 + 1499)**2
Let i = 33931 + -169653/5. Find d such that 14/5*d + 4 + i*d**2 = 0.
-5, -2
Suppose 3*x = -3*f + 6, 3*f - 7 = f - x. Let s be 15/f*(-3)/18*-4. Factor 44 - 5*y**s - 10 + 25 - 9 - 15*y.
-5*(y - 2)*(y + 5)
Let r(p) be the second derivative of p**4/84 + p**3/42 - 3*p**2/7 - 982*p. Factor r(t).
(t - 2)*(t + 3)/7
Factor 2*d**3 + 9768 - 12536 - 761*d - 384*d**2 + 50*d**2 - 1299*d.
2*(d - 173)*(d + 2)*(d + 4)
Let g(m) = m**3 + 6*m**2 + m - 2. Let q(t) = -6*t**3 - 35*t**2 + 27*t - 26. Let r(o) = -20*g(o) - 4*q(o). Factor r(y).
4*(y - 2)**2*(y + 9)
Suppose 120*d = -110*d + 25*d. Let i(b) be the third derivative of 0 + 1/60*b**5 + 0*b**3 + d*b + 1/48*b**4 - 34*b**2 - 1/80*b**6. Factor i(y).
-y*(y - 1)*(3*y + 1)/2
Solve 245/6*p**3 - 62/3 - 101/6*p**4 - 184/3*p + 35/2*p**2 + 1/2*p**5 = 0.
-1, -1/3, 2, 31
Suppose -q + 2232 = 3*n, 16*q - 19*q + 2238 = 3*n. Let y = n - 2209/3. Suppose -10/3*a**4 + 5*a**5 + 10/3*a**2 - y*a**3 + 5/3*a + 0 = 0. What is a?
-1, -1/3, 0, 1
Suppose 19*k - 617 = 352. Suppose -10 - 22*t - 22*t + k*t - t**2 = 0. What is t?
2, 5
Let l(a) be the first derivative of -a**6/24 - 5*a**5/4 - 183*a**4/16 - 347*a**3/12 + 11*a**2 + 117*a + 3807. Suppose l(d) = 0. Calculate d.
-13, -9, -2, 1
Let b(x) be the third derivative of x**8/40320 + x**7/2520 + 17*x**5/60 - x**4/24 - 6*x**2. Let v(p) be the third derivative of b(p). Factor v(m).
m*(m + 4)/2
Let l(h) = 2986*h + 45. Let p be l(6). Determine y so that -p + 17961 + 5*y + 5*y**2 = 0.
-1, 0
Suppose -d - 109 + 111 = 0. Suppose -34*q**2 + 58*q**2 + 6*q**d + 16*q - 32 - 16*q**3 + 2*q**4 = 0. Calculate q.
-1, 1, 4
Let n(y) = y**2 + 2*y. Let p(m) = 4*m**2 + 60*m + 50. Let l be (7/(56/2))/((-3)/(-12)). Let d(w) = l*p(w) - 6*n(w). Factor d(g).
-2*(g - 25)*(g + 1)
Let a = 18334 + 4523. Factor -16*j**3 - 22857 - 4*j**4 + 20*j**2 + a.
-4*j**2*(j - 1)*(j + 5)
Let p(s) be the second derivative of s**4/102 + 29*s**3/51 - 62*s**2/17 + 1069*s. Factor p(o).
2*(o - 2)*(o + 31)/17
Let f(j) be the first derivative of j**3/15 - 1963*j**2/5 + 3853369*j/5 - 1215. Factor f(m).
(m - 1963)**2/5
Let n = 3/3364 - -20163/23548. Suppose -2*s + 3*f - 2 = 1, -3 = -4*s - 3*f. Factor 3/7*x**3 + s + 3/7*x + n*x**2.
3*x*(x + 1)**2/7
Let y be -8*(-4)/(-8) + 19. Suppose 0 = 4*l + 5*a - y + 3, 4*l = 3*a + 12. Factor -15*b**2 - 112*b**l + 0*b + 115*b**3 + 12*b.
3*b*(b - 4)*(b - 1)
Let q(p) be the third derivative of -p**7/315 - 17*p**6/36 - 836*p**5/45 + 484*p**4/3 + p**2 + 514*p. Determine l so that q(l) = 0.
-44, 0, 3
Suppose -2*n + 18 = -5*n. Let z = 9 + n. Solve 10 + 43*j**2 + 39*j + 27*j**z - 4 + 29*j**2 = 0 for j.
-2, -1/3
Let y(a) = 224*a**3 - 168*a**2 - 3584*a - 3416. Let v(f) = 279*f**3 - 169*f**2 - 3583*f - 3415. Let n(k) = -4*v(k) + 5*y(k). Factor n(u).
