- 1/10*s**5 + u + 1/3*s**3 + 0*s**2 - 2*s. Determine t so that z(t) = 0.
-1, 0, 1
Let n(y) be the second derivative of 0*y**4 + 0*y**2 - 1/360*y**6 + 1/3*y**3 + 1/120*y**5 + 0 - 2*y. Let b(h) be the second derivative of n(h). Factor b(g).
-g*(g - 1)
Suppose 3*z + 5*s = -8, -5*z + 2*s + 12 = -16. Factor -3/2*j**3 + 0 - 1/2*j**5 - 2*j**z + 0*j + 0*j**2.
-j**3*(j + 1)*(j + 3)/2
Let h(b) = 39*b**3 + 64*b**2 + 23*b - 5. Let w(m) = 116*m**3 + 192*m**2 + 68*m - 16. Let g(s) = -8*h(s) + 3*w(s). Factor g(k).
4*(k + 1)**2*(9*k - 2)
Let c(x) be the first derivative of -x**4/10 - 2*x**3/5 + 8*x/5 - 3. Let c(s) = 0. Calculate s.
-2, 1
Let z be (-80)/35*(-28)/8. Let c = z + -6. Solve 0*m**4 + 0 + 0*m + 3/2*m**3 - 1/2*m**2 - c*m**5 = 0.
-1, 0, 1/2
Suppose -4*m = 3 - 15. Suppose -m*p = 2*p. Factor p*r + 0 - 2/5*r**3 - 2/5*r**2.
-2*r**2*(r + 1)/5
Let y = 148 + -144. Suppose -4/13*a + 4/13*a**3 + 10/13*a**y - 10/13*a**2 + 0 = 0. What is a?
-1, -2/5, 0, 1
Let p = 13 - 13. Suppose 163*h = 159*h + 16. Suppose 0 + 8/5*w**2 - 14*w**5 + 22/5*w**h + 8*w**3 + p*w = 0. What is w?
-2/5, -2/7, 0, 1
Let o(g) = 23*g**2 - 48*g + 37. Let b(j) = -8*j**2 + 16*j - 12. Let d(r) = 11*b(r) + 4*o(r). Solve d(x) = 0 for x.
2
Let v(y) be the second derivative of -1/7*y**5 + 0 + 0*y**2 + 4/21*y**4 + 4/105*y**6 + 2*y - 2/21*y**3. Factor v(h).
4*h*(h - 1)**2*(2*h - 1)/7
Let u(c) be the third derivative of c**6/132 + 7*c**5/330 - 2*c**4/33 - 4*c**3/33 + c**2. Factor u(f).
2*(f - 1)*(f + 2)*(5*f + 2)/11
Suppose 4*k = 16 + 16. Suppose 0 = -5*t + k + 7. Factor a**2 - 4 - 2*a - 2*a**2 + t.
-(a + 1)**2
Let n(f) = 5*f**2 + 1. Let z be n(1). Suppose 0 = -m - m + z. Factor 0*k + 3*k**3 + 2*k**2 - 4*k**m - k.
-k*(k - 1)**2
Let t(u) = -3*u**3 - u**2 + 20*u. Let p(w) = 2*w**3 + w**2 - 13*w. Let b(j) = 8*p(j) + 5*t(j). Determine o, given that b(o) = 0.
-4, 0, 1
Let w be (16 - 14)/(4/6). Factor 1/2*m**w - 1/2*m**2 - 1/2*m + 1/2.
(m - 1)**2*(m + 1)/2
Let h(m) = -5*m**3 + 6*m**2 + 7*m. Let u(n) = -21*n**3 + 24*n**2 + 27*n. Let g(d) = -9*h(d) + 2*u(d). Factor g(l).
3*l*(l - 3)*(l + 1)
Suppose 13 = 2*u - 3*u - 3*l, -4*u - 2 = 2*l. Suppose 0 = -5*y + 25. Factor -a**y - a**4 + 4*a**5 - 4*a**5 + a**u + a**3.
-a**2*(a - 1)*(a + 1)**2
Let v = 5633 + -17147/3. Let t = -82 - v. Factor t*w**2 + 2/3 - 4/3*w.
2*(w - 1)**2/3
Let x(t) be the third derivative of t**9/50400 + t**8/25200 - t**7/12600 + 3*t**5/20 + 3*t**2. Let g(s) be the third derivative of x(s). What is h in g(h) = 0?
-1, 0, 1/3
Let h = 4 + 1. Suppose k**4 - 2*k**5 - 2*k**2 + k**4 - 2*k**h + 4*k**4 = 0. Calculate k.
-1/2, 0, 1
Let l(y) be the third derivative of 5*y**8/84 - 26*y**7/105 + 2*y**6/15 + 4*y**5/15 + 4*y**2. Suppose l(w) = 0. What is w?
