r). Solve q(d) = 0 for d.
-2, -1, 0, 5
Let f = 135597/5 + -27119. Factor -18/5*g - 6/5*g**2 + 2*g**3 - f*g**4 + 0.
-2*g*(g - 3)**2*(g + 1)/5
Let w(n) be the third derivative of 2*n**7/105 + n**6/30 - 3*n**5/5 - 3*n**4/2 - 43*n**2. Factor w(p).
4*p*(p - 3)*(p + 1)*(p + 3)
Let q(h) be the third derivative of 4/3*h**3 + 22*h**2 - 1/10*h**5 + 0 - 2/3*h**4 + 3/20*h**6 + 0*h. Factor q(n).
2*(n + 1)*(3*n - 2)**2
Let g(u) be the third derivative of u**7/840 - u**6/30 + 11*u**5/120 - 17*u**3/2 + 41*u**2. Let b(o) be the first derivative of g(o). Let b(q) = 0. Calculate q.
0, 1, 11
Let t = 850 + -1685/2. Factor 3/2*y**3 - 3/2*y**4 + 9/2*y + t*y**2 + 0.
-3*y*(y - 3)*(y + 1)**2/2
Suppose 3*j + 5*g + 5 = 0, -5*j - 2*g = -3*g + 55. Let m(w) = 5*w**4 - 15*w**3 + 40*w**2 - 30*w. Let q(k) = k**3 - k. Let y(u) = j*q(u) + m(u). Factor y(r).
5*r*(r - 2)**2*(r - 1)
Let i(z) be the third derivative of z**5/30 - 41*z**4/12 + 40*z**3/3 - 244*z**2. Factor i(r).
2*(r - 40)*(r - 1)
Let o(c) = 2*c**3 + 2*c**2 - 3. Let u(v) = 15*v**3 + 15*v**2 - 20. Suppose 0*d + 3*d + 60 = 0. Let z(n) = d*o(n) + 3*u(n). Factor z(p).
5*p**2*(p + 1)
Let k(a) be the second derivative of a**6/5 + 9*a**5/20 - a**3/2 - 327*a. Solve k(o) = 0.
-1, 0, 1/2
Factor -2/5*z**3 - 6/5 - 2*z**2 - 14/5*z.
-2*(z + 1)**2*(z + 3)/5
Let x be 2/15 + (-186)/(-465). Factor 8/15*r + 2/15*r**4 + 2/15 + x*r**3 + 4/5*r**2.
2*(r + 1)**4/15
Let u(z) = -5*z**5 - 2*z**3 - 2*z**2 + 3*z - 4. Let x(m) = -12*m**5 - 2*m**4 - 3*m**3 - 4*m**2 + 5*m - 9. Let i(s) = 5*u(s) - 2*x(s). Factor i(o).
-(o - 2)*(o - 1)**3*(o + 1)
Suppose 5*h + 3*t = 23 - 3, -5*h + 20 = t. Suppose -5 = -h*c - k, 4*c - 4*k + 1 = k. Factor -1 - c + 2 - 2*n**3 + 2*n**4.
2*n**3*(n - 1)
Let g(d) = 4*d**2 - 22*d + 34. Let x(k) = 12*k**2 - 65*k + 103. Let o(q) = -7*g(q) + 2*x(q). Factor o(u).
-4*(u - 4)*(u - 2)
Let l = 82539/13 + -6349. Factor -l*j - 2/13*j**2 + 4/13.
-2*(j - 1)*(j + 2)/13
Let s(b) be the third derivative of 0*b**5 + 0*b + 0 - 2*b**2 + 1/2*b**4 - 1/40*b**6 + 0*b**3. Find q, given that s(q) = 0.
-2, 0, 2
Let d be (-8)/12 + 8/(-12)*-4. Factor -32/15*a - 2/5*a**3 - 8/15 - 26/15*a**d.
-2*(a + 2)**2*(3*a + 1)/15
Let t(s) be the third derivative of 0*s**3 + 0*s**4 + 0*s + 2/21*s**7 + 4/15*s**5 + 12*s**2 - 4/15*s**6 + 0 - 1/84*s**8. Factor t(m).
-4*m**2*(m - 2)**2*(m - 1)
Suppose 0 = -70*s + 130*s - 66*s. Let 0*k - 1/4*k**2 + s = 0. Calculate k.
0
Let h be 10/30 + (4 + -1)/(-9). Suppose h = v - 7*v + 18. Suppose -10*f - 6 - 2/3*f**v - 14/3*f**2 = 0. What is f?
-3, -1
Suppose 0 = 4*u + 6 + 10. Let x be -2*2/(u/6). Let -7*m**3 - 9*m**4 - 17*m**2 - x*m - m**2 - 17*m**3 - 3*m**2 = 0. What is m?
