.
2
Solve 20/9*v**2 + 2*v + 0 + 2/9*v**3 = 0 for v.
-9, -1, 0
Find s such that 1/12*s**3 + 0 - 5/12*s**2 + 1/2*s = 0.
0, 2, 3
What is n in -18*n**3 + 26*n**2 - 11*n**2 + n**4 + 2*n**5 + 3*n**2 - 3*n**4 = 0?
-3, 0, 1, 3
Solve -773*t**4 - 98*t**3 - 4 + 444*t**4 + 48*t + 398*t**4 - 15*t**2 = 0 for t.
-2/3, 2/23, 1
Let d(u) = 0 - 14*u - 1 + 17 + 4*u**2. Let b(n) = 4*n**2 - 13*n + 16. Let l be (6/(-8))/((-2)/(-8)). Let k(s) = l*d(s) + 2*b(s). Find r such that k(r) = 0.
2
Let y(g) be the second derivative of -5*g**7/42 + g**6/2 - 3*g**5/4 + 5*g**4/12 + 5*g - 10. Solve y(v) = 0 for v.
0, 1
Suppose 49*u = 69*u. Determine m so that 0 + 1/7*m**3 - 1/7*m + u*m**2 = 0.
-1, 0, 1
Let s be ((-50)/(-20))/((-28)/(-12) - (10 - 11)). Factor 15/4*x + s*x**2 - 3/4*x**3 + 9/4.
-3*(x - 3)*(x + 1)**2/4
Let r(k) = -k**2 - 3*k. Let m(d) = 2*d**2 + 6*d. Suppose -b + 8 = 13. Let u(w) = b*r(w) - 3*m(w). Factor u(y).
-y*(y + 3)
Suppose -1947 + 722*x**2 - 4*x**3 - 14181 - 960*x - 558*x**2 = 0. Calculate x.
-7, 24
Let n be 60/80*(1/(-3))/(6/(-8)). Factor n - 2/3*x**2 + 1/3*x.
-(x - 1)*(2*x + 1)/3
Let w(x) be the second derivative of -9*x**5/22 + 31*x**4/22 - 20*x**3/11 + 12*x**2/11 + 51*x. Let w(i) = 0. Calculate i.
2/5, 2/3, 1
Suppose -2*k**2 + 23*k - 3*k**2 - 3*k**3 - k**2 + 24 - 11*k = 0. What is k?
-2, 2
Solve 19/2*g**3 + 11/3*g**2 + 0 + 0*g + 5/6*g**4 = 0 for g.
-11, -2/5, 0
Let f(u) be the first derivative of -3*u**5/5 + 9*u**4/4 - 6*u**2 - 58. Suppose f(h) = 0. Calculate h.
-1, 0, 2
Let d be 1*134 - (-5 - 25/(-5)). Let l = d - 668/5. Factor 4/5*y + 2/5 + l*y**2.
2*(y + 1)**2/5
Let k = 5/2 - 7/4. Let x = 2/345 + 341/690. Factor 0 - x*w + 5/4*w**2 + k*w**3.
w*(w + 2)*(3*w - 1)/4
Let k = -1678 + 8392/5. Factor -k*l**2 - 6/5*l + 4.
-2*(l - 2)*(l + 5)/5
Suppose 6*t - 5*t = -c + 1, 2*t = 3*c + 12. Find z such that -29*z - 32*z**2 - 12 - 4*z**t + 5 + 4*z**3 - 4*z**3 = 0.
-7, -1/2
Suppose -9 = -l + 2*c, -5*l + c = 2*c - 12. Solve -2*h**l + 8/5*h**2 + 0*h + 2/5*h**4 + 0 = 0.
0, 1, 4
Let k(o) be the first derivative of -4*o**3 + 4*o**2 - 4*o - 8. Let c(z) = -z**2. Let x(n) = 8*c(n) - k(n). Factor x(y).
4*(y - 1)**2
Let q = -1011 + 7078/7. Find r such that -2/7 - 1/7*r + q*r**2 = 0.
-1, 2
Let s(l) be the second derivative of l**4/32 - 109*l**3/8 + 35643*l**2/16 - 2*l + 407. Factor s(v).
3*(v - 109)**2/8
Let w(m) = -1. Let u(t) = t**2 + 5*t - 3. Suppose 11*h - 16*h = -5. Let v(o) = h*u(o) + 3*w(o). Factor v(k).
(k - 1)*(k + 6)
Let p = -30 + 36. Let i(j) be the second derivative of 1/12*j**4 - p*j + 1/12*j**3 + 1/40*j**5 + 0*j**2 + 0. Factor i(g).
g*(g + 1)**2/2
Let n(c) be the first derivative of -9/4*c + 12 + 3/4*c**2 + 1/4*c**3. Let n(d) = 0. Calculate d.
