z(g) = 0. Calculate g.
-1, 1, 2, 5
Suppose 0 = -5*x - 8*d - 32, -17*x + 2*d = -12*x - 8. Determine v so that 1/3*v**3 - 1/3*v + x*v**2 + 0 = 0.
-1, 0, 1
Suppose 5*p + 583 = 276*p + 41. Find u, given that 0 - 4/7*u**p + 1/7*u**3 + 0*u = 0.
0, 4
Let s(d) be the first derivative of -19/6*d**2 - 14/3*d - 4/9*d**3 + 1/12*d**4 - 205. Solve s(i) = 0.
-2, -1, 7
Factor -79*k**2 + 1023 + 45*k**2 - 270*k + 452 + 29*k**2.
-5*(k - 5)*(k + 59)
Let j be (4 - 2)/(3/((-18)/(-4))). Suppose j*g - 17 = 34. Factor -z - z**2 + g*z - 45 - z**2 + 13.
-2*(z - 4)**2
Factor -368 + 368 + 22201*v + 97*v**2 + v**3 - 228*v**2 - 167*v**2.
v*(v - 149)**2
Let d = -4139 + 4145. Let j(c) be the third derivative of 0 + 0*c - 1/420*c**7 - 17*c**2 + 1/24*c**5 + 1/80*c**d + 1/24*c**4 - 1/672*c**8 + 0*c**3. Factor j(t).
-t*(t - 2)*(t + 1)**3/2
Let k(n) = 33*n**3 - 17*n**2 - 50*n. Let h(d) = -2*d**3 + 3*d**2 + d. Let p(r) = -17*h(r) - k(r). What is l in p(l) = 0?
0, 1, 33
Let q = 30 + -30. Let s be 4/30*(11 - q - 5). Factor 0*n**2 + 0 + s*n**3 - 4/5*n**4 + 0*n.
-4*n**3*(n - 1)/5
Let f(d) be the second derivative of -13*d - 4 - 2/3*d**6 + 1/9*d**7 + 11/9*d**4 - 4*d**3 + 8/3*d**2 + 29/30*d**5. Solve f(k) = 0 for k.
-1, 2/7, 1, 2
Let i(a) be the third derivative of 13*a**5/510 + 5*a**4/102 - a**3/17 - 3*a**2 + 6*a. Factor i(c).
2*(c + 1)*(13*c - 3)/17
Suppose 31*f - 29*f + 5*p + 14 = 0, -2*p = 8. Let k(w) be the first derivative of 40*w**2 + 5/4*w**4 + 60*w + 35/3*w**f + 6. Find q such that k(q) = 0.
-3, -2
Determine n so that 483*n**2 - 21/5*n**4 + 8373/5*n**3 - 2394/5 - 8373/5*n = 0.
-1, -2/7, 1, 399
Let g(x) be the third derivative of 61009*x**7/630 + 6669*x**6/40 - 82*x**5/15 + x**4/18 + 1124*x**2. Find s such that g(s) = 0.
-1, 0, 2/247
Factor -288/7 + 276/7*w + 87/7*w**2.
3*(w + 4)*(29*w - 24)/7
Let i(v) be the first derivative of v**4/8 + 3*v**3/8 - 3*v**2/4 - 51*v + 70. Let o(x) be the first derivative of i(x). Factor o(h).
3*(h + 2)*(2*h - 1)/4
Let k(m) be the first derivative of 34/45*m**5 + 0*m + 4/27*m**6 + 4/3*m**4 + 26/27*m**3 - 64 + 2/9*m**2. Suppose k(d) = 0. What is d?
-2, -1, -1/4, 0
Let a = 65 + -73. Let d(x) = -x - 4. Let g be d(a). Factor 9*l**4 + 11*l**2 + 20*l**3 - 3*l**g - 3*l**2 - 16*l.
2*l*(l + 2)**2*(3*l - 2)
Factor 18*l**2 + 34*l - 5568 + 5488 + 18*l.
2*(l + 4)*(9*l - 10)
Suppose 0 = -c + 5*r - 23, -c - 11 = -4*r + 7. Suppose -x = 2*d + 3 - 7, 0 = -c*d + 3*x + 12. Find b, given that -2/7*b**d + 0*b - 4/7*b**2 + 0 = 0.
-2, 0
Let s(u) be the second derivative of -8*u**2 - 19/3*u**4 + 0 - 5/2*u**5 - 120*u - 8/15*u**6 - 1/21*u**7 - 28/3*u**3. Factor s(k).
