, -2/3
Let w(r) = -5*r**3 - 995*r**2 + 2030*r - 1025. Let j(m) = 3*m**3 + 498*m**2 - 1015*m + 512. Let k(y) = 5*j(y) + 2*w(y). Determine t so that k(t) = 0.
-102, 1
Let j(i) be the first derivative of -4*i**3/3 + 52*i**2 + 224*i - 25. Find m, given that j(m) = 0.
-2, 28
Let r = -37 + 12. Let t = r - -27. Let 3*z**t - z - z**5 + z**3 + z**3 - z**2 - 1 - z**4 + 0*z**4 = 0. Calculate z.
-1, 1
Let p(g) be the second derivative of g**7/42 + g**6/30 - g**5/20 - g**4/12 + 277*g. Suppose p(b) = 0. Calculate b.
-1, 0, 1
Let z(s) be the third derivative of -s**5/330 - 7*s**4/132 - 2*s**3/11 - s**2 - 559. Factor z(y).
-2*(y + 1)*(y + 6)/11
Suppose g = -w + 16, -2*g + 2*w + w = -32. Factor 11*y + g + 8*y**3 + y**4 + 24*y**2 + 0*y**4 - 6*y + 27*y.
(y + 2)**4
Find d such that -4/5*d**4 - 8*d - 2/5*d**5 + 42/5*d**3 + 48/5 - 44/5*d**2 = 0.
-6, -1, 1, 2
Suppose 37*w + 115 = 60*w. Let o(r) be the second derivative of -1/35*r**w + 0*r**4 + 0*r**3 - 7*r + 0 + 1/105*r**6 + 0*r**2. Factor o(f).
2*f**3*(f - 2)/7
Let i(d) be the first derivative of d**6/2 + 6*d**5/5 - 2*d**3 + 16. Let p(s) = -3*s**5 - 7*s**4 - s**3 + 7*s**2. Let y(t) = -4*i(t) - 3*p(t). Factor y(n).
-3*n**2*(n - 1)*(n + 1)**2
Suppose 0 = 5*f - g + 40, 5*g - 60 = 3*f + 2*f. Let r be ((-21)/6)/f*(-2)/(-4). Determine t, given that 0*t - 1/2*t**2 + 1/4*t**4 + 0 - r*t**3 = 0.
-1, 0, 2
Let y(b) be the third derivative of -b**6/1140 + 9*b**5/190 - 17*b**4/76 + 25*b**3/57 - b**2. Suppose y(l) = 0. Calculate l.
1, 25
Suppose 3*j + 5*y = -5, 0 = j - 2*y - 1 - 1. Let v(g) be the second derivative of 1/30*g**5 - 1/9*g**4 + 4*g + 1/15*g**6 + 0*g**2 + 0 + j*g**3. Factor v(q).
2*q**2*(q + 1)*(3*q - 2)/3
Let j(g) = 8*g**2 - 4. Let i(v) = -2*v + 1. Let z be i(-2). Let o = -8 + z. Let d(b) = -7*b**2 + 3. Let l(x) = o*j(x) - 4*d(x). Factor l(n).
4*n**2
Let g(h) be the first derivative of h**3/15 - 88*h**2/5 + 7744*h/5 + 359. Let g(i) = 0. Calculate i.
88
Let k be 2/(-6)*(23 - 92). Suppose k*w - 22*w = 2. Solve 10/13*d + 12/13 + 2/13*d**w = 0.
-3, -2
Let h = -83 + 85. Let n be 0/3*(-1)/h. Suppose -2/9*i**3 + n + 2/9*i**4 + 0*i - 4/9*i**2 = 0. Calculate i.
-1, 0, 2
Factor 128/21*x - 2/21*x**2 + 0.
-2*x*(x - 64)/21
Let l(i) be the third derivative of i**7/840 - i**6/120 - 3*i**5/40 + 5*i**4/6 - i**3/6 - 23*i**2. Let h(m) be the second derivative of l(m). Factor h(v).
3*(v - 3)*(v + 1)
Suppose 7*t - t = 6. Let h(i) = i**5 + i**4 - i**2 + i + 1. Let c(m) = -5*m**5 + 4*m**4 - 3*m**3 + 2*m**2 - 2*m - 2. Let l(g) = t*c(g) + 2*h(g). Factor l(u).
-3*u**3*(u - 1)**2
Let q be (6/9)/(6/27). Let f(i) = 23*i + 2*i**2 - q - 29*i - 5. Let c(m) = -2*m**2 + 5*m + 7. Let h(w) = -6*c(w) - 5*f(w). Suppose h(p) = 0. What is p?
