e first derivative of 19 + 15/2*s + 5/6*s**3 - 5*s**2. Solve x(z) = 0 for z.
1, 3
Find v such that -14/9*v**4 - 4/9*v**5 + 22/9*v**2 - 10/9*v + 14/9*v**3 - 8/9 = 0.
-4, -1, -1/2, 1
Let i = -25 - -27. Suppose 53 + 5*s**i + 30*s - 70*s + 27 = 0. What is s?
4
Factor 1/4*g**2 + 19/4 - 5*g.
(g - 19)*(g - 1)/4
Let o(k) be the first derivative of 1/2*k**6 + 0*k**2 + 0*k + k**3 - 3/5*k**5 - 3/4*k**4 - 27. Factor o(m).
3*m**2*(m - 1)**2*(m + 1)
Let r = 58/177 + -284/1947. Factor 8/11*o**3 - r*o**4 - 6/11*o**2 + 0*o + 0.
-2*o**2*(o - 3)*(o - 1)/11
Let a(t) be the third derivative of -t**7/105 - 2*t**6/5 - 32*t**5/5 - 128*t**4/3 + 353*t**2 - 1. Factor a(w).
-2*w*(w + 8)**3
Let z(i) = -8*i**2 - 27*i - 53. Let r(a) = 3*a**2 + 2*a**2 + 9*a + a**2 - 3*a**2 + 18. Let u(b) = -17*r(b) - 6*z(b). Solve u(p) = 0.
-1, 4
Let h(y) be the third derivative of -y**5/30 - 5*y**4/12 - 4*y**3/3 - 83*y**2. Suppose h(w) = 0. What is w?
-4, -1
Suppose -3*r - 2*r + 43 - 28 = 0. Solve -8/13*n + 0 + 2/13*n**r + 0*n**2 = 0.
-2, 0, 2
Let n(w) be the third derivative of 0*w + 0*w**5 + 7/12*w**4 - 2*w**3 + 0 + 21*w**2 - 1/60*w**6. Factor n(l).
-2*(l - 2)*(l - 1)*(l + 3)
Let o(s) be the third derivative of -s**7/126 - s**6/9 + s**5/36 + 5*s**4/9 + 2*s**2 - 41. Factor o(v).
-5*v*(v - 1)*(v + 1)*(v + 8)/3
Let v(k) be the third derivative of -k**9/22680 + k**8/10080 + k**7/1890 - 5*k**4/12 + 14*k**2. Let b(z) be the second derivative of v(z). Factor b(x).
-2*x**2*(x - 2)*(x + 1)/3
Let j(a) be the first derivative of a**4 + 56*a**3/3 - 64*a**2 - 170. Suppose j(d) = 0. Calculate d.
-16, 0, 2
Let c(l) be the third derivative of l**7/280 - l**6/40 - 3*l**5/80 + 9*l**4/16 - 85*l**2. Factor c(v).
3*v*(v - 3)**2*(v + 2)/4
Let y(v) = -7*v**3 - 6*v**2 + 7*v + 6. Let j(l) = 8*l**3 - 9 + 0*l + 3 - 2*l**2 + 9*l**2 - 7*l. Let u(b) = 6*j(b) + 7*y(b). Let u(a) = 0. What is a?
-2, -1, 3
Let h(u) be the third derivative of u**7/1400 - u**6/600 - u**5/50 + u**4/10 + 17*u**3/6 - 5*u**2 - 1. Let g(a) be the first derivative of h(a). Factor g(n).
3*(n - 2)*(n - 1)*(n + 2)/5
Suppose -62*o - 5190 = -181*o - 227*o. Factor o - 25/2*w - 5/2*w**2.
-5*(w - 1)*(w + 6)/2
Let f(r) be the third derivative of r**6/300 - r**4/60 + 62*r**2. Factor f(z).
2*z*(z - 1)*(z + 1)/5
Factor 7*a**3 + 6*a**2 - 6*a**4 - 8*a**2 - 3*a**3 + 4*a + 16*a**2.
-2*a*(a - 2)*(a + 1)*(3*a + 1)
Let k(n) be the third derivative of -n**8/3360 + n**7/240 - n**6/80 - 23*n**5/60 + 12*n**2. Let h(a) be the third derivative of k(a). Factor h(p).
-3*(p - 3)*(2*p - 1)
Let w = -854 + 856. Let m(s) be the first derivative of -2/39*s**3 - 9 - 4/13*s + 3/13*s**w. Factor m(d).
-2*(d - 2)*(d - 1)/13
Let d(n) be the first derivative of 0*n + 0*n**2 + 5*n**4 + 5/3*n**3 - 5*n**5 + 19. Solve d(s) = 0.