-2/5, 0, 1, 2
Let j(a) = 5*a**4 - 2*a**3 - 7*a**2. Let g(w) = 16*w**4 - 6*w**3 - 22*w**2. Let i(d) = -6*g(d) + 20*j(d). Factor i(x).
4*x**2*(x - 2)*(x + 1)
Let l = -66 - -30. Let q be (-18)/l - 1/10. Suppose -q*u**2 + 12/5*u - 18/5 = 0. Calculate u.
3
Let n(d) = -d**3 + d. Let f be n(0). Let u be (4/(-5))/(-4 - 90/(-25)). Suppose -h**u - h**2 + 3 + f - 2*h + 1 = 0. What is h?
-2, 1
Suppose 3*p = 5*f - 4*f + 9, 4*f = 3*p. Let w(i) be the third derivative of 1/3*i**3 + 1/30*i**5 + 0 - i**2 - 1/6*i**p + 0*i. Factor w(c).
2*(c - 1)**2
Let p(z) = -31*z**3 - 2*z**2 - 3*z - 2. Let y be p(-1). Let n = 33 - y. Factor 0 - 2/3*w + w**n + 5/3*w**2.
w*(w + 2)*(3*w - 1)/3
Let q be (21/14)/(2/4). Let -5*d**5 + 2*d**2 - 1 + q*d**5 - d**4 + d**3 - d + d**3 + d**5 = 0. Calculate d.
-1, 1
Let i(f) = -3*f - 18. Let h be i(-6). Suppose -6/13*u**4 + 8/13*u**2 + h + 0*u + 0*u**3 - 2/13*u**5 = 0. What is u?
-2, 0, 1
Suppose c + 22 = 25. Factor 0*v**2 + 4/3 - 2*v + 2/3*v**c.
2*(v - 1)**2*(v + 2)/3
Factor 3*n + 14*n**4 - 10*n**4 - 7*n**4 - 3*n**3 + 3*n**2.
-3*n*(n - 1)*(n + 1)**2
Let n(v) be the second derivative of -121*v**4/6 - 44*v**3/3 - 4*v**2 + 9*v. Determine d, given that n(d) = 0.
-2/11
Let i = 302/21 + -96/7. Determine g so that -i*g**2 + 4/3 + 2/3*g = 0.
-1, 2
Let x(r) be the first derivative of -2/11*r**3 + 12/11*r**2 - 8/11*r - 1 - 5/22*r**4. Let x(s) = 0. What is s?
-2, 2/5, 1
Let g(j) be the first derivative of -j**7/105 + j**5/15 - j**3/3 - 3*j**2/2 - 2. Let x(q) be the second derivative of g(q). What is r in x(r) = 0?
-1, 1
Let l(g) be the first derivative of 0*g**2 + 4 - 3/16*g**4 - 1/10*g**5 + 0*g - 1/12*g**3. Determine c, given that l(c) = 0.
-1, -1/2, 0
Let g(p) be the first derivative of -p**4/6 - 32*p**3/45 - 13*p**2/15 - 4*p/15 - 51. Suppose g(m) = 0. Calculate m.
-2, -1, -1/5
Let y(x) be the first derivative of 3*x**5/5 + 3*x**4 + 2*x**3 - 6*x**2 - 9*x + 64. Factor y(d).
3*(d - 1)*(d + 1)**2*(d + 3)
Let c(n) = n**2 - 4*n + 2. Let s be c(5). Suppose -4*w + u = -8 - 6, -s = -w + 2*u. Factor -5/4*h**w + 1/2 - 2*h**2 - 1/4*h.
-(h + 1)**2*(5*h - 2)/4
What is n in 2/9*n - 10/9*n**2 + 8/9 = 0?
-4/5, 1
Find f such that 48*f - 103*f - 25 - 125*f + 5 - 405*f**2 = 0.
-2/9
Let x be ((-9)/(-6) - 2)/(-3). Let g(y) be the third derivative of 0 + 1/48*y**4 + 0*y + x*y**3 - 2*y**2 - 1/120*y**5. Factor g(t).
-(t - 2)*(t + 1)/2
Let s be (168/126)/(((-60)/(-9))/2). Factor -s*j**2 - 4/5*j + 0 + 16/5*j**3 - 2*j**4.
-2*j*(j - 1)**2*(5*j + 2)/5
Let b(c) be the third derivative of c**5/18 + 7*c**4/9 - 4*c**3/3 - 22*c**2. Find w, given that b(w) = 0.
-6, 2/5
Let i(s) = 5*s**3 - s**2 - 1. Let f be i(1). Factor 12/5*x**f - 2/5*x**4 + 24/5*x - 26/5*x**2 - 8/5.