-1, 1
Let l(t) be the first derivative of 5*t**7/273 + t**6/15 + 9*t**5/130 - t**4/78 - 2*t**3/39 - 53*t - 44. Let d(v) be the first derivative of l(v). Factor d(m).
2*m*(m + 1)**3*(5*m - 2)/13
Determine g so that -600 - 2/3*g**4 - 520*g - 52/3*g**3 - 458/3*g**2 = 0.
-10, -3
Let b(v) = 4*v**2 + 1. Let x be b(-1). Let d = 53/115 + -6/23. Determine t, given that 1/5*t**x - d*t + 2/5*t**4 + 0 - 2/5*t**2 + 0*t**3 = 0.
-1, 0, 1
Let t = 6052/7 + -864. Let n(z) be the second derivative of 1/105*z**6 - 1/14*z**4 + 1/35*z**5 + t*z**2 + 3*z + 0 - 4/21*z**3. Factor n(q).
2*(q - 1)**2*(q + 2)**2/7
Let l(y) be the second derivative of 4*y**2 - 3*y - 22/3*y**3 + 16/3*y**4 - 4 - 7/5*y**5. Factor l(h).
-4*(h - 1)**2*(7*h - 2)
Let x(s) = -2*s**2 - 8*s + 2. Let b(d) = 9*d**2 + 39*d - 13. Let o(u) = -2*b(u) - 11*x(u). Factor o(m).
2*(m + 2)*(2*m + 1)
Let u(r) = -r**3 - 8*r**2 + 150*r + 30. Let b be u(9). Let z(h) be the first derivative of -2 + h**2 - h - 1/3*h**b. Let z(i) = 0. What is i?
1
Suppose -15*k - 15 = -10*k. Let s be (k/((-315)/(-10)))/(2/(-9)). Determine h so that 3/7*h - s*h**2 + 3/7 - 3/7*h**3 = 0.
-1, 1
Let p(w) = -w**2 + w - 1. Let f(c) = -13*c**2 + 2*c - 12. Let o(q) = 4*f(q) - 36*p(q). Factor o(z).
-4*(z + 1)*(4*z + 3)
Let h(v) = 1. Suppose 2*u = 5*l + 24, 0*l = 3*l + 12. Let g(w) = -6*w**2 + 8*w. Let z(x) = u*h(x) - g(x). Factor z(i).
2*(i - 1)*(3*i - 1)
Suppose 3*n + 3 = 5*u, -29 = 3*u - 6*u - 5*n. Factor -4*h + 3*h**3 - 6*h - u + 3*h**2 + 0*h**3 + 7*h.
3*(h - 1)*(h + 1)**2
Factor 28/11*r - 48/11 - 2/11*r**3 + 2*r**2.
-2*(r - 12)*(r - 1)*(r + 2)/11
Suppose 91*h = 81*h + 40. Let i(l) be the first derivative of h - 3/8*l**2 - 1/6*l**3 - 1/4*l. Find x, given that i(x) = 0.
-1, -1/2
Factor -1/5*r**2 + 8/5*r + 9/5.
-(r - 9)*(r + 1)/5
Let q be -10*3/(-3) - -2. Let g be 1*-4*(-6)/q. Factor -18 - 18*y - y**g + 3 - 2*y**2 - 12.
-3*(y + 3)**2
Solve 0*z**2 - 2/11*z**3 + 0 + 2/11*z = 0.
-1, 0, 1
Let f(w) = -4*w**2 + w + 3. Let l(o) = -3*o**2 + 2*o + 2. Let q = 59 + -57. Let u(m) = q*f(m) - 3*l(m). Find b such that u(b) = 0.
0, 4
Let v(r) = 3*r**3 - 5*r - 9 - 6*r**3 - 6*r**2 + 4*r**3. Let q be v(7). Find m, given that -2*m**2 + 3*m**4 + 26 + 2*m**q - m**4 - 2*m**3 - 26 = 0.
-1, 0, 1
Let -9*h**4 - 3*h**5 + 8*h - 8*h - 6*h**4 - 12*h**3 = 0. What is h?
-4, -1, 0
Let y(p) be the first derivative of -2*p**6/105 + p**4/7 - 4*p**3/21 - 29*p + 14. Let m(w) be the first derivative of y(w). Factor m(t).
-4*t*(t - 1)**2*(t + 2)/7
Let g be 4*186/217*(-42)/8. Let c be (9/g)/(2/(-9)). Let 1/2*b**2 + 3/8*b - c - 1/8*b**3 = 0. Calculate b.
-2, 3
Let r be (9/(-60))/(102/(-90) - -1). Let v(u) be the first derivative of 0*u + 3/16*u**4 - r*u**2 + 1 + 1/2*u**3. Solve v(z) = 0.