-1/5, 0, 1
Let o be 6*3*(2 - (-25)/(-15)). Factor -10*j**4 + j**4 + o*j**4 + 4*j**4 + 16*j - 4*j**3 - 16.
(j - 2)**3*(j + 2)
Factor 3*j + 9*j**2 + 6 + 1 - 3*j**3 - 3*j**4 - 13.
-3*(j - 1)**2*(j + 1)*(j + 2)
Let m = 7 - 6. Suppose 3*f + 2*f - 2*t - 23 = 0, 4*t = -5*f - m. What is i in -5*i**3 + 2*i**2 + i**f + i + 5*i**3 = 0?
-1, 0
Let a(w) be the second derivative of -w**5/50 + 3*w**4/10 + 7*w**3/5 + 11*w**2/5 + 452*w. Factor a(u).
-2*(u - 11)*(u + 1)**2/5
Suppose 4*t = 32 + 48. Find y such that -5*y - 4*y + t*y**2 + 34*y + 6 - 1 = 0.
-1, -1/4
Let y(x) be the second derivative of x**7/189 + x**6/135 - 2*x**5/15 - 14*x**4/27 - 16*x**3/27 + 2*x - 3. Determine v, given that y(v) = 0.
-2, -1, 0, 4
Suppose 2*v = -15*v + 3*v. Let r(n) be the second derivative of 0*n**2 - 2*n - 1/3*n**3 + 1/6*n**4 + v. Suppose r(a) = 0. Calculate a.
0, 1
What is b in -2/13*b**2 + 0 - 6/13*b = 0?
-3, 0
Let h(u) be the first derivative of u**6/12 + u**5/30 - u**4/4 - u**3/9 + u**2/4 + u/6 - 869. Let h(i) = 0. What is i?
-1, -1/3, 1
Let p(a) = 16*a**2 + 5*a + 4. Let u be p(-1). Find w, given that -7*w**2 - 14*w**2 + 6*w**2 + 35 + 5*w**3 - u = 0.
-1, 2
Find y, given that 25/3*y**2 + 10*y**3 + 0 + 5/3*y**4 + 0*y = 0.
-5, -1, 0
Let u be 1 - 2 - 0 - -4. Factor u*f**2 + 3*f - 5*f - f.
3*f*(f - 1)
Let z(h) = h**2 - 20*h - 19. Let v be z(21). Suppose -5 - 11 - 464*t**v - 4*t**4 + 484*t**2 = 0. Calculate t.
-2, -1, 1, 2
Let t(g) be the second derivative of 1/4*g**4 + 36*g + 0*g**2 + 0 + 0*g**3. Find z, given that t(z) = 0.
0
Let s be (741/(-494))/(45/2*(-1)/6). What is u in -s*u**4 + 8/5 - 6/5*u**2 - 8/5*u**3 + 8/5*u = 0?
-2, -1, 1
Let i(p) be the third derivative of -p**7/210 - p**6/15 - p**5/4 + 84*p**2 + 1. Factor i(x).
-x**2*(x + 3)*(x + 5)
Let x(s) be the third derivative of s**7/490 + s**6/140 - 12*s**5/35 + 9*s**4/4 - 81*s**3/14 + 5*s**2 - 2. Solve x(l) = 0.
-9, 1, 3
Let a(d) be the third derivative of 1/7*d**8 + 53/20*d**5 - 4/5*d**7 - 25/8*d**4 + 9/40*d**6 + 0*d - 20*d**2 + 3/2*d**3 + 0. Solve a(o) = 0.
-1, 1/4, 1, 3
Let t(h) be the third derivative of -h**5/150 - 7*h**4/60 + h**2 + 11*h. Determine y, given that t(y) = 0.
-7, 0
Let o(t) be the second derivative of 0*t**6 - 1/16*t**5 + 6*t + 5/168*t**7 + 0*t**4 + 0*t**3 + 0*t**2 + 0. Factor o(i).
5*i**3*(i - 1)*(i + 1)/4
Let f = -1081/5 - -4339/20. Solve 0 - 3/4*j**2 - 9/4*j**3 + f*j**4 + 3/2*j + 3/4*j**5 = 0.
-2, -1, 0, 1
Let l(g) = g - 3. Let m be l(13). Suppose -3*a = -m + 1. Factor c**2 + 9 - c**2 + a - 12*c + 3*c**2.
3*(c - 2)**2
Let c(v) be the second derivative of -v**6/120 + v**5/10 - 7*v**4/16 + 11*v**3/12 - v**2 - 30*v + 1. Factor c(k).
-(k - 4)*(k - 2)*(k - 1)**2/4
Let v(c) = c**2 - 34*c. Let u be v(0). Let d(r) be the second derivative of 4/3*r**2 - 4/9*r**3 + 1/18*r**4 + 3*r + u. Factor d(q).