-2*(k + 1)**2*(k + 2)**3
Let i be -11 - (-19261)/110*11. Let k = i + -1915. Factor 3/10*f**2 + 0*f + k*f**3 + 0.
f**2*(f + 3)/10
Factor -137*w - 50*w + 187*w + w**4 - 12*w**2 + 4*w**3.
w**2*(w - 2)*(w + 6)
Suppose 29146*x + 14/15*x**3 - 4952/15*x**2 + 41772/5 = 0. Calculate x.
-2/7, 177
Let v(z) be the first derivative of z**6/360 - 7*z**5/15 + 98*z**4/3 + 86*z**3/3 - 53. Let d(o) be the third derivative of v(o). Find m, given that d(m) = 0.
28
Suppose 0 + 50*r**2 - 65/2*r**3 - 1/2*r**5 + 0*r + 7*r**4 = 0. What is r?
0, 4, 5
Let f(x) be the third derivative of x**8/672 - 3*x**7/140 + 3*x**6/40 + x**5/30 - x**4/2 - 72*x**2 - 10*x. Factor f(d).
d*(d - 6)*(d - 2)**2*(d + 1)/2
Let n(i) be the first derivative of i**7/600 + 13*i**6/900 - 43*i**5/600 + i**4/12 - 15*i**3 - 66. Let t(d) be the third derivative of n(d). Factor t(v).
(v - 1)*(v + 5)*(7*v - 2)/5
Let x(j) = j**3 + 25*j**2 + 121*j - 88. Let a be x(-18). Let 1/2*b**a + 20*b + 200 = 0. Calculate b.
-20
Suppose -31*f + 40*f = -45. Let z be 150/75*(825/(-2))/f. Factor 75/2*o**2 - z*o + 363/2.
3*(5*o - 11)**2/2
Let t(a) be the third derivative of 0 + 0*a**4 + 0*a + 1/72*a**6 + 1/90*a**5 + 1/1008*a**8 + 94*a**2 + 0*a**3 + 2/315*a**7. Factor t(i).
i**2*(i + 1)**2*(i + 2)/3
Let p(k) = 5 + 13*k - 8*k - 8*k. Let h be p(1). Factor -9*m + 10*m**2 - 7*m**h + 5*m**3 - m + 2*m**2.
5*m*(m - 1)*(m + 2)
Let p(v) = v**3 - v**2 + v + 1. Let d(j) = -2*j**3 + 37*j**2 - j - 70. Let m(h) = -d(h) - p(h). Let c(l) be the first derivative of m(l). Factor c(t).
3*t*(t - 24)
Let v(h) = h**4 + h**2 - h. Let j(x) = 3*x**4 - 37*x**2 + 32*x. Let w = 21 + -20. Let m(i) = w*j(i) + 2*v(i). Find g such that m(g) = 0.
-3, 0, 1, 2
Determine h, given that 1442/3*h + 0 + 2/3*h**2 = 0.
-721, 0
Let u = 335942 + -671883/2. What is j in -23/2*j**2 + 72 - u*j**3 - 60*j = 0?
-12, 1
Let k be 165*2/42 - 5/(-35). Suppose 3*b = 3*y + 3, -11*b + k*b = -4*y - 1. Solve 6/5*q**2 - 8/5 + 0*q + 2/5*q**b = 0.
-2, 1
Solve -63948 + 3/4*h**3 - 222*h**2 + 16863*h = 0.
4, 146
Let x = -560 + 554. Let p be x/12 - 2/(-4). Factor -1/4*o + p + 1/8*o**2.
o*(o - 2)/8
Let g(x) = x**3 - 28*x**2 + 98*x - 42. Let f be g(24). Let y be 132/693*14/f. Let -8/3*k**4 - y*k**5 - 16/3*k**3 + 0 - 4/3*k - 40/9*k**2 = 0. What is k?
-3, -1, 0
Let t(x) = -x**2 + 11*x + 6. Let v be t(8). Let k be (-36)/(-15) - v/75. Factor 3/4*d**3 + 3/4*d**k - 3/4*d**4 + 0 + 0*d - 3/4*d**5.
-3*d**2*(d - 1)*(d + 1)**2/4
Let w(a) = a**4 - 16*a**3 - 5*a**2 + 32*a. Let b(y) = -y**4 + 16*y**3 - 2*y**2 - 31*y. Let q(j) = -2*b(j) - 3*w(j). Factor q(z).
-z*(z - 17)*(z - 1)*(z + 2)
Let m(b) be the second derivative of 0 - 2*b + 6/5*b**2 + 3/100*b**5 + 0*b**3 - 3/20*b**4. Factor m(d).
3*(d - 2)**2*(d + 1)/5
Factor 1/4*b**2 - 23/2*b + 0.
b*(b - 46)/4
Determine a so that 9*a**3 - 5548*a**2 + 5560*a**2 - a**4 - 2*a**4 = 0.
