 - 8/5*q**2 + 0 - 2/5*q - 8/5*q**4 = 0.
-1, 0
Let l(t) be the first derivative of 0*t + 1/6*t**6 - 2 + 1/12*t**3 - 1/8*t**2 + 9/16*t**4 + 11/20*t**5. Determine i so that l(i) = 0.
-1, 0, 1/4
Let g(q) be the second derivative of -1/2*q**3 + 0 - 3/2*q**2 + 7*q + 1/40*q**6 + 3/20*q**5 + 3/16*q**4. Factor g(t).
3*(t - 1)*(t + 1)*(t + 2)**2/4
Let q(g) be the second derivative of -g**5/140 - g**4/21 - 5*g**3/42 - g**2/7 + 4*g. Factor q(k).
-(k + 1)**2*(k + 2)/7
Let z(r) be the second derivative of 0 - r - 5/24*r**4 - 1/8*r**2 + 1/8*r**5 + 5/24*r**3 + 1/168*r**7 - 1/24*r**6. Factor z(u).
(u - 1)**5/4
Suppose q - 5*q = -16. Suppose n + 14 = 5*x + 2*n, -17 = -q*x + 5*n. What is w in w - 2*w - 6*w**x + 6*w**2 + 2*w**4 - w = 0?
0, 1
Suppose -4*m + 10 = -6. Let b be m/14 - 4/14. Factor 0 + b*d**2 - 3/5*d**4 + 0*d + 0*d**3 + 3/5*d**5.
3*d**4*(d - 1)/5
Suppose 0 = 8*o - 9*o + 4. Let -8/3 + 11*v**3 + 7/3*v**o + 46/3*v**2 + 4*v = 0. Calculate v.
-2, -1, 2/7
Let q be (2/6)/((-45)/(-27)). Let z(s) be the first derivative of 0*s - 1 + 1/15*s**3 - q*s**2. Suppose z(p) = 0. Calculate p.
0, 2
Let k(b) be the second derivative of -b**7/12600 + b**6/900 - b**5/150 - b**4/3 + 4*b. Let a(j) be the third derivative of k(j). Solve a(u) = 0 for u.
2
Let i be (3 + -3)/(2*1). Let b(w) be the first derivative of 2 + 3/2*w**4 + 4/7*w**2 + 32/21*w**3 + i*w + 18/35*w**5. Factor b(u).
2*u*(u + 1)*(3*u + 2)**2/7
Factor -6*b**2 + 81*b**3 - 89*b**3 - 3*b**4 - 2*b - b**2.
-b*(b + 1)**2*(3*b + 2)
Let k(y) = -y**2 - 7*y + 5. Let b be k(-7). Let r(f) be the first derivative of 1 + 0*f**4 + 1/18*f**6 - 1/6*f**2 + 2/9*f**3 + 0*f - 2/15*f**b. Factor r(j).
j*(j - 1)**3*(j + 1)/3
Let y be 7/(-3)*(-11 - -8). Let i(z) be the third derivative of 0 + 0*z**4 + 2*z**2 - 1/105*z**y + 0*z - 1/60*z**6 + 0*z**5 + 0*z**3. Factor i(m).
-2*m**3*(m + 1)
Factor r**2 - 3*r - r + 5*r.
r*(r + 1)
Let w(k) be the second derivative of k**6/135 + k**5/30 - 4*k**3/27 - 6*k. Factor w(x).
2*x*(x - 1)*(x + 2)**2/9
Let y(j) be the first derivative of j**6/60 - j**5/15 - j**4/12 + 2*j**3/3 + 5*j**2/2 + 3. Let x(o) be the second derivative of y(o). Factor x(f).
2*(f - 2)*(f - 1)*(f + 1)
Let c(l) = l**2 - 1. Let t(g) = -9*g**4 - 15*g**3 - 14*g**2 - g + 7. Let z(j) = -14*c(j) - 2*t(j). Factor z(r).
2*r*(r + 1)*(3*r + 1)**2
Let i = 3 - -1. Suppose i*c + 9 = 33. Suppose -2*f**5 - 6*f**2 - c*f**4 + 12*f**2 + f - 2*f**3 + 3*f = 0. Calculate f.
-2, -1, 0, 1
Let f(n) be the first derivative of -n**3/12 + n**2/8 + n/2 + 3. Factor f(m).
-(m - 2)*(m + 1)/4
Let t(m) be the third derivative of 0 - 2/15*m**3 + 3*m**2 + 7/60*m**4 - 1/50*m**5 + 0*m. Factor t(g).
-2*(g - 2)*(3*g - 1)/5
Let z(h) = 4*h**2 - 6*h - 10. Let u(i) = -4 - 4*i**2 + 3 + 7*i**2 - 2*i**2. Let x(t) = 6*u(t) - z(t). Suppose x(v) = 0. What is v?
