m be q(11). Let w = m + 106/3. Determine y, given that 0*y + 0 + w*y**2 = 0.
0
Let c(q) be the third derivative of 1/10*q**6 - 1/3*q**4 - 1/15*q**5 + 0 + 21*q**2 + 0*q**3 + 0*q. Suppose c(n) = 0. Calculate n.
-2/3, 0, 1
Let v(x) = 12*x**3 - 45*x**2 - 83*x - 30. Let l(o) = 9*o**3 + 60 - 17*o**3 + 3*o**3 + 90*o**2 - 20*o**3 + 165*o. Let k(g) = -2*l(g) - 5*v(g). Solve k(t) = 0.
-1, -1/2, 6
Suppose -5*d + 2*v = -2, 4*v - v = 5*d + 2. Factor -a - 2 - 3*a**d + 0*a - 5*a + a.
-(a + 1)*(3*a + 2)
Let m(y) be the second derivative of y**5/50 + y**4/6 + 7*y**3/15 + 3*y**2/5 - y - 3. Factor m(r).
2*(r + 1)**2*(r + 3)/5
Let l(h) = 10*h**4 + 820*h**3 - 4040*h**2 + 6560*h - 55. Let z(f) = -f**4 - 91*f**3 + 449*f**2 - 729*f + 6. Let b(w) = -6*l(w) - 55*z(w). Solve b(d) = 0.
0, 3, 7
Suppose -6 = -7*z + 22. Let k = 5 - 3. Factor -z*l**2 + 3*l**2 + k*l**2 + l**3.
l**2*(l + 1)
Let q(s) be the first derivative of -3*s**5/5 + 33*s**4/2 - 97*s**3 - 396*s**2 - 432*s - 142. Solve q(k) = 0.
-1, 12
Factor -9*s**3 - 69*s - 3*s**2 + 12*s**3 + 63*s.
3*s*(s - 2)*(s + 1)
Let k = 15797/1560 + -81/8. Let z(c) be the third derivative of 0*c**4 + 0 + 0*c - 4/39*c**3 - k*c**6 + c**2 + 1/130*c**5. Factor z(g).
-2*(g - 2)**2*(g + 1)/13
Suppose 2 = -2*c, -2*k - 38*c + 36*c + 2 = 0. Factor 4/7*o**k + 1/7*o**3 - 4/7*o**4 - 1/7*o + 0.
-o*(o - 1)*(o + 1)*(4*o - 1)/7
Let c(q) be the first derivative of 0*q**2 + 0*q - 1/10*q**5 + 10 + 0*q**3 - 3/16*q**4 + 1/24*q**6. Let c(j) = 0. What is j?
-1, 0, 3
Factor 42*s**4 + 0*s**2 + 6*s**3 + 147/2*s**5 + 0*s + 0.
3*s**3*(7*s + 2)**2/2
Let o = 96931/7 + -13847. Factor o*c**3 + 4/7 - 6/7*c + 0*c**2.
2*(c - 1)**2*(c + 2)/7
Solve 7/10*k + 1/10*k**3 + 3/10 + 1/2*k**2 = 0.
-3, -1
Let b(y) = -2*y**2 + 9*y - 5. Let o be b(3). Factor -8*f + 27 + 7*f**2 - 2*f**o - 14*f**2 - 3 + 12*f**3 - 11*f**2.
-2*(f - 3)*(f - 2)**2*(f + 1)
Factor 3*g**2 + 64*g + 5*g**2 + 0*g**2 - 3*g**2 + 6*g.
5*g*(g + 14)
Let d(j) = 4*j**2 - j - 5. Let y(i) = -5*i**2 + 6. Let t(c) = -6*d(c) - 5*y(c). Factor t(l).
l*(l + 6)
Let n = -99 - -179. Find i, given that -30*i**3 - 6*i**3 + 24 - n*i**2 + 34*i + 58*i = 0.
-3, -2/9, 1
Let r(t) be the first derivative of t**8/448 - t**7/560 - t**6/96 + t**5/80 - 8*t**3/3 - 8. Let i(j) be the third derivative of r(j). Find f such that i(f) = 0.
-1, 0, 2/5, 1
Let z(m) be the third derivative of m**7/210 - 11*m**6/120 + 13*m**5/20 - 15*m**4/8 - 3*m**2 + 208. Solve z(v) = 0.
0, 3, 5
Let s(n) be the first derivative of 4*n - 2/3*n**3 + 9 + n**2. Let s(l) = 0. What is l?
-1, 2
Factor 25 - 2*q + 7*q + 2*q**2 - 7 + 10*q**2 + 28*q - 3*q**3.
-3*(q - 6)*(q + 1)**2
Let v be (-11 + 11)/(2 + 0). Let l(w) be the second derivative of -1/6*w**4 + w**3 + v - 2*w - 2*w**2. Let l(o) = 0. Calculate o.