-3, 0, 1
Suppose 10*x - 5*x - 10 = 0. Determine v, given that 10*v**2 - 4*v**4 - 4*v**x - 14*v**3 - 6*v**4 - 6*v + 4 + 20*v = 0.
-1, -2/5, 1
Let u = 1311 - 1308. Let r(x) be the first derivative of -8 - 2/21*x**u - 1/14*x**4 + 2/35*x**5 + 1/7*x**2 + 0*x. Factor r(d).
2*d*(d - 1)**2*(d + 1)/7
Let f(t) be the third derivative of 0*t**3 + 22*t**2 - 1/40*t**6 + 0*t - 1/35*t**7 - 1/112*t**8 + 0*t**5 + 0*t**4 + 0. Factor f(q).
-3*q**3*(q + 1)**2
Let g(f) be the first derivative of f**3/21 + 31*f**2/7 + 961*f/7 + 15. Factor g(w).
(w + 31)**2/7
Let n(t) be the second derivative of t**4/12 - t**3 - 5*t**2/2 - t. Let u be n(7). Factor -2*r**u + 5*r**2 - 4*r**2 - r.
-r*(r + 1)
Let p(y) be the third derivative of y**8/80640 - y**6/720 + 19*y**5/30 - 18*y**2. Let o(j) be the third derivative of p(j). Factor o(z).
(z - 2)*(z + 2)/4
Suppose -c = -k - 0 + 8, 0 = -3*c + 4*k - 20. Let o be (-2)/c - 424/(-336). Suppose 2/7*w**3 + 16/7*w + o*w**2 + 8/7 = 0. What is w?
-2, -1
Let m(a) be the first derivative of -a**3/6 + 13*a**2/4 + 7*a + 29. Determine q so that m(q) = 0.
-1, 14
Let v(a) = -7*a**3 + 10*a**2 + 60*a - 291. Let q(y) = -2*y**3 + 2*y**2 - 1. Let j(b) = -12*q(b) + 4*v(b). Factor j(g).
-4*(g - 6)**2*(g + 8)
Let u(w) = w - 1. Let b(k) = -k**2 + 14*k - 29. Let j(z) = b(z) - 4*u(z). Let j(f) = 0. What is f?
5
Suppose 14*y + 2*l = 15*y - 14, 4*l = -20. Let s(d) be the third derivative of 4/3*d**3 + 0*d - 1/3*d**y + 0 + 13*d**2 + 1/30*d**5. Factor s(n).
2*(n - 2)**2
Factor -23*j - j**3 + 35*j - j**4 + 4*j + 16*j**2.
-j*(j - 4)*(j + 1)*(j + 4)
Let k(m) be the third derivative of m**7/420 + m**6/540 - m**5/60 - m**4/36 - 5*m**3/3 - 11*m**2. Let g(p) be the first derivative of k(p). Factor g(i).
2*(i - 1)*(i + 1)*(3*i + 1)/3
Let v(k) be the second derivative of k**4/8 + 21*k**3 + 1323*k**2 + 45*k. Factor v(p).
3*(p + 42)**2/2
Let i be 13/4 - (4 - 1). Let w = 277 + -275. Let 0*f + i*f**w + 0 - 1/4*f**3 = 0. What is f?
0, 1
Let i(u) = 2*u**2 - 51*u + 304. Let j(q) = -10*q**2 + 256*q - 1512. Let m(b) = 14*i(b) + 3*j(b). Let m(h) = 0. What is h?
7, 20
Suppose -191*l = -186*l - 10. Solve -1/4*b**3 + 1/2*b**l + 0*b + 0 = 0 for b.
0, 2
Let v(k) be the first derivative of 5*k**6/21 + 16*k**5/35 - 9*k**4/14 - 16*k**3/21 + 4*k**2/7 + 120. Suppose v(j) = 0. What is j?
-2, -1, 0, 2/5, 1
Factor -40*g + 75 + 0*g**2 + 4*g**2 + g**2.
5*(g - 5)*(g - 3)
Let o(a) be the second derivative of 7/10*a**6 - 13*a + 0 - 3/2*a**2 + 6/5*a**5 + 1/7*a**7 - a**3 + 1/2*a**4. Factor o(z).
3*(z + 1)**4*(2*z - 1)
Let f = 208050/7 + -29721. Determine b so that -9/7*b + 6/7 + 0*b**2 + f*b**3 = 0.
-2, 1
Let y(i) be the third derivative of -i**7/7560 + i**6/540 - i**5/90 - 3*i**4/4 - 19*i**2. Let z(n) be the second derivative of y(n). Let z(u) = 0. Calculate u.
2
Let u(m) = m**2 + 6*m - 14. Let h be u(2). Let i = 13/18 - -107/18.