-3, 1
Let m(d) be the first derivative of -6*d**5/55 - 57*d**4/22 - 210*d**3/11 - 375*d**2/11 + 1500*d/11 + 540. Suppose m(l) = 0. Calculate l.
-10, -5, 1
Solve -117*y**2 - 65*y**3 - 5*y**5 + 147*y**2 + 0*y**5 + 40*y**4 = 0 for y.
0, 1, 6
Let i(k) be the first derivative of -2*k**3/33 + 70*k**2/11 + 142*k/11 - 317. Factor i(u).
-2*(u - 71)*(u + 1)/11
Let o(u) = 49*u**2 - 24*u. Let p(g) = 49*g**2 - 30*g - 4. Let v(f) = -f - 1. Let n(i) = p(i) - 5*v(i). Let d(r) = -4*n(r) + 3*o(r). Solve d(a) = 0.
2/7
Suppose 340*r + d = 344*r - 11, r - 1 = 2*d. Factor 0 + 3/2*f + f**r + 5/2*f**2.
f*(f + 1)*(2*f + 3)/2
Suppose 0 = 5*o + w - 16 + 11, -5*w = 4*o + 17. Let a(y) be the first derivative of -3/5*y - 1/15*y**3 + 2 + 2/5*y**o. Factor a(x).
-(x - 3)*(x - 1)/5
Let n(i) be the third derivative of 1/15*i**5 - 16/3*i**3 + 0 - 1/3*i**4 - 32*i**2 + 0*i. Factor n(a).
4*(a - 4)*(a + 2)
Let w(m) be the third derivative of -m**7/180 + 17*m**6/180 - 14*m**5/45 + m**4/3 + 14*m**3/3 - 28*m**2. Let a(u) be the first derivative of w(u). Factor a(j).
-2*(j - 6)*(j - 1)*(7*j - 2)/3
Determine i so that -16/9*i - 80/9*i**2 - 7/9*i**5 - 32/3*i**3 - 44/9*i**4 + 0 = 0.
-2, -2/7, 0
Suppose g = -g - 2. Let v(o) = 10*o**3 - 13*o**2 + 11*o - 2. Let n(f) = -f**3 - f**2. Let u(a) = g*v(a) - 3*n(a). Determine d, given that u(d) = 0.
2/7, 1
Let o(t) = -t**2 + 12*t - 30. Let a be o(6). Let u be 5/a - (-32)/(-48). Solve 1/6 - 1/6*g**2 - u*g + 1/6*g**3 = 0 for g.
-1, 1
Let a(j) = 180*j**3 + 325*j**2 - 615*j + 215. Let y(i) = -45*i**3 - 81*i**2 + 154*i - 54. Let u(l) = -6*a(l) - 25*y(l). Factor u(v).
5*(v + 3)*(3*v - 2)**2
Let v(u) = -7*u**2 - u + 3. Let d(y) = -y**2 - y + 1. Let k be 4 + (-5 - (-8 + 4)). Let n(s) = k*d(s) - v(s). Suppose n(a) = 0. What is a?
0, 1/2
Let t(r) be the second derivative of -5*r**4/12 - 20*r**3/3 - 30*r**2 + 66*r - 4. Factor t(w).
-5*(w + 2)*(w + 6)
Let z(q) = -7*q**3 - 13*q**2 - 4*q + 12. Let g(v) = -7*v**3 - 13*v**2 - 2*v + 12. Let c(l) = -6*g(l) + 5*z(l). Factor c(m).
(m - 1)*(m + 2)*(7*m + 6)
Let k(v) be the third derivative of -v**7/735 + 2*v**6/105 - 11*v**5/210 - 5*v**4/21 + 2*v**2 - 81*v. Let k(c) = 0. Calculate c.
-1, 0, 4, 5
Let p(u) be the second derivative of u**6/60 + u**5/10 + u**4/6 - 4*u**2 - 7*u. Let w(j) be the first derivative of p(j). Factor w(y).
2*y*(y + 1)*(y + 2)
Let b be 14/6*(216/21 - (-180)/(-20)). What is d in -1/4*d**b - 5/4 + 9/4*d - 3/4*d**2 = 0?
-5, 1
Let x(i) be the second derivative of -i**5/10 - 47*i**4/7 - 960*i**3/7 - 800*i**2/7 + 113*i. Determine l so that x(l) = 0.
-20, -2/7
Let s(r) be the second derivative of 0*r**2 + 4*r + 0 - 1/120*r**5 - 1/36*r**4 - 1/36*r**3. Factor s(v).
-v*(v + 1)**2/6
Let -176*k**5 + 32*k**2 - 16 - 2*k**3 - 4*k + 172*k**5 - 16*k**4 + 10*k**3 = 0. Calculate k.
