irst derivative of 2/15*f**a - 2 + 4/5*f - 3/5*f**2. Factor r(z).
2*(z - 2)*(z - 1)/5
Let t(m) be the first derivative of m**6/2 - 2*m**5/5 - 3*m**4/4 + 2*m**3/3 - 5. Factor t(w).
w**2*(w - 1)*(w + 1)*(3*w - 2)
Let v(y) be the third derivative of -y**5/20 - 3*y**4/8 + 10*y**2. Factor v(w).
-3*w*(w + 3)
Suppose -4 = -2*s + 8. Let b = 6 - s. Factor -1 + 1/2*k**3 + b*k**2 - 3/2*k.
(k - 2)*(k + 1)**2/2
Let g(i) be the third derivative of -1/480*i**6 + 0*i + 0*i**3 + 1/120*i**5 + 0 - 2*i**2 - 1/96*i**4. Find s such that g(s) = 0.
0, 1
Suppose -4*h = -7 - 1. Factor -6/11*b**h + 2/11*b**4 + 4/11*b**3 - 8/11*b + 8/11.
2*(b - 1)**2*(b + 2)**2/11
Suppose 0*k = 6*k + 792. Let f be -6*(2 + 280/k). Suppose 2*m - 42/11*m**2 - 4/11 - f*m**4 + 32/11*m**3 = 0. What is m?
1/2, 1, 2
Let x(k) = k**2 + k. Let o be 3/2 - 7/14. Let y(c) = 5*c**2 - 16*c + 27. Let n(j) = o*y(j) - 2*x(j). Suppose n(s) = 0. Calculate s.
3
Factor 50/3*o**3 + 30*o**2 - 45*o - 35/3*o**4 - 45 + 5/3*o**5.
5*(o - 3)**3*(o + 1)**2/3
Let s = 1988/15 + -11921/90. Let t(p) be the second derivative of -1/36*p**4 + 0*p**3 + 1/30*p**5 + 0 + p + 0*p**2 + s*p**6 + 2/63*p**7. Factor t(g).
g**2*(g + 1)**2*(4*g - 1)/3
Let w(o) be the second derivative of o**2 + 2*o + 0 - 1/90*o**5 + 0*o**3 + 0*o**4. Let a(k) be the first derivative of w(k). What is z in a(z) = 0?
0
Suppose 0 = -3*x + 17 - 8. Let o(c) be the first derivative of -1/2*c**4 + c**2 + x + 0*c**3 + 0*c. Solve o(i) = 0 for i.
-1, 0, 1
Suppose -2/3*h**3 + 0 + 2/3*h**2 - 2/9*h + 2/9*h**4 = 0. Calculate h.
0, 1
Let q(n) be the third derivative of n**6/24 + n**5/4 + 5*n**4/12 - 35*n**2. Solve q(r) = 0 for r.
-2, -1, 0
Suppose x - 5*x + 0*x = 0. Let c(h) be the third derivative of 0*h**3 + x*h**5 + 1/240*h**6 + 0*h + 0*h**4 + 0 - 2*h**2. Determine u so that c(u) = 0.
0
Determine d, given that -4*d**2 + 6*d + 7*d + 7*d**2 + 5*d = 0.
-6, 0
Let f be 33*(-5)/(-15) + -3. Let g(b) be the first derivative of -4*b**2 - 3 + f*b + 2/3*b**3. Factor g(k).
2*(k - 2)**2
Suppose 2*p - 4*p - 2 = 0. Let x(t) = 14*t**2 + 11*t + 6. Let a(y) = y**2 + y + 1. Let z(v) = p*x(v) + 5*a(v). Factor z(q).
-(3*q + 1)**2
Suppose -2 = -h, j - 1 = -2*h + 6. Suppose 10/7*g**2 + 6/7*g**j + 4/7*g + 0 = 0. Calculate g.
-1, -2/3, 0
Suppose -d + 3 = -6. Let z be (2/10)/(d/15). Find i such that 1/3*i**2 - 1/3 + 1/3*i**3 - z*i = 0.
-1, 1
Let q = -31/117 - -2/13. Let b = q + 7/9. Let -4/3*f**3 + 2/3*f**2 + 0 + 0*f + b*f**4 = 0. What is f?
0, 1
Let p(n) be the first derivative of 0*n - 2 - 1/20*n**5 + 1/4*n**2 + 1/12*n**3 - 3/16*n**4 + 1/24*n**6. Factor p(g).
g*(g - 2)*(g - 1)*(g + 1)**2/4
Let l(h) be the third derivative of -h**6/30 - 2*h**5/15 + 3*h**2. Suppose l(w) = 0. What is w?
-2, 0
Let g(a) = -a**4 + 2*a**3 - 3*a**2 - 4*a - 4. Let t(h) = h**2. Let q = -5 - -4. Let v(r) = q*g(r) - 6*t(r). Suppose v(c) = 0. Calculate c.
-1, 2
Let o = 117 - 194. Let j be o/(-30) - (-11)/(-66). Factor -3/5 - 12/5*a**2 - j*a.
-3*(2*a + 1)**2/5
Let a = 3 + 0. Solve 5*p**2 + p**3 - 4*p**4 - a*p**3 - 3*p**2 = 0 for p.
-1, 0, 1/2
Let w be (2 + -2)*4/(-8). Suppose 0 = -w*g - g. Factor -1/4*z**2 - 1/4*z**5 - 3/4*z**4 + g + 0*z - 3/4*z**3.
-z**2*(z + 1)**3/4
Let u(w) be the third derivative of w**8/10080 - w**7/1260 + w**5/30 + 2*w**2. Let s(g) be the third derivative of u(g). Factor s(p).
2*p*(p - 2)
Let l(n) be the second derivative of -n**5/120 - n**4/48 - 11*n**2/2 - 10*n. Let p(z) be the first derivative of l(z). Suppose p(d) = 0. What is d?
-1, 0
Let g(p) be the second derivative of -p**5/20 + 5*p**4/12 - 7*p**3/6 + 3*p**2/2 + 5*p. Solve g(a) = 0 for a.
1, 3
Let x(m) be the third derivative of -3*m**6/40 - m**5/10 + 12*m**2. What is v in x(v) = 0?
-2/3, 0
Suppose 0 = 8*a - a - 21. Factor 0 - 4*i + 18*i**2 + 27/2*i**4 - 27*i**a.
i*(3*i - 2)**3/2
Let -4/3*r**2 + 0 - 1/3*r**4 + 4/3*r**3 + 0*r = 0. Calculate r.
0, 2
Let s(k) be the third derivative of -k**5/60 - 5*k**4/12 - 3*k**3/2 - 2*k**2. Let v be s(-9). Factor v*j**2 - 1/5*j**3 + 0 + 0*j + 1/5*j**4.
j**3*(j - 1)/5
Let b(x) be the third derivative of 0 + 2/3*x**3 + 1/12*x**4 + 0*x + 2*x**2 - 1/30*x**5. Factor b(a).
-2*(a - 2)*(a + 1)
Let p(a) be the first derivative of 2*a**3/3 + 18*a**2 + 162*a + 27. Let p(o) = 0. Calculate o.
-9
Let j(y) be the second derivative of -y**6/24 + y**5/20 + y**4/12 + y**2/2 - y. Let t(m) be the first derivative of j(m). What is s in t(s) = 0?
-2/5, 0, 1
Suppose -4*s - 12 = 5*p, -2*s - 2 - 10 = 4*p. Let f = 4 + p. Factor -c**2 + f*c**2 + 2*c**2.
c**2
Let o(b) = b. Let p be o(8). Let g be ((-14)/(-49))/(p/14). Factor g*z**3 + 1/2*z**4 + 0 - 1/2*z - 1/2*z**2.
z*(z - 1)*(z + 1)**2/2
Let f be 1 - 2/(6/(-9)). Suppose 0 = -0*q - f*q + 24. Factor 4*o + o**2 + 3 - q*o - 2.
(o - 1)**2
Let g be (-26)/(-4) - 2/4. Suppose -l + g*l - 10 = -5*v, 0 = -4*v + 5*l + 17. Factor 4 + v*t**2 + 1/2*t**3 + 6*t.
(t + 2)**3/2
Suppose -3*l - 5 = -11. Suppose 0 = t - 5 + l. Let -1/5*s**t + 0*s + 0 + 2/5*s**2 = 0. Calculate s.
0, 2
Let z(m) be the first derivative of -2*m**3/27 - m**2/9 + 1. Solve z(h) = 0.
-1, 0
Determine g, given that 3/4*g + 1/2 + 1/4*g**2 = 0.
-2, -1
Let o(q) be the second derivative of -q**4/21 - 4*q**3/21 - 2*q**2/7 + q. Factor o(l).
-4*(l + 1)**2/7
Let j(a) = 4*a**2 + 5*a + 4. Let q(v) = -15*v**2 - 19*v - 15. Let f(g) = -22*j(g) - 6*q(g). Let f(i) = 0. What is i?
-1
Suppose -s + 3*s = -28. Let y be s/(-10) + (-18)/(-30). What is m in -6*m**2 - 4*m**3 + 0*m**y - 2*m - 2*m**4 - 2*m**3 = 0?
