*h**8. Factor n(r).
3*r*(r + 1)**3*(2*r - 1)
Let n(v) = v + 9. Let o be n(-9). Factor 1/5*x**5 + 1/5*x**4 + 0*x**2 + 0*x**3 + 0 + o*x.
x**4*(x + 1)/5
Suppose 0 - 1/4*n**2 + 163/4*n = 0. What is n?
0, 163
Let a(u) be the first derivative of 1/27*u**6 + 52/3*u**2 + 49 - 8/15*u**5 - 16*u - 268/27*u**3 + 19/6*u**4. Factor a(j).
2*(j - 3)**2*(j - 2)**3/9
Let v(c) be the third derivative of 6*c + 1/4*c**4 - 3*c**2 + 0 + 1/100*c**5 + 0*c**3. Determine t so that v(t) = 0.
-10, 0
Factor 3*m**2 - 6*m**2 - 1187*m - 1942*m.
-3*m*(m + 1043)
Let p(h) be the third derivative of -7*h**6/10 - 338*h**5/15 - 688*h**4/3 - 256*h**3/3 + 2*h**2 + 53. Factor p(b).
-4*(b + 8)**2*(21*b + 2)
Let s = 89 + -93. Let m(d) = -d**2 + 6*d + 4. Let w(c) = -c**2 + 8*c + 3. Let v(o) = s*w(o) + 5*m(o). Factor v(z).
-(z - 2)*(z + 4)
Let s(x) be the third derivative of 0*x**3 + 0 + 0*x**4 - 24*x**2 + 0*x - 1/120*x**5 + 1/420*x**7 - 1/480*x**6 + 1/1344*x**8. Factor s(p).
p**2*(p - 1)*(p + 1)*(p + 2)/4
Suppose -34*a + 16*a = -108. Let c be (-3 - (-18)/a)*(-6)/30. Factor 4/5*b**4 - b**3 + 2/5*b**2 + c*b - 1/5*b**5 + 0.
-b**2*(b - 2)*(b - 1)**2/5
Suppose 39*v - 26*v = 390. Suppose 2*y - v = -4*p, 0 = -11*p + 10*p - 4*y - 3. Factor 3/4*h**3 + 21/4*h**2 + 12*h + p.
3*(h + 2)**2*(h + 3)/4
Let n = 186393 + -559177/3. Factor 4/9*b + 2/9*b**3 - n*b**2 + 0.
2*b*(b - 2)*(b - 1)/9
Let d = -245 + 247. Let i(p) = 16*p**2 - 8*p. Let q(v) = v**2 - v. Let m(k) = d*i(k) - 36*q(k). Factor m(j).
-4*j*(j - 5)
Let k(h) be the second derivative of h**4/12 + 23*h**3/3 + 180*h**2 + 5174*h. Determine n, given that k(n) = 0.
-36, -10
Let y(c) be the first derivative of -3*c**5/5 + 21*c**4/2 + 49*c**3 + 51*c**2 + 1735. Solve y(b) = 0 for b.
-2, -1, 0, 17
Determine l, given that 48/5 - 24/5*l**3 + 78/5*l**2 + 124/5*l - 26/5*l**4 = 0.
-1, -12/13, 2
Let n(g) be the first derivative of 3/28*g**4 - 1/35*g**5 + 109 - 1/2*g**2 + 1/7*g**3 - 6/7*g. Factor n(c).
-(c - 3)*(c - 2)*(c + 1)**2/7
Let v(l) = 5*l**4 - 10*l**3 - 55*l**2 + 20. Let z(x) = -x**2 + x + 1. Suppose 5*k - 6*k = 1. Let n(r) = k*v(r) + 20*z(r). Factor n(p).
-5*p*(p - 4)*(p + 1)**2
Let k(y) = -2*y**4 - 11*y**3 + 19*y**2 + 73*y - 2. Let f(j) = j**4 - j**2 - j + 2. Let t(p) = f(p) + k(p). Factor t(h).
-h*(h - 3)*(h + 2)*(h + 12)
Let a(y) be the second derivative of -15/14*y**4 + 0*y**2 - 3/140*y**5 + 83*y - 225/14*y**3 + 0. Find i, given that a(i) = 0.
