1, 0, 2/5
Factor -152*t - 76/9*t**3 + 2/9*t**4 + 72 + 794/9*t**2.
2*(t - 18)**2*(t - 1)**2/9
Factor -13/2*u**2 + 66*u - 10.
-(u - 10)*(13*u - 2)/2
Let q(m) = 2*m - 5. Let l be q(5). Factor -2*i**4 - 4*i**4 + 4*i**3 + 28*i + 4*i**3 - 12 - 23*i**2 + l*i**4.
-(i - 3)*(i - 2)**2*(i - 1)
Factor -16/5*p**2 - 4*p - 8/5 - 4/5*p**3.
-4*(p + 1)**2*(p + 2)/5
Let c(z) = -3*z**3 - 5*z**2 - 12*z + 3. Let r be c(0). Factor -4/7*m + 2/7*m**4 - 6/7*m**2 + 0 + 0*m**r.
2*m*(m - 2)*(m + 1)**2/7
Let v(m) be the second derivative of 1/32*m**4 + 0*m**3 + 0*m**2 + 3/80*m**5 + 0 + 13*m + 1/80*m**6. What is a in v(a) = 0?
-1, 0
Find r, given that -1/2*r**3 + 0 - 1/6*r**5 + 5/6*r**4 - 5/6*r**2 + 2/3*r = 0.
-1, 0, 1, 4
Let n be ((-13)/(-159 - -3))/(7/126). Factor 3*f**2 - 9 + n*f**3 - 15/2*f.
3*(f - 2)*(f + 1)*(f + 3)/2
Let u(k) be the second derivative of -k**4/72 + 31*k**3/6 - 2883*k**2/4 - 102*k. Factor u(z).
-(z - 93)**2/6
Factor 4*n**2 + 6384*n**3 - n**2 - 6383*n**3.
n**2*(n + 3)
Factor -26/3*v - 76/