-1, -2/3, 0
Let s be (-17)/9 - (-81 + 79). Let b(h) be the first derivative of -s*h**3 + 2/3*h**2 + 4/3*h + 8 - 1/12*h**4. Factor b(j).
-(j - 2)*(j + 1)*(j + 2)/3
Let d(b) = 2*b**4 - b**3 - b**2 + 3. Suppose -78 - 26 = 4*n. Let i(v) = 9*v**4 - 5*v**3 - 4*v**2 + 13. Let q(f) = n*d(f) + 6*i(f). Let q(t) = 0. What is t?
0, 1
Let k(w) be the second derivative of 14*w + 2/3*w**4 + 2/21*w**7 - 4/5*w**5 + 0 + 0*w**6 + 2*w**3 - 4*w**2. Factor k(t).
4*(t - 1)**3*(t + 1)*(t + 2)
Let w be 2/(-10) + 58/(-10). Let b be ((-18)/(-81))/((w/(-9))/2). Find u such that 1/3*u**2 - b + u**3 - u + 1/3*u**4 = 0.
-2, -1, 1
Suppose -5 = 2*s + 1, 2*a - 3*s = 7. Let t be (-5 + -15)/5*a. Find l such that 4/3*l**5 - t*l**4 + 8/3*l**3 + 0*l + 0 + 0*l**2 = 0.
0, 1, 2
Let a be (0 + 3/(-9))*(-28)/4. Let t(j) be the first derivative of 4 - j**2 + 0*j - 3/4*j**4 - a*j**3. Factor t(y).
-y*(y + 2)*(3*y + 1)
Let v(b) be the second derivative of b**6/600 - b**5/75 + b**4/30 - 51*b**2/2 - b - 3. Let l(x) be the first derivative of v(x). Factor l(g).
g*(g - 2)**2/5
Let d(l) = -6*l + 71. Let o be d(11). Suppose -y - 11 = -4*b - 2*y, -o*y = 4*b - 7. Factor 1/2*s**5 - 1 - b*s**4 + 9/2*s - 8*s**2 + 7*s**3.
(s - 2)*(s - 1)**4/2
Let l = -180 + 193. Suppose 0 = -l*t + 6*t - 12*t. Factor -2/3*f**2 + 0*f - 1/3*f**3 + t.
-f**2*(f + 2)/3
Let g(l) be the third derivative of 2*l**5/105 + 83*l**4/42 - 4*l**3 + 187*l**2. Factor g(h).
4*(h + 42)*(2*h - 1)/7
Let t(p) be the second derivative of 2/21*p**7 + 2/3*p**4 + 2/3*p**3 - 2/15*p**6 + 0 - 2/5*p**5 - 2*p**2 + 12*p. Determine x, given that t(x) = 0.
-1, 1
Let d be 3 + -1 - (3 - 7 - -3). Let u(j) be the first derivative of -2/45*j**d - 2/15*j**2 + 0*j + 1/30*j**4 - 7. Let u(g) = 0. Calculate g.
-1, 0, 2
Let v(t) be the first derivative of -t**4/2 + 60*t**3 - 2700*t**2 + 54000*t + 104. Factor v(x).
-2*(x - 30)**3
Let y be -7*(-1)/((-28)/24). Let o be (6/(-12))/(1/y). Factor 4 + 4*v**o - 2*v**4 - 4 + 0*v**2 - 2*v**2.
-2*v**2*(v - 1)**2
Let m(b) be the second derivative of -1/15*b**5 - 2/3*b**3 + 3/2*b**2 + 0 - 5*b - 1/3*b**4. Let a(y) be the first derivative of m(y). Factor a(p).
-4*(p + 1)**2
Let s(z) be the third derivative of z**8/2352 - 11*z**7/1470 + 3*z**6/280 + 17*z**5/60 + 7*z**4/12 + 264*z**2. Factor s(p).
p*(p - 7)**2*(p + 1)*(p + 2)/7
Let v be -127 - -121 - (-48)/7. Find m such that -v*m - 2/7*m**2 + 0 = 0.
-3, 0
Let g(u) = -2*u**2 + 23*u + 402. Let w be g(21). Find p such that -14/9*p + 10/9*p**2 + 2/3 - 2/9*p**w = 0.
1, 3
Let l(a) = -23*a**3 + 40*a**2 + 246*a - 648. Let m(c) = -19*c**3 + 39*c**2 + 247*c - 648. Let w(j) = -5*l(j) + 6*m(j). Factor w(z).
(z - 2)*(z + 18)**2
Let g = -68154/11 + 6196. Suppose 10/11*i**2 - 16/11*i - g*i**3 + 8/11 = 0. Calculate i.
1, 2
Let l = 389/572 + 10/143. Factor -33/8*b**2 - 21/8*b**4 + l*b + 6*b**3 + 0.