-2*(x - 2)**2*(x - 1)**2/5
Let s(j) be the second derivative of 0 - 5/24*j**4 + 1/6*j**3 + 1/15*j**5 - 1/2*j**2 + 2*j. Let i(b) be the first derivative of s(b). Factor i(n).
(n - 1)*(4*n - 1)
Let k(j) be the third derivative of 0*j + 2*j**2 + 7/60*j**5 + 0 - 3/8*j**4 + 1/3*j**3. Find n, given that k(n) = 0.
2/7, 1
Let c(i) be the third derivative of -i**8/20160 - i**7/2520 - i**6/720 + i**5/30 - i**2. Let j(r) be the third derivative of c(r). Factor j(o).
-(o + 1)**2
Suppose -4*t - v - 2 = 3, 4*v + 20 = t. Let m = 5 - 2. Solve t*d + 0 + 0*d**2 - 2/5*d**m = 0.
0
Let d(g) be the first derivative of -g**7/2940 - g**6/420 - g**5/140 - g**4/84 - g**3 - 1. Let j(y) be the third derivative of d(y). Factor j(f).
-2*(f + 1)**3/7
Suppose 0 + 0*m - 3/5*m**3 + 6/5*m**2 = 0. What is m?
0, 2
Let i(f) = f**3 + 3*f**2 - 5*f - 1. Let w be i(-4). Suppose -2*x + 35 = 5*o, 3*o + 4*x - w*x = 20. Factor -t**2 + t**o + t + t**4 + 0*t**5 - t**2 + 1 - 2*t**3.
(t - 1)**2*(t + 1)**3
Suppose -10 = -5*m - 0. Suppose m*k**2 + 5*k**2 + 4 - 6*k - 3*k**2 - 2*k**2 = 0. What is k?
1, 2
Let r = -297/28 + 76/7. What is o in -r*o**3 + 0 - 1/4*o**4 + 1/4*o + 1/4*o**2 = 0?
-1, 0, 1
Suppose 67*g - 228 = 48*g. Solve g - 8*t + 4/3*t**2 = 0 for t.
3
Let j(w) be the third derivative of 1/480*w**6 + 0*w**4 + 0 + 0*w**3 + 0*w**5 + 0*w - 3*w**2. Factor j(s).
s**3/4
Factor 25/2*q**2 - 65/6*q - 5/3.
5*(q - 1)*(15*q + 2)/6
Let o be (((-1 + 1)/2)/1)/(-2). Factor -1/2*l + o - 1/2*l**2.
-l*(l + 1)/2
Factor 8 + 18*x**2 - 14*x**2 - 8*x**2 - 4*x.
-4*(x - 1)*(x + 2)
Let z(w) = -3*w**5 - 21*w**4 + 9*w**3 + 12*w**2 - 15*w. Let k(r) = r**5 + 10*r**4 - 4*r**3 - 6*r**2 + 7*r. Let a(h) = 9*k(h) + 4*z(h). Factor a(u).
-3*u*(u - 1)**3*(u + 1)
Suppose 5*l - 11 = 2*n, 2*n + 5 = 4*l - 3. Let f(x) be the first derivative of 1/3*x**l - 1/4*x**4 - 3 + 1/2*x**2 - x. What is c in f(c) = 0?
-1, 1
Let c = -13 + 32. What is d in -c*d**2 + 12*d**2 + 16*d + 5*d**2 - 32 = 0?
4
Let a(t) be the third derivative of -t**7/3360 + t**6/1440 + t**5/480 - t**4/96 - t**3/3 + 3*t**2. Let y(i) be the first derivative of a(i). Factor y(c).
-(c - 1)**2*(c + 1)/4
Factor 1/2*q**2 + 1/2*q - 3.
(q - 2)*(q + 3)/2
Let b(c) be the second derivative of -1/40*c**5 - 1/6*c**4 + 0*c**2 - c + 0 - 1/3*c**3. Solve b(t) = 0 for t.
-2, 0
Factor 5/3*p - 10/3*p**3 + 5/3*p**5 + 5/3 - 10/3*p**2 + 5/3*p**4.
5*(p - 1)**2*(p + 1)**3/3
Let u(h) be the first derivative of h**8/168 - h**7/35 + h**6/20 - h**5/30 + h**2 + 3. Let c(l) be the second derivative of u(l). What is i in c(i) = 0?
0, 1
Let s(m) = 6*m**4 + 3*m**3 - 9*m**2 + 2*m. Let p(u) = 13*u**4 + 6*u**3 - 18*u**2 + 4*u. Suppose 10*i + 15 = 7*i. Let z(j) = i*s(j) + 2*p(j). Factor z(b).
-b*(b - 1)*(b + 2)*(4*b - 1)
Let u(y) be the second derivative of y**6/45 - 2*y**5/15 + 2*y**4/9 + 29*y. Factor u(a).
2*a**2*(a - 2)**2/3
Let l(y) be the 