-2, -1
Let g be ((-200)/35)/10*(0 - 1). Suppose -2/7*h + 2/7*h**3 + g - 4/7*h**2 = 0. Calculate h.
-1, 1, 2
Let q = -4 + 7. Let 19*v**4 - 15*v**4 + 8*v - 5*v**3 + 6*v**3 + 15*v**q + 20*v**2 = 0. Calculate v.
-2, -1, 0
Let l be (-3 - 0/3) + 9. Factor l - 3 + 3*a + a - 2*a**2 - 5.
-2*(a - 1)**2
Let d(o) be the second derivative of o**4 + 3*o**2 + 0 + 6*o + 3/20*o**5 + 5/2*o**3. Factor d(q).
3*(q + 1)**2*(q + 2)
Suppose 0 = 2*w + 3*r - 1, -r = -3*w + 19 - 1. Suppose 2*m**w + 2 + 4*m**4 - 4*m**3 - 4*m**4 + 2*m - 4*m**2 + 2*m**4 = 0. What is m?
-1, 1
Let p(q) be the first derivative of 0*q + 4 + 4/5*q**5 + 3*q**4 + 0*q**3 - 8*q**2. Factor p(z).
4*z*(z - 1)*(z + 2)**2
Let r(j) be the first derivative of -14/9*j**4 - 1 + 98/45*j**5 + 0*j**2 + 0*j + 8/27*j**3. Let r(y) = 0. What is y?
0, 2/7
Let r(f) be the first derivative of -3*f**3/5 - 7*f**2/10 + 2*f/5 - 1. Solve r(a) = 0.
-1, 2/9
Let u = -7 - -11. Let l = u + -2. Factor 4*g**3 - 3*g**l - 2*g + 3*g - 2*g**2.
g*(g - 1)*(4*g - 1)
Let y(l) be the third derivative of -l**7/105 - l**6/20 - l**5/15 + 32*l**2. Find m, given that y(m) = 0.
-2, -1, 0
Let a = -30 - -30. Factor -8/3*h + a + 4*h**2 - 2*h**3 + 1/3*h**4.
h*(h - 2)**3/3
Let k(y) = 28*y**2 + 52*y. Let h(v) = -9*v**2 - 17*v. Let a(w) = -16*h(w) - 5*k(w). Find z such that a(z) = 0.
-3, 0
Factor 121*l**3 - 120*l**3 - 2*l + 2*l.
l**3
Factor -5/2*f**2 - 10/3*f**3 + 0*f + 0 - 5/6*f**4.
-5*f**2*(f + 1)*(f + 3)/6
Let q(d) be the first derivative of -7/5*d**5 - 5*d**3 + 19/4*d**4 - 1 + 2*d + 1/2*d**2. Factor q(n).
-(n - 1)**3*(7*n + 2)
Solve -q**4 + 1 + 0*q**3 + 3*q**2 + 0*q**2 - 4*q - 5 + 2*q**3 = 0.
-1, 2
Let f(j) = 18*j**2 - 17*j + 11. Let m(y) = -164*y**2 + 152*y - 100. Let k(s) = -28*f(s) - 3*m(s). Factor k(g).
-4*(g - 1)*(3*g - 2)
Let s be (-4)/14*10/12. Let k = s - -41/84. Determine y so that k*y**5 + 0 + 0*y - 1/4*y**2 + 1/4*y**4 - 1/4*y**3 = 0.
-1, 0, 1
Let r(v) be the third derivative of -v**8/336 - v**7/70 + v**6/120 + 7*v**5/60 - 2*v**3/3 - 11*v**2. Suppose r(t) = 0. What is t?
-2, -1, 1
Let a(n) = -n**3 + 7*n**2 - 3*n + 3. Let j be a(5). Let s = 153/4 - j. Determine w so that 0 - s*w**3 + 0*w**2 + 0*w = 0.
0
Suppose 2*o = 4*o - 8. Let i(g) be the third derivative of -1/90*g**5 + 1/9*g**o + 0 - g**2 - 4/9*g**3 + 0*g. Solve i(a) = 0 for a.
2
Suppose -k + 6*k - 13 = q, -2*q + 7 = k. Let a be 2/9 + q/18. Factor 0 + 2/3*t - a*t**2.
-t*(t - 2)/3
Let t(w) be the second derivative of w**7/189 - w**6/135 - w**5/90 + w**4/54 + 7*w. Suppose t(q) = 0. Calculate q.
-1, 0, 1
Let h(w) = -4*w**3 + w + 1. Let c be h(-1). Suppose -c - 11 = -3*l - 2*f, 6 = -l + 3*f. Factor 0 + 2/5*d**2 + 2/5*d**l + 0*d.
2*d**2*(d + 1)/5
Let b(y) be the first derivative of 4*y**5/5 - 4*y**4 + 8*y**3 - 8*y**2 + 4*y - 16. Factor b(u).
