11)**2/17
Let s = -80 - -82. Let k = 1530 - 1530. Determine i so that k + 2/3*i + 4/3*i**3 + 5/3*i**s + 1/3*i**4 = 0.
-2, -1, 0
Suppose -2*u - 3*h + 5 = -10, -u + 4*h - 9 = 0. Let y(p) = -33*p + 861. Let g be y(26). Factor 5*f**3 + 8*f - 10*f**u + 3*f**g + 0*f**3.
-2*f*(f - 2)*(f + 2)
Factor -1/3*j + 11*j**2 + 1/3*j**3 - 11.
(j - 1)*(j + 1)*(j + 33)/3
Let c(k) be the second derivative of -k**7/35 + 33*k**6/25 + 21*k**5/5 + k**4/5 - 69*k**3/5 - 21*k**2 + 1576*k. Let c(t) = 0. What is t?
-1, 1, 35
Let c be 3536/111384 + (-4142)/(-504). Factor -7*h + c*h**2 + 1.
(3*h - 2)*(11*h - 2)/4
Let m = -2671943/11 - -242905. Solve 38/11*u - 6/11*u**2 - m = 0.
1/3, 6
Let o = 689473/348788 - -4/7927. Let t = o - -3/11. Factor 1/2 + t*z + 7/4*z**2.
(z + 1)*(7*z + 2)/4
Suppose -352 = -190*s + 182*s. Determine f so that -32*f**3 + 10 + 26 + 30*f - 427*f**4 + 2*f**5 + 435*f**4 - s*f**2 = 0.
-6, -1, 1, 3
Let d(a) be the first derivative of -5*a**6/2 + 14*a**5 - 5*a**4/4 - 130*a**3/3 - 20*a**2 - 3365. Determine y so that d(y) = 0.
-1, -1/3, 0, 2, 4
Let g(a) be the second derivative of a**4/72 - 43*a**3/18 - 455*a**2/12 + 2136*a - 3. Solve g(q) = 0.
-5, 91
Suppose 36 = 2*o + 32. Suppose 4*y - 458 = 2*y - 5*m, 3*m = -5*y + 1107. Suppose 8*h + y*h**2 - 187*h**o + 4*h - 12*h**3 = 0. What is h?
-1/3, 0, 3
Let j(g) be the third derivative of -g**6/30 + g**5/30 + g**4/3 - 5*g**3/6 - 34*g**2. Let d(k) be the first derivative of j(k). Suppose d(f) = 0. What is f?
-2/3, 1
Let j(d) = -133*d**2 - 9*d - 17. Let o be j(2). Let f be -6 + -217*18/o. Factor -4/9*t + 1/9*t**3 - 1/9*t**4 + 2/3*t**2 - f.
-(t - 2)**2*(t + 1)*(t + 2)/9
Let m(k) be the third derivative of k**7/210 + 17*k**6/120 - k**5/60 - 17*k**4/24 + 899*k**2. Factor m(q).
q*(q - 1)*(q + 1)*(q + 17)
Find a such that -32*a**2 + 0*a + 0 - 212/13*a**3 - 2/13*a**4 = 0.
-104, -2, 0
Let y(t) = 4*t**4 + 20*t**3 + 8*t**2 - 56*t + 12. Let f(l) = l**4 + l**3 + 2. Let c(k) = 6*f(k) - y(k). Solve c(p) = 0 for p.
-2, 0, 2, 7
Let q(r) be the second derivative of -r**6/72 + 3*r**5/4 + 95*r**4/24 - 20*r**3 - r**2 + 49*r. Let c(z) be the second derivative of q(z). Factor c(f).
-5*(f - 19)*(f + 1)
Let s be 7 + 2/(0 - (-4)/(-10)). Suppose -2*d - 2*x = -2, 2*d - s*x = 1 - 3. Factor -2/5*h**5 - 6/5*h**4 + d*h + 0*h**3 + 0 + 8/5*h**2.
-2*h**2*(h - 1)*(h + 2)**2/5
Let h(a) = a**3 - 7*a**2 - 6*a + 50. Let q be h(7). Suppose -2809*t + 2813*t - q = 0. Solve 16/13*r + 32/13 + 2/13*r**t = 0 for r.
-4
Let z = 1/8447 + 33783/42235. Let j(u) be the first derivative of -4/5*u**2 + 0*u - 1/5*u**4 + 24 + z*u**3. Factor j(y).
-4*y*(y - 2)*(y - 1)/5
Let o = -5695/296 - -735/37. Let d(u) be the second derivative of 0*u**2 + 0 - 10*u - 3/40*u**5 - u**3 + o*u**4. Suppose d(r) = 0. Calculate r.