1, 2
Let u = -872 + 377. Let w be u/22*(-4)/6. Factor -3*q**3 + w*q - 2 - 3*q**2 + 4 - 11.
-3*(q - 1)**2*(q + 3)
Let r(u) be the second derivative of 7*u + 0 + 0*u**5 + 0*u**3 + 1/6*u**6 + 0*u**4 + 0*u**2. Suppose r(y) = 0. Calculate y.
0
Let l(h) be the second derivative of h**6/45 - 13*h**5/30 - h**4/6 + 41*h**3/9 - 26*h**2/3 + 107*h. Determine b, given that l(b) = 0.
-2, 1, 13
Let k(a) be the first derivative of -a**3/6 + 8*a**2 - 861. Factor k(j).
-j*(j - 32)/2
Let k(s) be the third derivative of s**5/20 + 7*s**4/4 + 33*s**3/2 - 15*s**2. Determine m so that k(m) = 0.
-11, -3
Let i be (-224)/128 + 102/40. Find f, given that 3/5*f**2 - i + 1/5*f**3 + 0*f = 0.
-2, 1
Factor -3 - 51*g**2 + 284*g - 368*g - 9*g**3 - 33.
-3*(g + 2)*(g + 3)*(3*g + 2)
Let h(q) be the second derivative of q**7/14 - q**6/2 + 21*q**5/20 - 3*q**4/4 + 9*q - 2. Suppose h(r) = 0. What is r?
0, 1, 3
Let l(f) = 2*f**3 - 77*f**2 - 23*f - 435. Let q be l(39). What is g in -87*g**3 - q*g**2 - 3/2*g**5 - 81/2 - 351/2*g - 37/2*g**4 = 0?
-3, -1/3
Let s = 37 + -32. Solve -192*j - 4*j**s - 121*j**3 + 62*j**2 - 96*j**2 - 64 - 36*j**4 - 7*j**3 - 190*j**2 = 0.
-2, -1
Let t(h) = -21*h**4 + 36*h**3 + 141*h**2 - 114*h - 153. Let z(p) = 3*p**4 - 5*p**3 - 20*p**2 + 16*p + 22. Let k(b) = 2*t(b) + 15*z(b). Factor k(q).
3*(q - 2)**2*(q + 1)*(q + 2)
Suppose 3*o - 3 - 6 = 0. Let -2*i**2 + o*i**3 - i - 2*i + i - 6*i = 0. Calculate i.
-4/3, 0, 2
Let d(y) be the first derivative of -y**4/30 - 122*y**3/45 - 203*y**2/3 - 1682*y/5 - 100. Factor d(u).
-2*(u + 3)*(u + 29)**2/15
Let g be (-16)/(-10)*3/6*5. Suppose -3*r - u + 2 = 0, -3*r + g = -3*u - 14. Suppose -2*o**r + 3/4*o**3 - o + 0 + 9/4*o**4 = 0. Calculate o.
-2/3, 0, 1
Let n(w) be the first derivative of 4*w**3/3 - 6*w**2 - 16*w + 113. Factor n(z).
4*(z - 4)*(z + 1)
Find w such that 0 + 34/7*w**2 - 8/7*w**3 - 8/7*w = 0.
0, 1/4, 4
Let p = 42978 + -42973. Factor -1/3*k**2 + 5/3*k**p - 11/3*k**4 + 0 + 0*k + 7/3*k**3.
k**2*(k - 1)**2*(5*k - 1)/3
Let j(i) = -17*i**3 - 583*i**2 + 611*i + 11. Let q(y) = -9*y**3 - 291*y**2 + 306*y + 6. Let h(t) = 6*j(t) - 11*q(t). What is g in h(g) = 0?
-100, 0, 1
Let l(j) be the third derivative of 0 + 0*j + 1/168*j**8 + 0*j**3 - 7*j**2 + 3/4*j**4 - 2/5*j**5 + 4/105*j**7 - 1/30*j**6. Factor l(t).
2*t*(t - 1)**2*(t + 3)**2
Let q be ((-1)/90)/(49/(-21)*4). Let t(i) be the third derivative of 2/21*i**3 + i**2 - 1/21*i**4 - q*i**6 + 0 + 0*i + 1/84*i**5. Determine r so that t(r) = 0.
1, 2
Let g be (-40)/14*(-118)/(-295)*(-13 + 7). Suppose 0 - 6/7*r**5 + g*r**2 + 18/7*r**3 - 12/7*r**4 + 24/7*r = 0. Calculate r.
-2, -1, 0, 2
Solve 0 - 1560/7*g**2 - 2/7*g**5 - 1352/7*g - 60/7*g**4 - 554/7*g**3 = 0 for g.
-13, -2, 0
Let c(w) be the second derivative of -w**6/40 - 3*w**5/40 - w**4/16 + 4*w + 7. Factor c(f).
-3*f**2*(f + 1)**2/4
Determine y, given that -12/7*y - 3/7*y**4 + 12/7*y**3 + 18/7*y**2 - 15/7 = 0.
-1, 1, 5
Let u(s) = 270*s - 5937. Let w be u(22). What is n in 7/6*n**4 - 1/3*n**w + 1/3*n - 7/6*n**2 + 0 = 0?
-1, 0, 2/7, 1
Factor 1/7*a**4 + 0 - 9/7*a**3 - 12/7*a + 20/7*a**2.
a*(a - 6)*(a - 2)*(a - 1)/7
Suppose -3*k - 4*t = 8, 3*t - 3 = -5*k + 2. Let y(j) be the first derivative of 2/9*j - 2/27*j**3 + 1/9*j**2 - 1/18*j**k + 5. Solve y(u) = 0.
-1, 1
Let u be (-82)/360 + -6*8/(-192). Let k(f) be the second derivative of 0*f**3 + 0*f**2 - 1/15*f**5 + 1/18*f**4 + 0 + 5*f + u*f**6. Let k(r) = 0. Calculate r.
0, 1
Let v be ((3834/(-1420))/((-42)/8))/(6/28). Suppose v*h**2 - 8/5*h**3 + 2/5*h**4 + 2/5 - 8/5*h = 0. Calculate h.
1
Suppose 7*m = 9*m - 6. Suppose 2*v - 3*f = 38, 4*f + 50 = m*v - 8. Determine n, given that 44/3*n + 37/3*n**3 - 8/3 - v*n**2 - 7/3*n**4 = 0.
2/7, 1, 2
Let x = 253 - 249. Let t be (0 + 0)/(0 + 2). Factor 2*j**5 + 2*j**4 + t*j**x - j**4 + j**4.
2*j**4*(j + 1)
Let s(z) = 2*z**2 - 4*z + 2. Let f be s(3). Suppose -2*j - 4 = -2*c - 0*c, -c + f = 5*j. Solve -2 + 4*m + 2*m + 0*m - 6*m**3 - 1 + c*m**4 = 0 for m.
-1, 1
Let s = -259 - -259. Let x(w) be the first derivative of 2 + 1/4*w**4 + s*w**2 + w**3 + 1/18*w**6 - 1/3*w**5 + 0*w. Suppose x(g) = 0. Calculate g.
-1, 0, 3
Let z(o) be the second derivative of -o**6/69 - o**5/10 + 5*o**4/69 - 77*o. Factor z(v).
-2*v**2*(v + 5)*(5*v - 2)/23
Let t(l) be the first derivative of 5*l**4/4 - 130*l**3/3 + 625*l**2/2 - 500*l - 299. Find j such that t(j) = 0.
1, 5, 20
Let s = -211 + 208. Let h be (10/s)/(14/6 - 5). Factor -1/4 - 3/4*p**3 + h*p**2 - 1/4*p.
-(p - 1)**2*(3*p + 1)/4
Suppose -14*g**3 + 158*g - 10*g**4 + 4 + 30*g**2 - 144*g - 24*g**2 = 0. Calculate g.
-1, -2/5, 1
Let u = -2656 + 2658. Suppose 4*i = -3 + 11. Factor u - i*l + 1/2*l**2.
(l - 2)**2/2
Factor 216*f + 64 + 7/8*f**3 - 111/4*f**2.
(f - 16)**2*(7*f + 2)/8
Let k(c) be the second derivative of c**6/15 - 3*c**5/5 + 4*c**4/3 - 2*c - 12. Solve k(t) = 0 for t.
0, 2, 4
Let y be (9/18)/((-1)/(-4)). Find m such that -3*m**4 + 5 + 6*m - 12*m**3 + 8*m**2 + 0 + 6*m**5 - 8 - y*m**2 = 0.
-1, 1/2, 1
Let l(k) be the second derivative of 9*k - 1/6*k**2 + 0*k**5 + 0*k**3 + 1/18*k**4 + 0 - 1/90*k**6. Factor l(n).
-(n - 1)**2*(n + 1)**2/3
Let w(j) be the first derivative of 3*j**5/5 + 9*j**4/4 - 3*j**3 - 33*j**2/2 - 18*j + 478. Factor w(o).
3*(o - 2)*(o + 1)**2*(o + 3)
Let l(a) be the second derivative of a**6/30 + 3*a**5/20 + a**4/3 + a**2/2 + 5*a. Let j(z) = 2*z**3 + 4*z**2. Let x(t) = 6*j(t) - 4*l(t). Factor x(u).
-4*(u - 1)**2*(u + 1)**2
Let -2/5*c**4 + 0*c - 12/5*c**2 + 0 + 2*c**3 = 0. What is c?
0, 2, 3
Let a(l) be the third derivative of l**9/60480