4*(u - 57)*(u + 1)*(u + 15)
Let v(d) be the first derivative of d**6/6 + 209*d**5/15 + 131*d**4/12 - 481*d**3/9 + 23*d**2 - 5219. What is b in v(b) = 0?
-69, -2, 0, 1/3, 1
Let z(f) be the third derivative of -f**8/896 - f**7/280 + 5*f**6/64 + f**5/80 - 3*f**4/8 + 3*f**2 + 109. Suppose z(v) = 0. Calculate v.
-6, -1, 0, 1, 4
Let h = -1270 + 1270. Let l(v) be the second derivative of 0*v**2 - 1/60*v**6 + 0 + 1/24*v**4 + h*v**5 - 1/168*v**7 + 8*v + 1/24*v**3. Factor l(r).
-r*(r - 1)*(r + 1)**3/4
Let m(w) be the second derivative of -w**4/24 + 17*w**3/12 + 21*w**2 + 1882*w - 2. Solve m(t) = 0 for t.
-4, 21
Let s(g) be the third derivative of 0*g**3 + 3*g**2 + 0*g**4 + 1/24*g**5 - 1/240*g**6 + 0*g + 0. Factor s(m).
-m**2*(m - 5)/2
Let g(l) be the third derivative of 29*l**5/30 - 89*l**4/12 + 2*l**3 - 10863*l**2. Solve g(z) = 0 for z.
2/29, 3
Let z(m) be the second derivative of -m**2 + m**4 + 106*m + 4/3*m**3 - 2/5*m**5 + 0 - 1/3*m**6. Suppose z(x) = 0. What is x?
-1, 1/5, 1
Let n be (2 + 660/54)*(47 + -35) + 0/2. Factor -2/3*j**3 + 64/3*j**2 + 0 - n*j.
-2*j*(j - 16)**2/3
Suppose 2*a + 4 = 5*k, -78*a + 79*a - 2*k = 8. Suppose -159/2*j**2 + 75/2*j**4 + 18 - 81/2*j**3 + a*j + 33/2*j**5 = 0. Calculate j.
-2, -3/11, 1
Let d = -44899/5 - -8980. Let f(j) be the first derivative of -2916/5*j - 486/5*j**2 - d*j**4 - 36/5*j**3 - 1. Solve f(s) = 0 for s.
-9
Let k(i) be the second derivative of -15*i**2 + 3/20*i**5 - 1 - 153*i + 3/2*i**4 + 3/2*i**3. Factor k(n).
3*(n - 1)*(n + 2)*(n + 5)
Let o(j) be the first derivative of j**6/4 + 12*j**5/5 + 3*j**4/2 - 11*j**3 - 15*j**2/4 + 21*j + 213. Let o(d) = 0. Calculate d.
-7, -2, -1, 1
Let b(z) be the second derivative of -z**4/12 + 2*z**3 - 9*z**2 + z. Let c be b(10). Factor 76*q - 147*q - q**c + 72*q.
-q*(q - 1)
Let x = 85 - 53. Suppose -31*s - x = -35*s. Solve -s*r**2 - 14*r**3 + 2*r**5 - 4*r**4 - 119 + 119 = 0 for r.
-1, 0, 4
Determine g, given that -1576 + 178*g**2 + 362*g**2 + 64*g**3 + 10*g**4 - 5174 + 9*g**4 - 17*g**4 = 0.
-15, -5, 3
Let x(g) = -2*g**3 + 768*g**2 - 184*g + 70658. Let o be x(384). Factor -22/7*n + 2/7*n**o - 52/7.
2*(n - 13)*(n + 2)/7
Let v(x) be the first derivative of 13*x**3/12 - 89*x**2/8 - 7*x/2 - 440. What is o in v(o) = 0?
-2/13, 7
Let j(u) = -u**3 - 3*u**2 + u + 2. Let c be j(-3). Let o(s) = -2*s**3 - s**2 + 1. Let m be o(c). Factor 3*f**2 - 2*f + f + m*f - 2*f**2.
f*(f + 1)
Let c(a) be the first derivative of 44 - 7*a**2 + 6*a**4 - 9/10*a**5 + 41/6*a**3 - 6*a. Let c(r) = 0. Calculate r.
-1, -1/3, 2/3, 6
Let s = 515 + -526. Let l(g) = 3*g**2 + 76*g - 79. Let u(k) = 15*k**2 + 379*k - 394. Let r(h) = s*l(h) + 2*u(h). Solve r(m) = 0 for m.
