j**3 + 10*j**2 = 0. Calculate j.
-2/11, 1
Let k = -22/1333 - -1421/5332. Let n(q) be the second derivative of 0 + 1/5*q**6 - 45*q - 3/8*q**5 + 0*q**3 + 0*q**2 + k*q**4 - 1/28*q**7. Factor n(d).
-3*d**2*(d - 2)*(d - 1)**2/2
Let v be -3*(8/(-20) + (-7764)/90). Factor -5*w**3 - 49*w**2 + 29 + v*w - 26*w**2 - 119 - 90.
-5*(w - 2)*(w - 1)*(w + 18)
Let v(b) be the second derivative of -1/20*b**5 - 2/45*b**6 + 153*b + 0*b**2 + 1/36*b**4 + 0*b**3 + 0. Factor v(r).
-r**2*(r + 1)*(4*r - 1)/3
Let y(h) be the third derivative of 4/105*h**6 + 10/21*h**3 + 76/105*h**5 + 0*h - 79/84*h**4 + 0 - 46*h**2. Factor y(o).
2*(o + 10)*(4*o - 1)**2/7
Let k be ((-10)/4)/((-7)/(-4 - -18)). Suppose 0 = 2*n - 5*p + 2*p - 39, 5*n - 85 = k*p. Suppose n*c + 3*c - 9 + 19 + 5*c**2 = 0. What is c?
-2, -1
Factor -9*o**2 - 1/3*o**4 + 0 - 58/3*o + 10*o**3.
-o*(o - 29)*(o - 2)*(o + 1)/3
Let o(z) = -3*z**2 - 236*z - 486. Let a(l) = -18*l**2 - 1178*l - 2427. Let y(k) = 2*a(k) - 11*o(k). Determine x so that y(x) = 0.
-2, 82
Suppose 0 = -4*k + 4*r + 56, -1415*k + 5*r = -1418*k - 54. Factor 1/4*t**5 + 0*t**4 + 0*t + 0*t**k - 1/4*t**3 + 0.
t**3*(t - 1)*(t + 1)/4
Let n(d) be the second derivative of d**6/70 - 111*d**5/70 - 75*d**4/28 - 3*d - 397. Suppose n(f) = 0. What is f?
-1, 0, 75
Let r be (-9 - (207 - -8))*1/(-2). Factor -32*f - 16*f + r*f**2 + 23 + 18 - 41 + 20*f**3.
4*f*(f + 6)*(5*f - 2)
Find f such that -56148*f**3 - 42119/4*f - 42117*f**2 - 1755/2 + 16*f**4 = 0.
-1/4, 3510
Let z(w) = 39*w**2 + 228*w + 525. Let s(q) be the first derivative of 11/3*q**3 + 65/2*q**2 + 150*q - 5. Let j(n) = -18*s(n) + 5*z(n). Solve j(b) = 0 for b.
-5
Let m(d) = 20*d**4 + 56*d**3 + 28*d**2 + 8*d. Let s(q) = -1151*q + 1154*q - 4 + 19*q**3 + 7*q**4 + 4 + 9*q**2. Let c(h) = -3*m(h) + 8*s(h). Factor c(l).
-4*l**2*(l + 1)*(l + 3)
Let 36125000/11 + 17000/11*r + 2/11*r**2 = 0. What is r?
-4250
Let o(f) be the third derivative of -100*f**2 - 5*f**4 - 70/3*f**3 + 1/24*f**6 + 0 - 1/4*f**5 + 0*f. Factor o(k).
5*(k - 7)*(k + 2)**2
Let b(h) be the second derivative of 9*h**4/10 + 43*h**3/5 - 6*h**2 - 1864*h. Factor b(i).
6*(i + 5)*(9*i - 2)/5
Let x be (-2)/3 - 207/(-270). Let g(t) be the first derivative of 1/15*t**3 - x*t**2 - 2/5*t - 4. Factor g(j).
(j - 2)*(j + 1)/5
Let w(c) = c + 3. Let n(b) = -b**2 + 3*b + 36. Let m(y) = y. Let l(f) = 6*m(f) + n(f). Let p(v) = -2*l(v) + 18*w(v). Let p(x) = 0. Calculate x.
-3, 3
Factor 0 + 0*u + 3/7*u**2 + 4/7*u**5 - 2/7*u**3 - 5/7*u**4.
u**2*(u - 1)**2*(4*u + 3)/7
Let v(n) = 28*n**2 + 28*n - 21. Let d be v(-14). Suppose -5075 + d + 4*z**2 - 60*z = 0. What is z?
0, 15
Let b be 111/6 + (-3)/2. Determine u, given that 17*u**2 + 13 - b*u**2 + 18*u + 8 - 3*u**2 = 0.