-15, 0
Let x be (-6)/15 - (555560/350 - -4). Let f = x + 1592. Solve 6/7*d**2 - f*d**3 + 2/7*d - 4/7 - 2/7*d**4 = 0.
-2, -1, 1
Let y(v) be the first derivative of v**4/34 + 976*v**3/51 + 59536*v**2/17 + 321. Factor y(m).
2*m*(m + 244)**2/17
Let d(j) be the second derivative of 2/3*j**2 - 1/72*j**4 + 21 - j + 1/18*j**3. Factor d(y).
-(y - 4)*(y + 2)/6
Let j(k) = -8*k**4 + 23*k**3 - 60*k**2 - 23*k**3 + 7 - 68*k**3. Let d(b) = 3*b**4 + 23*b**3 + 20*b**2 - 2. Let w(i) = -7*d(i) - 2*j(i). Factor w(t).
-5*t**2*(t + 1)*(t + 4)
Let m(b) be the second derivative of b**5/70 - 41*b**4/14 + 1056*b**3/7 + 39204*b**2/7 + 2276*b - 1. Solve m(v) = 0.
-9, 66
Suppose 4*b - 26 = 14. Let o(l) = -l**3 - l**2 + l - 1. Let u(t) = -12*t**3 - 12*t**2 + 14*t - 10. Let f(n) = b*o(n) - u(n). Find v, given that f(v) = 0.
-2, 0, 1
Suppose 15*p = -323 - 277. Let m be 3/(-2)*(-9)/((-270)/p). Let 3/5*s + 0 + 3/5*s**3 - 6/5*s**m = 0. What is s?
0, 1
Let d(o) be the third derivative of 0*o**6 + 1/1008*o**8 + 0*o + 0*o**4 + 36*o**2 + 0 + 0*o**3 - 1/210*o**7 + 1/45*o**5. Determine v, given that d(v) = 0.
-1, 0, 2
Suppose 5*a - 205 + 185 = 0. Let q(s) be the third derivative of 0 - 3/7*s**3 + 0*s - 1/735*s**7 + 1/7*s**a + 9*s**2 - 1/105*s**6 + 1/105*s**5. Factor q(v).
-2*(v - 1)**2*(v + 3)**2/7
Let b = -179 + 187. Find k such that 33*k**2 - b + 35 + 168*k**2 + 165*k**2 + 180*k - 66*k**2 = 0.
-3/10
Let x(n) = n**3 + 824*n**2 + 815*n - 56. Let u(z) = -10*z**3 - 7415*z**2 - 7335*z + 490. Let s(o) = -4*u(o) - 35*x(o). What is f in s(f) = 0?
-163, -1, 0
Let j be 368/322 - (-36)/42. Suppose 32/7 + 24/7*f + 4/7*f**j = 0. Calculate f.
-4, -2
Let l = -49 - -54. Suppose -4*h - l*y = -5716, 2*y + 4306 = 3*h + y. Factor -4 - 4*s**4 - h*s + 8*s**2 + 1434*s.
-4*(s - 1)**2*(s + 1)**2
Let y(t) be the third derivative of 1/1008*t**8 + 2*t - 49/60*t**5 + 0*t**4 - 86*t**2 + 0*t**3 + 0 - 17/630*t**7 + 91/360*t**6. Factor y(w).
w**2*(w - 7)**2*(w - 3)/3
Suppose 0 = 7*n - 9 - 12. Suppose 0 = -n*h + 6*h - 48. Factor -20*g**2 - 50*g - h - 8*g - 6*g + 100*g**3.
4*(g - 1)*(5*g + 2)**2
Suppose -3*u + 5*u - 4*b = 36, 0 = -4*b - 12. Suppose 5*s - 18 = 2*k, 0 = -7*k + 4*k - u. Factor -2/7*r**3 + 6/7*r**s - 6/7 + 2/7*r.
-2*(r - 3)*(r - 1)*(r + 1)/7
Determine p, given that 37*p - 929*p + 1574*p**2 - 484 - 28*p**3 + 142 - 294*p**2 - 18 = 0.