-1, 0
Suppose 4*z + 5*v = 33, -25 = -4*z + v + 2*v. Let c = 4 + -2. Let 3*y**3 + 7*y**c - 2*y**3 - z*y**2 = 0. What is y?
0
Let t be 6 + (-2 - (0 - 2)). Suppose t*x - 6 = 4*x. Factor -x - u**3 - 2*u**4 + 3 - u**5.
-u**3*(u + 1)**2
Let b be 5 + 0 - (-12)/4. Let l(d) = 5*d**3 - 4*d**2 - d - 3. Let n(o) = 14*o**3 - 12*o**2 - 2*o - 8. Let c(q) = b*l(q) - 3*n(q). Factor c(j).
-2*j*(j - 1)**2
Let m(v) be the third derivative of -v**8/33600 + v**7/4200 - v**6/1200 - v**5/20 - 2*v**2. Let s(x) be the third derivative of m(x). Let s(w) = 0. What is w?
1
Factor -8/3 - 10/3*s - 2/3*s**2.
-2*(s + 1)*(s + 4)/3
Let h = -2/577 - 16729/1154. Let x = 15 + h. Factor -s**2 - x + 1/2*s**5 + s**3 + 3/2*s**4 - 3/2*s.
(s - 1)*(s + 1)**4/2
Let c(n) = -n**2 + 65. Let q be c(0). Let a be q/15 + 2/3. Find b, given that -2*b**4 + 4*b + 10*b**a - 14*b**3 - 4*b**4 - b**2 + 7*b**2 = 0.
-1, -2/5, 0, 1
Let o be 2 + 21/(-6) - -2. Let t(m) be the first derivative of -2 + o*m**3 - 1/2*m + 1/4*m**4 + 0*m**2. Suppose t(a) = 0. What is a?
-1, 1/2
Let a(i) be the second derivative of i**5/180 + i**4/36 + i**3/18 - i**2/2 + 3*i. Let d(w) be the first derivative of a(w). Let d(o) = 0. What is o?
-1
Let x be (-32)/3 + (-1)/3. Let i be 1/(x/(-2) + -2). Factor -i*f**3 + 0 + 8/7*f**2 - 8/7*f.
-2*f*(f - 2)**2/7
Factor 0 + 76/5*l**2 + 24/5*l - 28/5*l**3.
-4*l*(l - 3)*(7*l + 2)/5
Factor -5*c**2 - c**4 + 0*c**5 + 2*c**3 + 2*c - c**5 + c**3 + 2*c**4.
-c*(c - 1)**3*(c + 2)
Let u(t) be the second derivative of t**7/35 - 8*t**6/75 + 7*t**5/50 - t**4/15 + 8*t. Factor u(g).
2*g**2*(g - 1)**2*(3*g - 2)/5
Let s(t) = 29*t**3 - 77*t**2 - 66*t + 16. Let a(c) = -19*c**3 + 51*c**2 + 44*c - 11. Let i(j) = -8*a(j) - 5*s(j). Factor i(f).
(f - 4)*(f + 1)*(7*f - 2)
Suppose -2 + 17 = 5*v. Let n(q) be the first derivative of 4*q - 3*q**2 + 2/3*q**3 - v. Determine s, given that n(s) = 0.
1, 2
Factor 2/5*i**3 + 0*i**2 + 0*i + 0.
2*i**3/5
Let j(a) = -a**2 + 6*a - 5. Let b be j(4). What is u in -2*u**2 + 6*u - 4 - b*u**2 + 5*u**2 - 2*u**2 = 0?
1, 2
Let v(a) be the second derivative of a**7/420 - a**6/60 + a**4/3 + 7*a**3/6 - 2*a. Let n(t) be the second derivative of v(t). Factor n(q).
2*(q - 2)**2*(q + 1)
Factor 12*b + 13*b + 118 + 20*b**2 - 108 + 5*b**3.
5*(b + 1)**2*(b + 2)
Let x(j) be the second derivative of j**5/30 - j**4/12 - 2*j**3/3 - 3*j**2/2 - 2*j. Let c(v) be the first derivative of x(v). Determine k so that c(k) = 0.
-1, 2
Let k = 38/279 - -8/93. Let j be (-3)/(-12)*(-16)/(-18). Determine c so that 2/9*c - k - 2/9*c**3 + j*c**2 = 0.
-1, 1
Let g = 12 + -9. Let h(a) be the second derivative of 0*a**2 - a - 1/10*a**5 + 0 + 0*a**g - 1/6*a**4. Let h(k) = 0. What is k?
-1, 0
Let d(i) = i + 3. Let k be d(0). Factor -1 + y**4 - y**3 + 8*y**3 + 2*y - 7*y**3 - 2*y**k.
(y - 1)**3*(y + 1)
Factor v**3 - 10/3*v**2 + 8