2*(q - 2)**2/3
Suppose -2*s = 8, -3*l = -3*s + 2*s - 22. Determine m, given that 18*m**2 - l*m**4 + 29*m**2 + m**4 - 2*m**2 - 5*m**3 - 55*m + 20 = 0.
-4, 1
Let b(r) be the second derivative of r**4/4 + r**3 - 12*r**2 + 8*r. Let b(t) = 0. What is t?
-4, 2
Let p be 4 + (-17)/(-4) + (-2)/8. Suppose 0 = p*x + 6*x - 28. Factor 1/4 + 3/4*q - 1/4*q**x - 3/4*q**3.
-(q - 1)*(q + 1)*(3*q + 1)/4
Let u(p) be the first derivative of -2*p**5/45 + p**4/3 - 22*p**2/9 - 10*p/3 - 81. Suppose u(b) = 0. Calculate b.
-1, 3, 5
Let q(a) be the first derivative of 4*a**2 - 6*a - 2/3*a**3 + 11. Factor q(z).
-2*(z - 3)*(z - 1)
Let 8/11*j**2 + 0 + 2/11*j**3 + 0*j - 5/11*j**4 + 1/11*j**5 = 0. Calculate j.
-1, 0, 2, 4
Let -3/5 + 3/5*z**2 + 0*z = 0. Calculate z.
-1, 1
Find z such that -32 - 9/2*z**2 - 1/4*z**3 - 24*z = 0.
-8, -2
Let m be 9/(54/(-24)) - -80. Let k = m - 76. Factor -4/7*s**2 + 0*s + k.
-4*s**2/7
Determine h, given that -4*h**3 - 61 - 6*h + 61 + h**3 - 9*h**2 = 0.
-2, -1, 0
Factor 2/15*g**2 + 18/5*g + 52/15.
2*(g + 1)*(g + 26)/15
Let u be (-11)/(-3) - (-1)/3. Let x(w) be the third derivative of -5*w**2 + 1/12*w**u + 0 + 0*w + 1/120*w**5 + 1/4*w**3. Factor x(z).
(z + 1)*(z + 3)/2
Let 87*c**2 + 89*c - 493 - 493 + 988 = 0. What is c?
-1, -2/87
Let b be ((-6)/(-15))/((-4)/(-2)). Let v = -267 + 269. Factor 9/5 + 3*s + 7/5*s**v + b*s**3.
(s + 1)*(s + 3)**2/5
Let l(k) be the third derivative of k**7/84 + 11*k**6/16 - 128*k**2. Factor l(f).
5*f**3*(f + 33)/2
Let u be ((-29)/116)/(1/(-52) - 0). Suppose -u*s - 5*s = -36. Suppose -4/3*l**s + 0*l**3 + 0*l + 4/3*l**4 + 0 = 0. Calculate l.
-1, 0, 1
Let b be 33/12 - 1/(-4). Factor -4 + b*w**2 + 12*w + 0 + 4.
3*w*(w + 4)
Let s(f) = 6*f**2 - f + 2. Let o(i) = 39*i**2 - 123*i + 12. Let v(y) = o(y) - 6*s(y). What is g in v(g) = 0?
0, 39
Let d(r) be the third derivative of r**9/15120 + 11*r**5/60 - 6*r**2. Let m(i) be the third derivative of d(i). Suppose m(z) = 0. What is z?
0
Let z(r) be the second derivative of r**8/6720 - r**7/2520 - r**6/720 + r**5/120 + 11*r**4/12 + 8*r. Let k(w) be the third derivative of z(w). Solve k(m) = 0.
-1, 1
Let w(p) be the second derivative of -1/40*p**6 + 5*p + 0 + 3/2*p**2 + 0*p**3 + 0*p**4 + 1/20*p**5. Let h(u) be the first derivative of w(u). Factor h(a).
-3*a**2*(a - 1)
Let s(g) be the first derivative of 2*g**6/7 - 74*g**5/35 + 30*g**4/7 + 10*g**3/7 - 76*g**2/7 + 24*g/7 - 663. Let s(o) = 0. What is o?
-1, 1/6, 2, 3
Let i(b) be the third derivative of -5*b**8/336 - 2*b**7/15 + 23*b**6/30 - 8*b**5/15 + 3*b**2 - 29. Suppose i(n) = 0. Calculate n.
-8, 0, 2/5, 2
Let g(s) be the second derivative of 1/98*s**7 - 1/14*s**4 - 1/42*s**3 - 1/70*s**5 + 15*s + 2 + 1/14*s**2 + 1/42*s**6. Solve g(u