-4, -1, 1
Let d(c) be the third derivative of -1/75*c**5 + 0*c + 1/150*c**6 - 1/30*c**4 + 0 + 2/15*c**3 - 5*c**2. Find z, given that d(z) = 0.
-1, 1
Let z(n) be the third derivative of -n**6/240 + 13*n**5/40 - 25*n**4/16 + 37*n**3/12 - n**2 - 12*n. Determine v, given that z(v) = 0.
1, 37
Let p(v) = -6*v - 14 - 5*v - 10*v + 14*v**2 + 20*v + v**3. Let g be p(-14). Suppose g - 3/7*o**3 + 0*o**2 + 0*o = 0. What is o?
0
Let d(a) be the second derivative of -40*a + 15*a**2 + 5/6*a**3 + 0 - 35/12*a**4. Suppose d(t) = 0. Calculate t.
-6/7, 1
Factor -54*s**3 + 84*s - 4*s**4 + 22*s**2 - 30*s**3 - 18*s**2.
-4*s*(s - 1)*(s + 1)*(s + 21)
Let o(m) be the second derivative of m**2 + 0 - 1/6*m**4 - 23*m - 7/12*m**3 + 7/40*m**5. Solve o(y) = 0.
-1, 4/7, 1
Let c(q) = q**2 - 49*q - 90. Let z(m) = -4*m + 8 + 0*m + 10 + 14*m. Let k(g) = 4*c(g) + 22*z(g). Factor k(n).
4*(n + 3)**2
Let o(n) = 8*n**2 + 21*n + 38. Let p(q) = -q**2 + 3*q - 1. Let a(h) = o(h) + 5*p(h). Suppose a(t) = 0. What is t?
-11, -1
What is i in 30/7*i**3 + 12/7*i - 2/7*i**5 + 34/7*i**2 + 0 + 6/7*i**4 = 0?
-1, 0, 6
Solve 70 - 45/4*q**3 - 5/4*q**4 - 25/2*q**2 + 45*q = 0 for q.
-7, -2, 2
Suppose 59*o**4 - 6*o**4 + 47*o**4 + 272 - 482*o**3 + 276*o**2 + 1074*o - 1238*o**3 - 2*o = 0. Calculate o.
-2/5, 1, 17
Let w = 112/19 - 11741/1995. Let p(x) be the third derivative of 1/336*x**8 + 1/120*x**6 + 0*x**4 + 0*x**5 + 4*x**2 + 0*x**3 - w*x**7 + 0 + 0*x. Factor p(y).
y**3*(y - 1)**2
Let l = -193 - -197. Let o(s) be the first derivative of 2/5*s**5 - 3/8*s**l + 3/4*s**2 - 5/6*s**3 + 1 + 1/2*s. What is n in o(n) = 0?
-1, -1/4, 1
Suppose 12 = -21*z + 25*z. Let b(f) = f**3 + 2*f - 1. Let p be b(1). Factor 2*o + o**p + 3 - z + 3 - 2.
(o + 1)**2
Suppose c - 6*c - 30 = -v, -10 = 2*v + 4*c. Suppose v*f - 2*y - 12 = -2, 8 = 4*f - 3*y. Factor -2/9 - 2/3*q - 4/9*q**f.
-2*(q + 1)*(2*q + 1)/9
Suppose 0*y + 2/3*y**3 - 16/3*y**2 + 0 = 0. Calculate y.
0, 8
Let w(o) be the first derivative of o**8/784 - o**7/70 + o**6/35 + 4*o**5/35 + 5*o**2 - 6. Let l(v) be the second derivative of w(v). Factor l(d).
3*d**2*(d - 4)**2*(d + 1)/7
Let k(r) = 1160*r**2 - 1405*r + 135. Let x(j) = 43*j**2 - 52*j + 5. Let z(t) = -2*k(t) + 55*x(t). Let z(f) = 0. Calculate f.
1/9, 1
Factor -6 + 4*j**2 - 3*j**2 + 0*j**2 + 2*j**3 - 10*j - 6*j**2 + 3*j**2.
2*(j - 3)*(j + 1)**2
Determine r so that -92/7*r**3 + 424/7*r**2 + 72/7 - 388/7*r - 16/7*r**4 = 0.
-9, 1/4, 1, 2
Suppose -59 - 3*d**2 - 27*d**2 + 2*d**3 - 7 + 92*d + 2*d = 0. Calculate d.
1, 3, 11
Factor 0*m - 50/3 + 2/3*m**2.
2*(m - 5)*(m + 5)/3
Let b(h) be the first derivative of h**3/4 - 105*h**2/4 + 3675*h/4 + 22. Determine x, given that b(x) = 0.
35
Let n(p) = -p + 1. Let i(r) be the third derivative of -r**5/30 + r**4/6 - 7*r**3/3 + 8*r**2. Suppose -5*s - 10 = -4*s. L