4*(u - 1)**4
Let q be 4/(-30)*100/(-10). Factor 4/3*h**2 + q*h + 1/3*h**3 + 0.
h*(h + 2)**2/3
Let l(t) be the second derivative of -t**4/3 + 4*t**3/3 + 6*t**2 - t. Find z such that l(z) = 0.
-1, 3
Let u be (-1)/(-2) - (-3)/2. Find t, given that 1/5*t**4 + 0*t**3 + 0*t + 1/5 - 2/5*t**u = 0.
-1, 1
Determine i, given that 0*i + 2/9*i**2 + 4/9*i**3 + 2/9*i**4 + 0 = 0.
-1, 0
Let f(h) be the third derivative of h**5/150 + h**4/20 - 4*h**3/15 + 8*h**2. Factor f(n).
2*(n - 1)*(n + 4)/5
Let b(p) = -3*p - 3. Let o be b(-2). Suppose 0*r + r = o. Suppose 2*x**5 - 3*x**3 - x**5 + x**r + 0*x + x = 0. Calculate x.
-1, 0, 1
Suppose -3 = s - 7. Factor s*a**2 - 5*a**2 + a + 0*a**2.
-a*(a - 1)
Suppose -q**3 + 0*q - 7 - 3*q - 4*q**2 + 7 = 0. Calculate q.
-3, -1, 0
Factor 0*i**3 - 3/4*i**2 + 0 + 0*i + 3/4*i**4.
3*i**2*(i - 1)*(i + 1)/4
Let i(u) be the first derivative of -u**6/6 - u**5/5 + u**4/4 + u**3/3 - 6. Factor i(v).
-v**2*(v - 1)*(v + 1)**2
Let v(p) be the third derivative of -p**8/3192 + 11*p**7/1995 - 17*p**6/570 + 23*p**5/285 - 29*p**4/228 + 7*p**3/57 + 26*p**2. Factor v(i).
-2*(i - 7)*(i - 1)**4/19
Let a(t) be the second derivative of 1/40*t**5 + 0 - 1/12*t**3 + 1/48*t**4 - 1/8*t**2 + 3*t. Factor a(y).
(y - 1)*(y + 1)*(2*y + 1)/4
Let b be (2 + -1)/((-8)/(-16)). Let 0 + 2/3*u + 7/3*u**b = 0. Calculate u.
-2/7, 0
Suppose 5*h = 2 + 8. Find s such that -2/5*s**4 + 0 + 0*s + 4/5*s**3 - 2/5*s**h = 0.
0, 1
Suppose 3*t - 2 + 8 = 0. Let z(c) = c**3 + 2*c**2 + 5*c. Let l(a) = -3*a**3 - 5*a**2 - 11*a - 1. Let s(x) = t*l(x) - 5*z(x). Suppose s(b) = 0. What is b?
-2, 1
Let q(s) be the third derivative of s**6/96 - s**5/40 + s**4/96 - 9*s**2. Determine j so that q(j) = 0.
0, 1/5, 1
Let p = -1759967/7 + 250954. Let h = p + 471. Suppose 8/7*m + 2/7*m**2 + h = 0. Calculate m.
-2
Let o = -1/67 + 70/201. Factor -2/3 + n - o*n**2.
-(n - 2)*(n - 1)/3
Let -4096/7*z + 8192/7 - 64/7*z**3 + 768/7*z**2 + 2/7*z**4 = 0. Calculate z.
8
Determine t so that 0 + 2*t + 8/3*t**2 + 2/3*t**3 = 0.
-3, -1, 0
Let j(s) = s**2 - 5*s + 2. Let f be 2 + 5*15/25. Let b be j(f). Factor 2/7 - 8/7*h + 6/7*h**b.
2*(h - 1)*(3*h - 1)/7
Let z(s) be the third derivative of 2*s**7/105 + s**6/6 + 3*s**5/5 + 7*s**4/6 + 4*s**3/3 - 15*s**2. Factor z(i).
4*(i + 1)**3*(i + 2)
Let v(u) be the second derivative of u**5/5 + 4*u**3 + 7*u**2 - 7*u. Let k(p) = -3 - 5*p + 0*p - p**3 + 0*p. Let q(n) = -14*k(n) - 3*v(n). Factor q(c).
2*c*(c - 1)*(c + 1)
Determine k, given that -5*k**4 - 12*k**3 + 22*k**4 - 9*k**5 + 7*k**4 + 0*k**3 = 0.
0, 2/3, 2
Let n be ((-2)/5)/((-1)/5). Let k = -47 - -145/3. What is u in -k*u - 2/3 - 2/3*u**n = 0?
-1
Let d(a) = 4*a**4 - 2*a**2 - 12*a + 4. Let g(f) = 9*f**4 - f**3 - 4*f