-1, 7
Let h(w) be the third derivative of -5*w**7/42 - 77*w**6/120 - w**5/10 + 186*w**2. Factor h(m).
-m**2*(m + 3)*(25*m + 2)
Solve -3464 - 431*x**2 + 145*x**2 + 146*x**2 + 144*x**2 - 1724*x = 0 for x.
-2, 433
Suppose -17*h + 16*h + 7 = 0. Suppose 0 = h*g + 3*g - 100. Factor -g*q**2 + 0*q**2 - 132*q + 157*q - 10.
-5*(q - 2)*(2*q - 1)
Let h(m) = m**2 + 47*m + 46. Let f(b) = -3*b**2 - 140*b - 137. Let g = -455 - -459. Let a(v) = g*f(v) + 14*h(v). Factor a(l).
2*(l + 1)*(l + 48)
Suppose -12 = -571320*g + 571316*g. Suppose -1/3*r**4 + 0 - 5/3*r**2 + 4/3*r**g + 2/3*r = 0. What is r?
0, 1, 2
Suppose -4*b + 3*n + 4860 = 0, 4*n = -2*b - n + 2404. Let f = b - 2421/2. Factor -3 + f*a**2 + 3/2*a.
3*(a - 1)*(a + 2)/2
Find a such that 6*a**3 + 30*a**2 + 109*a**2 - 575*a - 11*a**3 - 6*a**2 + 7*a**2 = 0.
0, 5, 23
Suppose -4*t - 476 = -4*x, -t = 3*t. Factor -35*k - 27*k**3 + x*k**3 - 40*k - 84*k**2 + 67*k.
4*k*(k - 1)*(23*k + 2)
Solve -397*f + 63*f + 13*f**2 + 270 + 62 - 11*f**2 = 0 for f.
1, 166
Let h(g) be the third derivative of 17/180*g**6 + 174*g**2 + 1/3*g**4 + 0 + 1/105*g**7 + 14/45*g**5 + 0*g + 0*g**3. Let h(z) = 0. Calculate z.
-3, -2, -2/3, 0
Let f(k) be the first derivative of -22*k**6/15 - 13*k**5 - 42*k**4 - 152*k**3/3 + 16*k**2 - 127*k + 135. Let m(v) be the first derivative of f(v). Factor m(l).
-4*(l + 2)**3*(11*l - 1)
Determine z so that -231*z + 3115 + z**3 + 604*z + 53 + 40*z + 206*z**2 + 1187*z = 0.
-198, -4
Let m = 14 + -11. Let v(k) be the second derivative of 0*k**4 + 0*k**m + 0 + 1/60*k**5 + 1/90*k**6 - 17*k + 0*k**2. Factor v(r).
r**3*(r + 1)/3
Find t such that -477/4 + 1/4*t**2 + 11*t = 0.
-53, 9
Suppose 157 = -13*x + 92. Let r be (x/10 - (-8)/20)*-14. Factor k**4 - r*k**3 + 0 + 0*k + 2/5*k**2.
k**2*(k - 1)*(5*k - 2)/5
Let q(c) be the first derivative of 375*c**5 - 1875*c**4 + 3700*c**3 - 3600*c**2 + 1728*c - 1883. Determine t, given that q(t) = 0.
4/5, 6/5
Let r(y) be the first derivative of y**5/3 + y**4/2 - 4*y**3/3 + 15*y**2/2 + 43. Let o(t) be the second derivative of r(t). Factor o(n).
4*(n + 1)*(5*n - 2)
Let s(h) = h**2 + 8*h + 2. Suppose 11*m = -16*m + 6*m. Let b be s(m). Suppose 0 + 9/2*y - 3*y**4 - 4*y**3 - 1/2*y**5 + 3*y**b = 0. Calculate y.
-3, -1, 0, 1
Let v be (-8645)/364 - 1/4. Let q be (-40)/(-105)*v - -10. Determine o so that q*o + 2/7*o**2 + 4/7 = 0.
-2, -1
Let z(n) be the third derivative of 3*n**6/40 - 131*n**5/20 - 23*n**4 + 90*n**3 + 13737*n**2. Factor z(a).
3*(a - 45)*(a + 2)*(3*a - 2)
Let j(n) = -20*n. Let u be j(-1). Let z = 231 + -204. Factor -z + u*l**2 + 27*l**3 + 25*l + 27 - 32*l**3.
-5*l*(l - 5)*(l + 1)
Let x be -8*2/16 + 2*2. Find p, given that x*p**3 + 20*p**2 + 3*p**3 - 5*p**4 + 14*p**3 - 80*p = 0.
-2, 0, 2, 4
Let p = -237 - -241. Suppose -35*j**2 - p*j**4 - 70*j**5 + 75*j**3 - 10*j + 8*j**5 + 37*j**5 - j**4 = 0. What is j?