-27, 1
Let v(n) be the second derivative of -1/20*n**5 + 0*n**3 + 0 + 1/30*n**6 + 35*n + 0*n**2 - 1/6*n**4. Factor v(m).
m**2*(m - 2)*(m + 1)
Let n(w) be the first derivative of -w**5/20 - 3*w**4 - 72*w**3 - w**2 + 5*w + 28. Let a(t) be the second derivative of n(t). Find l such that a(l) = 0.
-12
Factor 2/9*h**3 - 52/9*h**2 - 1792/3 - 1216/9*h.
2*(h - 42)*(h + 8)**2/9
Let y = 598961/8 + -74867. Determine w so that 1/8*w**2 - 3*w - y = 0.
-1, 25
Let -183*a**5 + 177*a**4 - 3267*a**3 - 3268*a**3 + 6541*a**3 = 0. Calculate a.
-2/61, 0, 1
Let t = 5497 - 5493. Let j(s) be the second derivative of 40*s + 35/36*s**t + 0 + 5/2*s**3 + 5/3*s**2. Suppose j(r) = 0. What is r?
-1, -2/7
Factor -116*q**2 - 2*q**4 - 368/3 - 200*q - 82/3*q**3.
-2*(q + 2)**3*(3*q + 23)/3
Suppose 11*d - 18 = 20*d. Let g be 3/d - (-4 + (7 - 6)). Suppose g*w**3 + 0*w**2 + 0*w + 0 = 0. What is w?
0
Let g be ((-1)/15)/((-407)/1221). Factor -g*q**2 + 0 - 3/5*q.
-q*(q + 3)/5
Let h = 40 + -38. Let r be (-3)/((21/h)/(-7)). Factor 14*u**3 - 40*u**3 + 3*u**r + 23*u**3.
-3*u**2*(u - 1)
Suppose 2/9*n**2 - 10/9*n - 100/9 = 0. What is n?
-5, 10
Let y be -15 + 4 + 1 - -2. Let o be (y/(-88))/(1/4). Factor 2/11*l**3 - 6/11*l - o*l**2 + 0.
2*l*(l - 3)*(l + 1)/11
Factor -123/5*h - 186 - 3/5*h**2.
-3*(h + 10)*(h + 31)/5
Let h(i) be the third derivative of i**7/210 - 17*i**6/30 + 611*i**5/30 - 187*i**4/2 + 363*i**3/2 + 7*i**2 - 23. Find j such that h(j) = 0.
1, 33
Find a, given that -640 + 16*a**2 - 17301*a - 17308*a + 2*a**3 + 6*a**2 + 34577*a = 0.
-8, 5
Suppose 0 = 4*f - 3*a + 5*a + 2, -5*a - 29 = -2*f. Let v be (-264)/27 + 10 - f/(-18). Suppose v*r**2 - 1/3*r - 2/3 = 0. Calculate r.
-1, 2
Let h(q) = -q**3 + 59*q**2 - 86*q - 92. Let n be h(58). Let b = n + 29188/17. What is j in -2/17 - 14/17*j**2 + b*j = 0?
1/7, 1
Suppose 18/11 + 3/11*o**3 + 47/11*o + 32/11*o**2 = 0. What is o?
-9, -1, -2/3
Let r be (-5868)/(-2592) - 10/(-16). Let 4/3*s**3 + 2/9*s**4 + 8/9 + r*s**2 + 8/3*s = 0. Calculate s.
-2, -1
Suppose 0 = -11*z + 26*z - 75. Suppose -3*c - 9 = -3*b, -4*c + 14 = z*b - 1. Factor 2/3*w**2 + 4/3*w**3 + c*w**4 - w - 2/3 - 1/3*w**5.
-(w - 2)*(w - 1)*(w + 1)**3/3
Let q(z) be the first derivative of z**4/14 - 4*z**3/3 + 5*z**2 + 100*z/7 - 479. Determine u, given that q(u) = 0.
-1, 5, 10
Let -36*t**4 + 4240*t - 21*t**5 + 33*t**3 - 4252*t - 9*t**2 + 45*t**2 = 0. What is t?
-2, -1, 0, 2/7, 1
Let h(c) be the third derivative of -25*c**2 - 1 + 0*c + 2738/3*c**3 - 37/3*c**4 + 1/15*c**5. Determine y so that h(y) = 0.
37
Find c, given that 2/11*c**2 - 1246/11 + 164/11*c = 0.
-89, 7
Let a(g) = -10*g**2 - 1072*g + 1110. Let s(w) = 46*w**2 + 4267*w - 4439. Let d(h) = -18*a(h) - 4*s(h). Determine r, given that d(r) = 0.
1, 556
Find d, given that 6*d**4 + 5931/2*d**2 + 4899/2*d - 543/2*d**3 - 1587/2 = 0.
-1, 1/4, 23
Let f(i) be the third 