1)). Factor 12/7*h - 4/7 - q*h**2.
-(3*h - 2)**2/7
Let d(k) = -k**2 + 9*k - 23. Let p(h) = 4*h**2 - 44*h + 114. Let j(f) = -14*d(f) - 3*p(f). Solve j(r) = 0.
-5, 2
Let u(q) = q**3 - 5*q**2 + 4*q. Let x be u(4). Let t(m) = m**3 + 3*m**2 - 2*m. Let b be t(x). Factor 4/3*d**4 + b + 2*d**3 - 2/3*d + 0*d**2.
2*d*(d + 1)**2*(2*d - 1)/3
Let j be (-3 + 34/10)*205/41. Find c such that 4/5*c**4 + 0*c**3 + 2/5*c**5 - 4/5*c**j + 0 - 2/5*c = 0.
-1, 0, 1
Find m such that -39/4*m + 9/2*m**2 + 5 + 1/4*m**3 = 0.
-20, 1
Let k(t) be the first derivative of -1/240*t**5 - 7/2*t**2 - 1/32*t**4 + 0*t**3 + 0*t + 7. Let w(r) be the second derivative of k(r). Let w(d) = 0. Calculate d.
-3, 0
Suppose 0 = 4*b - 3*n - 369, -5*b - 10*n = -11*n - 453. Let v be (27/b)/((-6)/(-8)). Factor 8/5*p**4 + 8/5*p**2 + v*p + 12/5*p**3 + 2/5*p**5 + 0.
2*p*(p + 1)**4/5
Let r(j) be the third derivative of -j**6/2160 + j**5/720 + 5*j**3 + 29*j**2. Let o(t) be the first derivative of r(t). Factor o(w).
-w*(w - 1)/6
Let t = 127543/36 - 21071/6. Let n = 125/4 - t. Solve 4/9*c + n - 4/9*c**3 - 2/9*c**4 + 0*c**2 = 0 for c.
-1, 1
Suppose o - 5*i = 20, 17*o + 3 = 5*i + 23. Let o*t**2 + 0*t - 2/9*t**5 + 0 + 4/9*t**4 - 2/9*t**3 = 0. What is t?
0, 1
Let d be -8*360/288*(-4)/10. Factor -5/7*i + 2/7 + 1/7*i**3 + 3/7*i**2 - 1/7*i**d.
-(i - 1)**3*(i + 2)/7
Let g = 52 + -75. Let w = g - -37. Solve -20 + 4*v - 6*v - 9*v**2 - w*v + 24 = 0.
-2, 2/9
Let c(l) be the third derivative of -l**6/24 + 2*l**2 + 4*l. Let c(r) = 0. What is r?
0
Let x be -1 - 12/(-10)*40/16. Suppose -10*o**x - 12*o + 9*o**2 - o**2 = 0. Calculate o.
-6, 0
Let a(d) be the second derivative of -d**5/130 + 71*d**4/39 - 1632*d**3/13 - 10368*d**2/13 - 361*d - 2. Factor a(x).
-2*(x - 72)**2*(x + 2)/13
Let w(c) = -22*c**3 + 140*c**2 + 388*c + 78. Let h(n) = -2*n**3 - 2*n - 1. Let r(l) = -4*h(l) + 2*w(l). Factor r(b).
-4*(b - 10)*(b + 2)*(9*b + 2)
Suppose 0*w = 3*t + 2*w - 3, -4*t - 3*w = -4. Let r be 2 + (t - (-35)/(-15)). Factor r*y**3 + 4/9*y**2 - 2/9*y + 0.
2*y*(y + 1)*(3*y - 1)/9
Let q = 3770 - 18847/5. Determine f so that 1/5*f**2 + q*f + 2/5 = 0.
-2, -1
Factor 1364668*k**2 - 1364666*k**2 + 10*k**4 + k**5 - 24*k**3 + 12*k - 12 + 11*k.
(k - 1)**3*(k + 1)*(k + 12)
Solve -7/2*p**2 + 50 + 20*p - 1/2*p**3 = 0 for p.
-10, -2, 5
Let y(n) be the third derivative of -3*n**7/35 + 23*n**6/20 - 97*n**5/30 + 43*n**4/12 - 2*n**3 + 856*n**2. Determine l so that y(l) = 0.
1/3, 1, 6
Determine u, given that 38*u - 15*u**3 - 3*u**3 - 28 + 106*u**2 - 100*u**2 + 4*u**3 - 2*u**4 = 0.
-7, -2, 1
Suppose 0 = -3*w - 0 + 6. Let r = 1189/264 + -1/264. Factor -3*p**3 - 4*p + r*p**4 - 10*p**w + 0.
p*(p - 2)*(3*p + 2)**2/2
Let o(m) be the second derivative of 0*m**2 + 2/15*m**6 + 0*m**5 - 1/3*m**4 + 0 + 0*m**3 + 16*m. Solve o(p) = 0 for p.