-2/7, 1, 45
What is f in 0*f + 0 + 29*f**3 - 7*f**2 - 65/4*f**4 + 7/4*f**5 = 0?
0, 2/7, 2, 7
Solve -17956/3 + 265/3*n**4 + 1/3*n**5 + 53600/3*n - 53065/3*n**2 + 17155/3*n**3 = 0 for n.
-134, 1
Suppose 136 = 7*p - 3*p. Let u be (p - 31)*(-1)/3*-2. Find l, given that -8*l**u + 0*l**4 + 32*l**3 - 8*l**5 + 9 + 2*l**4 - 9 = 0.
-2, 0, 1/4, 2
Let k(f) = 2*f + 66. Let h be k(-30). Find s such that 2 + h*s + 17*s**3 - 25*s**3 + 10*s**3 + 6*s**2 = 0.
-1
Let f(v) be the third derivative of v**5/180 + 79*v**4/72 - 40*v**3/9 - 2*v**2 - 15*v + 5. Factor f(h).
(h - 1)*(h + 80)/3
Factor 3*i**2 + 25272*i + 2*i**2 - 24092*i + 1175.
5*(i + 1)*(i + 235)
Let 1722*p**3 + 740*p + 1729*p**3 + 144*p**2 - 5170*p**3 + 600 + 1723*p**3 = 0. What is p?
-30, -5, -1
Factor -13/2*r**3 - 10 - 89/2*r - 41*r**2.
-(r + 1)*(r + 5)*(13*r + 4)/2
Let j(b) be the third derivative of 2/15*b**5 - 4*b**2 + 2/3*b**4 - 1/105*b**7 - 1/30*b**6 + 0 + 0*b**3 + b. Factor j(m).
-2*m*(m - 2)*(m + 2)**2
Let h(s) = 10*s**3 - 141*s**2 + 470*s - 586. Let z(t) = -5*t**3 + 72*t**2 - 235*t + 292. Let b(n) = -4*h(n) - 7*z(n). Solve b(g) = 0.
3, 4, 5
Let q(c) be the first derivative of -c**3/18 - 53*c**2/12 - 25*c - 3453. Let q(r) = 0. What is r?
-50, -3
Let o = 149 - 113. Factor -15*c + 98*c**2 - 32*c**2 - o*c - 30 + 15*c**3.
3*(c - 1)*(c + 5)*(5*c + 2)
Let g(d) = 70*d**2 + 20*d + 25. Let t(j) = 59*j**2 + 21*j + 20. Let o(b) = -4*g(b) + 5*t(b). Factor o(f).
5*f*(3*f + 5)
Let l(n) be the first derivative of n**4/12 + 110*n**3/9 - 113*n**2/6 - 74*n - 2575. Factor l(k).
(k - 2)*(k + 1)*(k + 111)/3
Let z(o) be the first derivative of o**4/3 - 44*o**3 + 2178*o**2 - 4*o + 32. Let w(l) be the first derivative of z(l). Factor w(h).
4*(h - 33)**2
Let x(g) be the first derivative of 2*g**3 - 73*g**2 - 100*g - 1076. Factor x(a).
2*(a - 25)*(3*a + 2)
Let s(b) = -4*b - 2 - 13*b**2 - 15*b**2 + 2 + 27*b**2. Let v be s(0). Factor -1/5*p**5 + v + 2/5*p**2 + 0*p**3 - 2/5*p**4 + 1/5*p.
-p*(p - 1)*(p + 1)**3/5
Let q = 84 - 82. Let k(u) = u**3 + 2*u**2 + 3. Let y be k(-2). Determine z, given that -7*z**2 + 2*z - 6*z + 6*z**q + y - 6 = 0.
-3, -1
Determine k, given that 399*k - 2019*k + 1616 + 998*k**2 - 994*k**2 = 0.
1, 404
Let m = -298 + 300. Suppose -539*a**2 - 1825346 + 59998*a - 10*a**3 - 43*a**m + 12*a**3 - 3544*a = 0. What is a?
97
Let k(t) be the second derivative of 0*t**2 + 10*t - 1/15*t**6 + 0*t**5 + 0*t**4 + 0*t**3 - 2 + 1/6*t**7. Suppose k(c) = 0. