*2. Let l(x) be the third derivative of t(x). Suppose l(s) = 0. What is s?
2/7, 1
Suppose 5*x + 12 = 22. Let u(y) be the third derivative of 0*y - y**x + 0 - 1/80*y**5 - 5/96*y**4 + 1/12*y**3. Determine r, given that u(r) = 0.
-2, 1/3
Let z(j) = -2*j**2 - 8*j + 2. Let f be z(-4). Factor 3/2*x - 1 - 1/2*x**f.
-(x - 2)*(x - 1)/2
Let v(s) = s**2 + 5*s + 1. Let i be v(-5). What is t in t**2 - 2*t + i + 0*t**2 + 0*t**2 = 0?
1
Let g(o) = 3*o**3 - 5*o**2 - 3*o - 5. Let l(h) = h**3 - 2*h**2 - h - 2. Let b(x) = -4*g(x) + 10*l(x). Find k, given that b(k) = 0.
-1, 0, 1
Let w(y) be the first derivative of -9/14*y**2 - 3/28*y**4 + 2 - 5/7*y**3 + 27/7*y. Suppose w(r) = 0. What is r?
-3, 1
Let q = -24 - -54. Let m be (q/25)/(3/2). Suppose -24/5*w**2 + m + 6/5*w + 14/5*w**3 = 0. Calculate w.
-2/7, 1
Let m(z) = z**2 + 9*z + 11. Suppose 0 = 2*v - 11 + 27. Let g be m(v). Factor -g*t**3 - 9*t - 3*t**2 + 0*t**3 - t**4 + 8*t.
-t*(t + 1)**3
Let g(u) be the first derivative of -u**6/300 - u**5/150 + u**4/30 + u**2/2 + 1. Let n(m) be the second derivative of g(m). Let n(f) = 0. What is f?
-2, 0, 1
Let h(w) be the first derivative of -w**6/120 + w**5/20 - w**4/8 + w**3/6 + w**2/2 - 3. Let x(c) be the second derivative of h(c). Let x(y) = 0. Calculate y.
1
Let u be (-4 - -4)*(3 - 2). Let u*p + 0 - 2/7*p**2 = 0. Calculate p.
0
Let q(w) = -w**3 + 4*w**2 + 5*w + 2. Let a be q(5). Factor y**2 - 2*y**4 + 2*y**2 + y**2 - a.
-2*(y - 1)**2*(y + 1)**2
Let g be ((-1)/320)/(33/(-44)). Let c(o) be the third derivative of 0*o + 0*o**5 + 0 + g*o**6 + 0*o**3 - 1/48*o**4 - 3*o**2. Solve c(k) = 0.
-1, 0, 1
Factor 1/2*u**2 - 4*u + 8.
(u - 4)**2/2
Let u = -36 - -34. Let g be 3/6*u - -4. Suppose -2/5*m + 1/5*m**2 + 0 + 1/5*m**g = 0. What is m?
-2, 0, 1
Let g(z) be the third derivative of z**5/60 - z**4/16 + z**3/12 - 4*z**2. Solve g(k) = 0.
1/2, 1
Let p = 84/5 - 16. Solve -1/5 - 4/5*f**3 - 1/5*f**4 - 6/5*f**2 - p*f = 0.
-1
Let o(g) be the first derivative of 9*g**4/4 + 20*g**3/3 + 13*g**2/2 + 2*g + 1. Factor o(x).
(x + 1)**2*(9*x + 2)
Let t(p) be the third derivative of p**8/504 + 2*p**7/135 + p**6/27 + 4*p**5/135 + 28*p**2. Factor t(r).
2*r**2*(r + 2)**2*(3*r + 2)/9
Factor -41*z**4 - 42*z**2 + 33*z**3 + 38*z**4 + 12*z**3.
-3*z**2*(z - 14)*(z - 1)
Let n(r) be the first derivative of -3*r**4/4 - r**3 + 24. Suppose n(o) = 0. What is o?
-1, 0
Suppose 7 = -5*a + 22. Let n be (-2)/(-2)*(-49)/(-28). Find d such that -1/2*d**2 + 0*d + 0 - n*d**a = 0.
-2/7, 0
Let -16/5*v**2 - 8/5 + 36/5*v = 0. Calculate v.
1/4, 2
Suppose -7*u + 5*u = -8. Suppose z = u - 1. Solve 0 + 2/7*s**z + 0*s + 0*s**2 + 2/7*s**4 = 0 for s.
-1, 0
Find f such that 4/7*f + 8/7*f**2 + 3/7*f**3 + 0 = 0.
-2, -2/3, 0
Factor 0*i**2 - 2/3*i**5 - 4/3*i**4 + 0*i + 0 - 2/3*i**3.