0, 1, 4
Let f(w) be the first derivative of 90*w + w**3 + 93/2*w**2 - 61. Let f(l) = 0. Calculate l.
-30, -1
Factor -1/2*h**3 - 13*h**2 + 0 - 105/2*h.
-h*(h + 5)*(h + 21)/2
Let u(o) be the second derivative of -o**6/90 + o**5/12 + 29*o**4/18 + 44*o**3/9 - 2987*o. Factor u(c).
-c*(c - 11)*(c + 2)*(c + 4)/3
What is h in 0 - 16/9*h - 2/3*h**4 + 56/9*h**2 - 52/9*h**3 + 2*h**5 = 0?
-2, 0, 2/3, 1
Suppose -974*z + 126348 = 35766. Factor z*g**2 + 9 + 46/3*g**4 + 3/2*g**5 + 117/2*g + 172/3*g**3.
(g + 1)*(g + 3)**3*(9*g + 2)/6
Let r be 2/16 + 6 + (-260)/32. Let p(a) = -2*a**3 - 3*a**2 + 3*a. Let q(x) = -2*x**3 - 3*x**2 + 3*x - 1. Let u(o) = r*q(o) + 3*p(o). Factor u(s).
-(s - 1)*(s + 2)*(2*s + 1)
Let d = 280783/2 + -140374. Factor 0*x - d*x**3 + 0 + 25*x**2.
-5*x**2*(7*x - 10)/2
Let f be (-178)/154 + 2 + (-576)/2112. Factor -32/7*l**2 - f*l + 4/7*l**3 + 32/7.
4*(l - 8)*(l - 1)*(l + 1)/7
Suppose 38*y = 34*y - 2 + 6. Solve -1/6*w**2 + 5/6*w - y = 0 for w.
2, 3
Let d(v) be the first derivative of -2/65*v**5 + 37 + 0*v**2 + 2/13*v**4 - 4/39*v**6 + 2/39*v**3 + 0*v. Suppose d(l) = 0. What is l?
-1, -1/4, 0, 1
Determine a so that -5/3*a**2 - 5/2 - 14/3*a + 2/3*a**3 + 1/6*a**4 = 0.
-5, -1, 3
Let n(p) = -p**3 + p**2. Let b be n(0). Suppose -5*h = 10*h - 45. Factor -2*g**h + 0*g**2 + g**2 + b*g**3 + 2*g - g**4.
-g*(g - 1)*(g + 1)*(g + 2)
What is m in 45522*m**4 - 9223893*m - 900*m**5 - 4568236*m**3 - 156462*m**4 - 7397835*m - 1102736 - 63241188*m**2 = 0?
-41, -2/15
Let v(m) be the second derivative of -m**6/48 + 41*m**5/60 - 2*m**4/3 + 91*m**2 + 94*m + 2. Let a(g) be the first derivative of v(g). Factor a(c).
-c*(c - 16)*(5*c - 2)/2
Let i be (12425/(-1176))/(-25) + 15/(-40). Let f(a) be the first derivative of 8 + 0*a**5 + 0*a**2 - 1/14*a**4 + 0*a**3 + i*a**6 + 0*a. Let f(h) = 0. What is h?
-1, 0, 1
Let m(g) be the second derivative of -g**5/30 - 5*g**4/18 + 22*g**3/9 - 16*g**2/3 + 114*g + 7. Determine h, given that m(h) = 0.
-8, 1, 2
Let b(m) be the first derivative of -12*m**5/5 + 2*m**4 + 52*m**3/3 + 16*m**2 - 1773. Factor b(h).
-4*h*(h + 1)**2*(3*h - 8)
Let d(r) be the third derivative of -62*r**2 - 39*r**3 - 41/8*r**4 + 0*r + 0 - 1/20*r**5. Factor d(n).
-3*(n + 2)*(n + 39)
Suppose -8*b = -0*b + 8. Let k be ((-279)/(-6))/3 - b/(-2). Factor 10*f**2 - 3*f + 4*f**2 - 5*f**3 + 7*f + k*f**3.
2*f*(f + 1)*(5*f + 2)
Suppose -53*v + 51*v + 8 = 0. Let w(s) be the first derivative of 4/25*s**5 + 41 - 32/15*s**3 - 8/5*s**v + 576/5*s + 192/5*s**2. Factor w(k).
4*(k - 6)**2*(k + 2)**2/5
Suppose 115*a + 19746 = 62066. Let u = -3160/9 + a. Solve u*n**3 + 0 - 44/3*n**4 - 16/3*n**2 + 2*n**5 + 0*n = 0.
0, 2/3, 6
Suppose 0 = -47*b + 961 + 4585. Suppose -b*v = -125*v + 14. Factor -1/6*s**4 - 2/3 + s**3 - 13/6*s**v + 2*s.