-1, 0, 4
Let s be 7/(-6)*84664/(-3899). Solve 0 + 8*d - 16/3*d**4 - 76/3*d**3 - s*d**2 = 0 for d.
-3, -2, 0, 1/4
Suppose 3*v = 5*v. Suppose v*b = -3*b + 57. Factor -43*k**2 + 18*k**2 + 4*k + k**3 + b*k**2 - 8 + 8*k.
(k - 2)**3
Let d(h) be the first derivative of -h**4 + 52*h**3/3 + 136*h**2 - 2019. Determine l so that d(l) = 0.
-4, 0, 17
Let q(v) be the second derivative of 0 + 0*v**2 - 1/6*v**4 + 11*v + 0*v**3 + 1/10*v**5. Find d, given that q(d) = 0.
0, 1
Let q(x) = -119*x**2 + 450*x - 144. Let z(a) be the third derivative of -a**5/2 + 14*a**4/3 - 6*a**3 + 4*a**2. Let t(w) = -2*q(w) + 9*z(w). Factor t(m).
-4*(m - 3)*(8*m - 3)
Factor -22*y**2 - 96*y - 296/3 + 2/3*y**3.
2*(y - 37)*(y + 2)**2/3
Let p(c) be the first derivative of -159 - 2/3*c**3 + 11/3*c**2 - 4*c. Factor p(h).
-2*(h - 3)*(3*h - 2)/3
Let w(n) be the first derivative of -7*n**6/6 + 55*n**5 + 432*n**4 + 3208*n**3/3 + 728*n**2 - 720*n + 7817. Determine u, given that w(u) = 0.
-2, 2/7, 45
Let q(j) be the third derivative of -1/18*j**3 - 2*j**2 + 16 + 1/30*j**5 + 0*j - 5/72*j**4. Factor q(k).
(k - 1)*(6*k + 1)/3
Suppose 6*g = 2*g - 2*f + 12, 0 = -3*g + 4*f - 2. Let 5*s + 5*s - s**2 - 20 + 4*s - g*s = 0. What is s?
2, 10
Factor 954*y**2 + 48*y**4 - 4*y**4 + 0*y**3 - 37*y**3 - 968*y**2 + 7*y**5.
y**2*(y - 1)*(y + 7)*(7*y + 2)
Let u(l) be the first derivative of -l**7/840 - 17*l**6/1800 - 26*l**3/3 - 2*l**2 + 208. Let h(f) be the third derivative of u(f). Factor h(x).
-x**2*(5*x + 17)/5
Let j(w) = 10*w**2 - 15*w. Let f(v) = -11*v**2 + 14*v. Let k(x) = -5*f(x) - 6*j(x). Factor k(s).
-5*s*(s - 4)
Let b be 1 + (-40)/(-12) + (-10)/(-6). Let o be 550/50 - 63/b. Let o*u**3 + 1/6*u**5 + 0*u + 0*u**2 + 0 + 2/3*u**4 = 0. Calculate u.
-3, -1, 0
Let f(q) = 6*q**3 + 328*q**2 - 658*q + 334. Let x(n) = -20*n**3 - 984*n**2 + 1972*n - 1003. Let y(t) = 14*f(t) + 4*x(t). Let y(c) = 0. What is c?
-166, 1
Let z(g) be the first derivative of g**3 + 51/2*g**2 + 0*g - 127. Factor z(m).
3*m*(m + 17)
Determine o, given that -2/5*o**2 - 28 - 142/5*o = 0.
-70, -1
Suppose 910 = -10*w + 446*w + 19*w. Suppose -16/5*o + 0 + 2*o**4 - 44/5*o**3 + 56/5*o**w = 0. Calculate o.
0, 2/5, 2
Let m(y) be the third derivative of 0*y + 0 - 1728*y**3 - 12*y**4 + 79*y**2 - 1/30*y**5. Factor m(b).
-2*(b + 72)**2
Let p be 6/(-10) - 1802/(-170). Factor -360 + 2*j**3 + 6*j - p*j**2 + 2*j**4 + 360.
2*j*(j - 1)**2*(j + 3)
Let w = -47455 - -616921/13. Factor w*i + 0 + 2/13*i**4 + 10/13*i**3 + 14/13*i**2.
2*i*(i + 1)**2*(i + 3)/13
Let n(k) be the second derivative of 3*k**5/70 + 40*k**4/21 + 47*k**3/21 - 130*k**2/7 - 24*k + 61. Factor n(o).
2*(o - 1)*(o + 26)*(3*o + 5)/7
Suppose -3898*w + 59 + 117 + 348 - 9*w**4 - 2378*w**3 - 2620*w**3 + 33 + 8348*w**2 = 0. What is w?
-557, 1/3, 1
Let i(h) be the first derivative of 333*h**5/5 - 129*h**4/4 + 2*h*