-2*i**3*(i + 1)**2/3
Let k(t) be the third derivative of -1/30*t**6 + 1/12*t**4 + 0*t**5 + 0 + 0*t + 0*t**7 + 0*t**3 - 2*t**2 + 1/168*t**8. Factor k(g).
2*g*(g - 1)**2*(g + 1)**2
Let y(h) = -5*h**4 + 10*h**2 + 10*h - 10. Let k(c) = -5*c**4 + c**3 + 11*c**2 + 11*c - 12. Let l(g) = -5*k(g) + 6*y(g). Factor l(z).
-5*z*(z - 1)*(z + 1)**2
Let d(c) be the first derivative of -c**4/9 + 10*c**3/27 - c**2/9 - 4*c/9 - 8. Factor d(l).
-2*(l - 2)*(l - 1)*(2*l + 1)/9
Let f(q) be the third derivative of 0*q + 1/6*q**4 - 1/45*q**5 - 1/2*q**3 + q**2 + 0. Solve f(g) = 0.
3/2
Let b(u) = -u**4 + u**3 + u**2 + u - 1. Let c(j) = 28*j**4 - 16*j**3 - 40*j**2 - 32*j + 36. Let w(x) = -24*b(x) - c(x). Factor w(f).
-4*(f - 1)**2*(f + 1)*(f + 3)
Suppose -20*l = -19*l - 2. Let y(f) be the first derivative of -2 + 2*f + 7/2*f**l + 8/3*f**3 + 3/4*f**4. Solve y(v) = 0 for v.
-1, -2/3
Let j(i) be the third derivative of -169*i**7/945 - 143*i**6/270 - 23*i**5/90 + 11*i**4/27 - 4*i**3/27 + 4*i**2. Factor j(f).
-2*(f + 1)**2*(13*f - 2)**2/9
Solve 0*f**2 - 1/4*f**4 + 0*f**3 + 0*f + 0 - 1/4*f**5 = 0.
-1, 0
Suppose 2*b + 0 = 4. Let y(j) be the second derivative of 0 - j + 1/3*j**b + 4/9*j**3 + 5/18*j**4 + 1/15*j**5. Find r such that y(r) = 0.
-1, -1/2
Let p(q) = -32*q + 258. Let j be p(8). Determine i, given that 0*i + 0 - 2/9*i**j = 0.
0
Let y be (-370)/148*(2 + (-1 - 3)). Determine g, given that -5/3*g**y + g**3 + 0 + 2/3*g - 7/3*g**4 + 7/3*g**2 = 0.
-1, -2/5, 0, 1
Let k(r) be the second derivative of -5*r**4/36 + 25*r**3/18 - 5*r**2 + r. Determine j so that k(j) = 0.
2, 3
Suppose 4*x + 18 = -b, 3*b - 3*x - 1 = 20. Let h(s) = s**3 + 9*s**2 - 2*s - 18. Let l be h(-9). Let 1/4*n**b + l*n + 0 = 0. Calculate n.
0
Let u(r) = -r**3 - 23*r**2 - 293*r - 993. Let f(i) = -i**3 - 24*i**2 - 294*i - 994. Let w(z) = -7*f(z) + 6*u(z). What is q in w(q) = 0?
-10
Let o be ((-516)/27)/4 - 35/(-7). Solve -2/9*b**2 + 0 + o*b = 0 for b.
0, 1
Let m(a) be the first derivative of -1/3*a**3 - 2*a - 1 + 3/2*a**2. Suppose m(s) = 0. What is s?
1, 2
Let x(f) = f**2 + 0 - 2*f + 0*f**2 + 1 + 5*f. Let d(u) = u**2 + 4*u + 1. Let l(h) = 5*d(h) - 6*x(h). Let l(z) = 0. Calculate z.
1
Let p = -38 + 20. Let h = -3 - p. Factor -h*s**2 - 4/3 - 8*s - 25/3*s**3.
-(s + 1)*(5*s + 2)**2/3
Let n be -1 + (1 + -1)/2. Let j = 3 + n. Determine o so that -6*o**2 + 0 - 3*o - 4*o**3 - o - j - o**4 + 1 = 0.
-1
Let n(y) be the second derivative of y**5/120 - y**4/12 + y**3/3 - y**2 + 2*y. Let r(z) be the first derivative of n(z). Find i, given that r(i) = 0.
2
Let s(c) be the second derivative of -c**4/96 - 5*c**3/48 - c**2/4 - 13*c - 2. Factor s(w).
-(w + 1)*(w + 4)/8
Let z(r) be the second derivative of r**4/60 - r**3/10 + r**2/5 + 6*r. Determine c so that z(c) = 0.