-(s - 2)**2*(s - 1)**2/6
Suppose -28*c + 13*c = -7*c - 16. Let o(m) be the second derivative of -1/8*m**4 - 6*m - 3/4*m**c + 0 + 1/2*m**3. Suppose o(d) = 0. Calculate d.
1
Let r(j) be the third derivative of j**5/390 - 31*j**4/52 + 92*j**3/39 - 114*j**2 - 21*j. Suppose r(a) = 0. Calculate a.
1, 92
Let g(m) be the third derivative of 0*m + 0*m**4 + 0*m**3 + 60*m**2 + 77/150*m**6 - 98/75*m**5 + 0 + 1/420*m**8 - 32/525*m**7. Factor g(x).
4*x**2*(x - 7)**2*(x - 2)/5
Suppose 506*k + 341 = 1626 + 233. Factor -27 + 3/2*v**4 - 15/2*v**k + 63/2*v + 3/2*v**2.
3*(v - 3)**2*(v - 1)*(v + 2)/2
Let y = -56159 - -280817/5. Factor 2*p**3 - 24/5*p**2 + 12/5 - y*p.
2*(p - 3)*(p + 1)*(5*p - 2)/5
Let t(v) be the second derivative of v**6/5 - 3*v**5/20 + v**4/4 - v - 9. Let r(n) = n**5 - 19*n**4 + 10*n**3 - 8*n**2. Let z(m) = 3*r(m) + 8*t(m). Factor z(q).
3*q**3*(q - 2)*(q - 1)
Suppose -104 = -16*a - 40. Suppose a*n = 4*m + 24, -3*m = 3*n - 0 - 6. Determine f so that 12/19*f**3 - 8/19 - 2/19*f**n - 26/19*f**2 + 24/19*f = 0.
1, 2
Suppose -52*t = -12 + 24 - 168. Let q(z) be the third derivative of 14*z**2 - 1/50*z**6 - 1/15*z**4 + 0*z + 1/15*z**5 + 0*z**t + 0. Let q(d) = 0. Calculate d.
0, 2/3, 1
Suppose -7*y + 814 = 4*v + 786, 2*y - 8 = 3*v. Determine s, given that -4*s**2 + v + 12*s + 1/3*s**3 = 0.
0, 6
Let d(h) be the first derivative of h**6/75 + h**5/25 - 7*h**4/30 + 4*h**3/15 + 70*h - 68. Let u(k) be the first derivative of d(k). Factor u(y).
2*y*(y - 1)**2*(y + 4)/5
Let i(x) be the second derivative of 25/18*x**3 - 13/6*x**2 + 0 - 16*x + 1/18*x**4. Suppose i(o) = 0. What is o?
-13, 1/2
Let g = 43 - 298/7. Let c(d) be the second derivative of -4/21*d**3 - g*d**2 + 41*d + 0 - 1/42*d**4. Find h, given that c(h) = 0.
-3, -1
Let b(m) be the first derivative of -4*m**3/9 - 40*m**2 + 244*m/3 + 123. Factor b(f).
-4*(f - 1)*(f + 61)/3
Let w be ((9 + -3)*2/(-4))/(-1). Suppose w*i - 8 = -r, -3*r = 5*i - 24 + 8. Solve -4/7*k**3 - 6/7*k**r - 2/7*k + 0 = 0.
-1, -1/2, 0
Let g = -625241/4 + 156312. Factor -g*t**2 + 1/2*t**3 + 7/4*t - 1/2.
(t - 2)*(t - 1)*(2*t - 1)/4
Let y be 1/(7/(-714)*-6). Let d(r) = 2*r - 31. Let i be d(y). Factor 5/6*z**i + 5/3 - 5/6*z - 5/3*z**2.
5*(z - 2)*(z - 1)*(z + 1)/6
What is s in -8/5*s**3 + 1/5*s**4 + 0 + 78/5*s - 71/5*s**2 = 0?
-6, 0, 1, 13
Let y be (36/(-216))/(3/(-9)). Let h be (-1)/24*(-25 - 2)/9. Factor y*v**2 + h*v + 0.
v*(4*v + 1)/8
Let u be 2*(5 + -5 - -2). Factor 26*i + 20 - 217*i**u - 6*i**2 - 202*i**4 + 421*i**4 - 10*i**3.
2*(i - 5)*(i - 2)*(i + 1)**2
Let r(v) be the first derivative of -5*v**3/3 + 240*v**2 + 3060*v - 2655. Factor r(w).
-5*(w - 102)*(w + 6)
Suppose 0 + 89/3*g**4 + g**5 + 0*g - 104/3*g**2 + 94*g**3 = 0. Calculate g.
-26, -4, 0, 1/3
Let 8/7 + 109*w**4 - 230/7