-3*b*(b - 1)**2*(7*b - 2)/8
Suppose 170/13*o**3 - 152/13*o + 32/13*o**4 - 18/13*o**5 + 0*o**2 - 32/13 = 0. What is o?
-2, -1, -2/9, 1, 4
Suppose -6*l + 18 = -0*l. What is o in -5*o + 5*o**4 + 5 + 4 - 5*o**5 - 10*o**2 + 10*o**l - 4 = 0?
-1, 1
Factor -66 + 2*g**2 + 48*g - 119*g + 55*g.
2*(g - 11)*(g + 3)
Let r(t) = 6*t**3 - 1882*t**2 - 230629*t - 9533098. Let m(w) = w**3 - 376*w**2 - 46126*w - 1906620. Let s(k) = 22*m(k) - 4*r(k). Determine h so that s(h) = 0.
-124
Let c(p) = p**3 + p**2 - 2*p - 1. Let b(s) = -s**3 - 12*s**2 + 37*s - 34. Let v(a) = b(a) + 2*c(a). Let v(i) = 0. Calculate i.
3, 4
Solve -1/4*q**2 + 1/4*q + 3/2 = 0 for q.
-2, 3
Let f(z) be the second derivative of -55*z**4/12 + 75*z**3 - 40*z**2 + z + 12. Solve f(s) = 0.
2/11, 8
Factor 3*h + 384*h**2 + 54*h**4 + 457219*h**3 + 3*h**5 - 456931*h**3 - 3*h.
3*h**2*(h + 2)*(h + 8)**2
Let u(i) be the second derivative of -96/5*i**2 - 3/5*i**4 + 3/100*i**5 + 24/5*i**3 + 0 - 5*i. Factor u(m).
3*(m - 4)**3/5
Let h(m) = m**2 + 16*m - 14. Let i be h(-20). Suppose -3*u + 6*u = i. Solve -24*j**3 + u*j**4 + 16*j**2 - 4*j - 2*j**4 - 4*j**5 - 4*j**4 = 0 for j.
0, 1
Factor 216*l**2 + 32*l**3 + 7/2 - 111/2*l.
(l + 7)*(8*l - 1)**2/2
Suppose -57*g - 33 = -54*g. Let q be (-4)/(-5) + g/20. Factor 1/4*y**5 + 0*y + 3/4*y**3 + 0 + q*y**2 + 3/4*y**4.
y**2*(y + 1)**3/4
Solve 4/7*m + 6/7*m**2 + 2/7*m**3 + 0 = 0.
-2, -1, 0
Let n(k) be the first derivative of 20*k - 4/3*k**3 - 8*k**2 - 28. Factor n(s).
-4*(s - 1)*(s + 5)
Factor 2/5*a**3 + 0 - 8/5*a - 6/5*a**2.
2*a*(a - 4)*(a + 1)/5
Let m(z) be the second derivative of -z**4/32 + 3*z**3/16 + 3*z + 2. Solve m(v) = 0 for v.
0, 3
Let w be -2 + 1 + (630/21 - 25). What is n in -5/2*n**2 + w*n + 1/2*n**3 - 2 = 0?
1, 2
Factor 9 + 0 + 16*q**2 + 3*q + 15*q**3 - 6 - 5 + 4*q**4.
(q + 1)**2*(q + 2)*(4*q - 1)
Let i = -114 + 120. Suppose 0 = i*x - 17 - 1. Solve -30/11*z**2 - 250/11 - 150/11*z - 2/11*z**x = 0 for z.
-5
Let y(h) be the third derivative of h**8/15120 - h**7/3780 + h**6/3240 - h**4/12 - h**2. Let m(x) be the second derivative of y(x). Factor m(k).
2*k*(k - 1)*(2*k - 1)/9
Let w(j) = -2*j - 10. Let f be w(-7). Let l = 7 - f. Factor 2*r + 0*r + 34*r**2 - r**l - 35*r**2.
-r*(r - 1)*(r + 2)
Let h(x) be the third derivative of -7*x**6/240 - x**5/10 + x**4/12 - 2*x**2 + 170*x. Factor h(f).
-f*(f + 2)*(7*f - 2)/2
Suppose 0*x - 5*x = -25. Suppose -34 = -x*g - 9. Factor -4*t**2 + t**2 + t**3 + g*t**2.
t**2*(t + 2)
What is d in 242/3*d**2 + 44/3 + 74*d**3 + 6*d**4 - 238/3*d = 0?
-11, -2, 1/3
Factor 2/5*q**3 - 8/5*q + 0 + 0*q**2.
2*q*(q - 2)*(q + 2)/5
Let t(g) be the first derivative of -5*g**9/3024 + g**7/84 - g**5/24 - g**3 + 7. Let u(k) be the third derivative of t(k). Factor u(o).
-5*o*(o - 1)**2*(o + 1)**2
Suppose 0*k + 32/13*k**3 - 24/13*k**2 + 0