-1, 0, 1
Suppose -2*l + 8 = 0, 4*j - 22*l + 48 = -40. Factor -6/7*s**2 + 8/7*s**3 + j + 0*s.
2*s**2*(4*s - 3)/7
Let l(h) be the second derivative of h**4/48 - h**3/3 + 3*h**2/2 - 28*h + 2. Suppose l(r) = 0. Calculate r.
2, 6
Factor -232/5*b**2 + 44*b**3 - 54/5*b**4 + 16/5*b + 0.
-2*b*(b - 2)**2*(27*b - 2)/5
Suppose -7*w + 3*w + 12 = 0. Let s(m) = 15*m**2 + 40*m + 60. Let r(z) = 8*z**2 + 19*z + 30. Let n(v) = w*s(v) - 5*r(v). Let n(p) = 0. What is p?
-3, -2
Let l(v) be the first derivative of 9/20*v**5 - 11 - 5/4*v**3 + 3/16*v**4 + 3/2*v - 3/8*v**2. Let l(a) = 0. What is a?
-1, 2/3, 1
Let x be 60*((-10)/(-125))/((-2)/(-10)). Suppose -x = 14*b - 22*b. Let 0 + 1/9*r**2 - 1/9*r**b + 0*r = 0. What is r?
0, 1
Factor -16/3*a - 11/3*a**2 - 5/3.
-(a + 1)*(11*a + 5)/3
Let l(c) be the first derivative of -3*c**5/5 + 6*c**4 - 142. Find n, given that l(n) = 0.
0, 8
Suppose 5*u - 14 = -3*o, -u - 2 = 5*o + 4. Factor 8*a**3 + 54 - 54 + u*a**4.
4*a**3*(a + 2)
Let c be (-6 - -7)*38/95. Factor -2/5*x + 0*x**2 + c*x**3 + 0.
2*x*(x - 1)*(x + 1)/5
Suppose -32*c + 34*c = 8. Suppose -5*z = c*j - 41, -3 + 1 = -3*j + 2*z. Determine k so that -8/3*k**3 - 12*k**2 - 24*k - 2/9*k**j - 18 = 0.
-3
Determine a so that 0 + 0*a + 0*a**2 + 41/2*a**4 - 4*a**3 - 5/2*a**5 = 0.
0, 1/5, 8
Let o(p) = p + 17. Suppose 15 = 80*w - 81*w. Let z be o(w). Factor -75/7*l**4 - 12/7 + 33/7*l**z + 36/7*l - 90/7*l**3.
-3*(l + 1)**2*(5*l - 2)**2/7
Factor 0*n**2 + 4/3*n + 0 - n**3 + 1/3*n**4.
n*(n - 2)**2*(n + 1)/3
Find q such that -1/10*q**2 - 1/10*q**3 + 0*q + 1/10*q**4 + 1/10*q**5 + 0 = 0.
-1, 0, 1
Let b be (12/56)/(-9*11/(-132)). Suppose -b*r**2 + 8/7 + 32/7*r - 8/7*r**3 = 0. Calculate r.
-2, -1/4, 2
Suppose 0 = -8*n - 2*n + 270. Let p be 1 - (33/n - 8/36). Find x, given that p*x - 2/5 + 2/5*x**2 = 0.
-1, 1
Let t be -6*12/(-117)*176/55. Let q = t + -10/13. Factor 2/5 - 6/5*y - q*y**4 + 4/5*y**2 + 2/5*y**5 + 4/5*y**3.
2*(y - 1)**4*(y + 1)/5
Let -164*a + 9*a**2 - 9*a**2 + 4*a**2 - 4135 + 4295 = 0. Calculate a.
1, 40
Let x(w) = w**2 + 6*w + 6. Let v be x(-6). Suppose -v*q + 9 = -3*q. Factor -5*g + 4*g + 3*g - q*g - g**2.
-g*(g + 1)
Let h be -6 + 11 - (-701)/(-195). Let b = -8/39 + h. Solve 3/5*z**4 - 9/5*z**2 + b*z + 0 + 0*z**3 = 0 for z.
-2, 0, 1
Let n(r) be the third derivative of 1/7*r**4 + 0 + 0*r + 8/7*r**3 + 1/140*r**5 + 16*r**2. Factor n(g).
3*(g + 4)**2/7
Let b(h) be the third derivative of h**8/40320 + h**7/3360 + h**5/20 - 41*h**2. Let c(y) be the third derivative of b(y). Solve c(o) = 0 for o.
-3, 0
Suppose 97*s + s - 261 = 11*s. Determine f so that -4/5*f**2 + 0*f**s + 0 - 2/5*f**5 + 2/5*f + 4/5*f**4 = 0.
-1, 0, 1
Suppose -5*u = s + 10, 5*s + 6*u - 28 = 7*u. Let z(n) be the third derivative of n**3 - 1/30*n**s + 6*n**2 + 1/6*n**4 + 0 + 0*n. Factor z(p).
-2*(p - 3)*(p + 1)
Let h(x) be the third derivative of -x**8/5040 + x**7/90 - 49*x**6/180 + x**5/15 + 3*x**2 - 5*x. Let r(o) be the third derivative of h(o). Solve r(g) = 0 for g.
7
Suppose 19 = 3*w - 2*f, 0*w + 5*w = f + 27. Find z, given that -z**2 + w - 1 - 1266*z + 1263*z = 0.
-4, 1
Let c(h) be the third derivative of -1/12*h**5 + 1/42*h**7 + 5/48*h**4 + 0*h + 0 + 0*h**3 - 5/672*h**8 - 4*h**2 + 0*h**6. Solve c(s) = 0 for s.
-1, 0, 1
Let k(m) be the first derivative of -m**6/21 - 2*m**5/35 + 11*m**4/14 - 2*m**3/3 - 10*m**2/7 + 16*m/7 - 249. Find z, given that k(z) = 0.
-4, -1, 1, 2
Let r = 3/265 - 5044/795. Let x = 131/15 + r. Factor 6/5*d**4 - 11/5*d**3 + x*d - 8/5 - 1/5*d**5 + 2/5*d**2.
-(d - 2)**3*(d - 1)*(d + 1)/5
Suppose -g + 5 = -4*w, -4*g = 3*w - 15 - 5. What is z in -4/3*z**3 - 8/9*z**2 + 0 - 2/9*z - 2/9*z**g - 8/9*z**4 = 0?
-1, 0
Let x(i) = -20*i**3 + 24*i**2 + i - 36. Let q(r) = -11*r**3 + 12*r**2 + r - 18. Let o(h) = -7*q(h) + 4*x(h). Factor o(t).
-3*(t - 3)*(t - 2)*(t + 1)
Let i be (-9)/(-108)*40 + -3. Suppose 0 + 2/3*w**2 - i*w**3 - 1/3*w = 0. What is w?
0, 1
Let n be 8/28 - 187/(-7). Let r = n + -23. Suppose -12*o**3 - o + 5*o - r*o**4 - 4*o = 0. Calculate o.
-3, 0
Let s(o) = 10*o**5 + 45*o**4 + 65*o**3 + 25*o**2 - 5. Let w(p) = p**5 + p**4 - p**2 - 1. Let n(u) = -s(u) + 5*w(u). Factor n(z).
-5*z**2*(z + 1)**2*(z + 6)
Let c(g) = -111*g + 557. Let x be c(5). Determine o so that -4/7*o + 22/7*o**x - 82/7*o**4 - 8*o**5 + 0 + 0*o**3 = 0.
-1, 0, 1/4, 2/7
Let z be (6/(-4))/(27/144*-4). Factor 3/7*d**5 + 11/7*d**4 + 6/7*d**z - 1/7*d - 1/7 + 2*d**3.
(d + 1)**4*(3*d - 1)/7
Let c(m) be the first derivative of 0*m**2 - 4/3*m**3 + 4*m - 15. Factor c(s).
-4*(s - 1)*(s + 1)
Determine k, given that -1/9*k**2 + 52/9 - k = 0.
-13, 4
Let i be 7 + -10 + (-132)/(-16). Factor i*m**3 - 1/2 - 3/4*m + 5*m**2.
(m + 1)*(3*m - 1)*(7*m + 2)/4
Let i = -254 + 258. Suppose 6*t - 2*s + 4 = 5*t, -20 = -t - i*s. Solve 2/13*z**3 + 0*z**2 + 0*z - 2/13*z**t + 0 = 0.
0, 1
Suppose 0 = 1965*b - 1948*b - 34. Determine o so that 2/11*o**5 + 0*o + 24/11*o**3 + 12/11*o**4 + 0 + 16/11*o**b = 0.
-2, 0
Let d be (-9)/4*(-14)/21. Factor 1/2*m**4 + 0 + 3/2*m**2 - d*m**3 - 1/2*m.
m*(m - 1)**3/2
Let s(d) = -1 - 3*d + 0*d**2 + 4*d**2 + 3*d**2. Let q be s(1). Factor q - 3/2*k**2 + 3/2*k.
-3*(k - 2)*(k + 1)/2
Let s(q) = 8*q - 1. Let b be s(1). Factor 2*c**2 + c - 2*c**2 - 4*c**2 + 3*c**3 + c**4 + b*c**2.
c*(c + 1)**3
Let b(x) = 21*x - 1428. Let n be b(68). Suppose n + 2*s + 7/2*s**2 = 0. Calculate s.
-4/7, 0
Suppose -3*u + 8*u - 2*s - 90 = 0, 0 = -3*s - 15. Factor -u*j + j**2 - 171 - 5*j**2 + 171.
-4*j*(j + 4)
Suppose -y + 4 = -4. Suppose -y*g + 7 + 17 = 0.