1, 2
Let p(h) = -3 - 1 - 3 - 2*h + 1. Let t be p(-4). Solve t*y**5 - 10*y**5 + 2*y**2 - 12*y**3 + 3 - 3 + 18*y**4 = 0 for y.
0, 1/4, 1
Let l = -6 + 1. Let f = 7 + l. Determine b so that -2/5*b**5 + 0 + 6/5*b**4 + 0*b - 6/5*b**3 + 2/5*b**f = 0.
0, 1
Let u(r) = -r**2 - 3*r. Let g be u(0). Let v(n) be the second derivative of g*n**3 + n - 1/15*n**6 + 1/10*n**5 + 0*n**2 + 0*n**4 + 0. Factor v(c).
-2*c**3*(c - 1)
Let m = -126 + 380/3. Factor m*s**2 + 1/3 + s.
(s + 1)*(2*s + 1)/3
Let u(l) = l**3 - l**2 - l + 1. Let n(d) = 2*d**5 + 8*d**4 + 12*d**3 + 2*d**2 - 2*d + 2. Let y(s) = -n(s) + 2*u(s). Factor y(i).
-2*i**2*(i + 1)**2*(i + 2)
Let i(s) = 2*s**3 + 4*s**2 + 6*s. Let o = 4 + -4. Suppose -r = -j, 2 + o = 2*r - j. Let a(k) = k**2 + 1. Let z(l) = r*a(l) + i(l). What is c in z(c) = 0?
-1
Let d(u) = u**3 + 2*u**2 - 3*u - 3. Let f be d(-2). Factor n**f + n**3 - n**3 + 2*n**4 - 3*n**4.
-n**3*(n - 1)
Suppose 28 = -2*n + 5*b, 9*n - 2*b + 28 = 4*n. Let i(t) = t**3 + 3*t**2 - 5*t - 2. Let m be i(n). Suppose 2/7*y**m + 2/7*y**3 - 2/7*y - 2/7 = 0. Calculate y.
-1, 1
Factor 2*b**3 + 2/5*b**4 + 0*b + 0 + 0*b**2.
2*b**3*(b + 5)/5
Let w(p) = p**5 - 3*p**4 - p**3 - 3*p**2 + 3. Let v(m) = 2*m**4 + 2*m**2 - 2. Let n(k) = -6*v(k) - 4*w(k). Factor n(j).
-4*j**3*(j - 1)*(j + 1)
Let n(r) be the second derivative of r**4/3 - 2*r**3/3 + 7*r. Factor n(p).
4*p*(p - 1)
Let n = 9 + -5. Let -30*p**2 - 3 + 0*p**5 + 12*p + 3*p**5 + 30*p**3 + 4*p**n + 3*p - 19*p**4 = 0. What is p?
1
Let b(z) be the first derivative of z**5/50 - z**4/10 + z**3/5 - z**2/5 + 5*z + 1. Let j(k) be the first derivative of b(k). Suppose j(a) = 0. What is a?
1
Let o(y) be the second derivative of y**6/360 + y**5/30 + y**4/8 + y**3/2 + 2*y. Let d(p) be the second derivative of o(p). Factor d(z).
(z + 1)*(z + 3)
Let p(u) be the second derivative of u**8/26880 - u**7/5040 - u**6/2880 + u**5/240 - u**4/12 + 2*u. Let a(b) be the third derivative of p(b). Factor a(y).
(y - 2)*(y - 1)*(y + 1)/4
Suppose 0 = -c - 4*h - 75, 4*c - 5*h + 237 = -0*c. Let r be (-39)/c + (-2)/7. Suppose 2/3*x**3 + r*x**4 - 1/3 + 0*x**2 - 2/3*x = 0. What is x?
-1, 1
Suppose d - 6*d + 20 = 0. Let w(u) be the first derivative of 0*u**2 + 1/10*u**5 + 2 + 1/6*u**3 + 0*u - 1/4*u**d. Let w(n) = 0. Calculate n.
0, 1
Let u(d) be the third derivative of d**8/448 + d**7/140 - d**6/160 - d**5/40 + 5*d**2. Find z such that u(z) = 0.
-2, -1, 0, 1
Let x be 4 + -1 + (1 - 2). Let h**3 - 2*h**x - 9*h**3 - 4*h**4 - 2*h**2 = 0. Calculate h.
-1, 0
Let f(k) be the first derivative of 2*k**5/5 - k**4/2 - 2*k**3 + k**2 + 4*k + 6. Factor f(p).
2*(p - 2)*(p - 1)*(p + 1)**2
Suppose 4*l + 2*t + 3 = 1, 2*t = -3*l. Let i(k) = k + 1. Let j(r) = -r**3 + 5*r + 4. Let u(v) = l*i(v) + j(v). Factor u(d).
-(d - 2