-2, -1/5, 0, 1
Let a(k) = -3*k - 12. Let h be a(-14). Suppose 0 = 10*m - h. What is q in -q + q + 364*q**3 - 374*q**m - 5*q**4 = 0?
-2, 0
Let s(n) be the first derivative of -2*n**5/25 - 7*n**4/2 + 2*n**3/15 + 7*n**2 - 84. Suppose s(t) = 0. What is t?
-35, -1, 0, 1
Let d be (-12 - 387/(-36))*-4*(-44)/(-40). Let p(n) be the first derivative of -4/3*n**3 + d*n**2 - 6*n + 45 - 1/4*n**4. Find a, given that p(a) = 0.
-6, 1
Suppose -5*y + 212 = 2*h, 5*y + 0*h + h = 216. Suppose 5*o - 8 = -4*k, -4*k - 2*o = -6*o - y. Factor 4*l - 5 + 2*l**2 - k + 14.
2*(l + 1)**2
Let u = 6073/2 + -3036. Let v(o) be the first derivative of -u*o**6 + 2*o**3 - 3/2*o**4 - 9/5*o**5 + 17 + 3*o + 9/2*o**2. Factor v(t).
-3*(t - 1)*(t + 1)**4
Suppose 0 = -359*a + 360*a - 8. Factor -11 - 6*n**3 - 8 - 20*n**2 - 9 + 52*n + a*n**3 - 6*n**3.
-4*(n - 1)**2*(n + 7)
Factor 0 + 0*i - 4/5*i**3 + 1344/5*i**2.
-4*i**2*(i - 336)/5
Let k(o) be the second derivative of -o**7/8820 + o**6/504 - o**5/105 + 37*o**4/4 - o**2 + 67*o. Let s(u) be the third derivative of k(u). Factor s(i).
-2*(i - 4)*(i - 1)/7
Let d(y) be the third derivative of 2/175*y**7 - 85*y**2 + 0*y**3 + 1/840*y**8 + 0*y**4 + 0 + 0*y + 4/75*y**5 + 1/25*y**6. Suppose d(t) = 0. What is t?
-2, 0
Let o(c) = -c - 1. Let q be o(-21). Let z(t) = q*t - 21 - 865*t**2 + 0 + 861*t**2. Let g(d) = 1. Let f(n) = -5*g(n) - z(n). Let f(w) = 0. What is w?
1, 4
Let v = -269 - -80701/300. Let m(y) be the third derivative of -3*y**2 + 0*y + 0 + 1/5*y**3 - v*y**5 - 1/120*y**4. Factor m(k).
-(k - 2)*(k + 3)/5
Determine m so that 2239*m**2 - 2519*m + 5072 + 1058*m - 2*m**3 + 1455*m**2 - 1382 - 5921*m = 0.
1, 1845
Let b(v) = -v**2 - 7*v + 1. Let z be b(-6). Let o = -4 + z. Find w, given that 0 - 3*w - 1 + 6*w + w**2 - o = 0.
-4, 1
Determine z, given that -8*z**2 - 29*z + 47*z**3 - 35*z**2 - 83*z**3 + 60*z - 16 + 5*z**4 + 59*z = 0.
-2, 1/5, 1, 8
Let s(y) be the first derivative of y**3 - 3*y**2 + 3*y + 3080. Factor s(a).
3*(a - 1)**2
Let z(v) be the third derivative of 0 + 1/42*v**4 - 8/105*v**5 + 19*v**2 + 1/14*v**3 + 0*v. Factor z(a).
-(4*a + 1)*(8*a - 3)/7
Suppose 97*d + 116*d = 0. Let v(s) be the third derivative of 13/2*s**4 + d*s + 4*s**3 + 7/2*s**5 + 18*s**2 + 0 - 49/40*s**6. Factor v(j).
-3*(j - 2)*(7*j + 2)**2
Let t(s) = -8407*s + 235396. Let p be t(28). Determine y so that -16*y**2 + 4 + p*y - 33/4*y**4 - 19*y**3 - 5/4*y**5 = 0.
-2, -1, 2/5
Let i(c) = 2341*c**3 + 12*c**2 - 10*c - 10. Let g(d) = -19899*d**3 - 102*d**2 + 84*d + 84. Let z(y) = 5*g(y) + 42*i(y). Suppose z(o) = 0. Calculate o.
-2/391, 0
Suppose -4*z = q - 52, -72*q = -66*q - z + 13. Let a = -26/11 - -204/77. Let q + a*t + 0*t**2 - 2/7*t**3 = 0. What is t?
-1, 0, 1
Let j(r) = -3*r**4 + 5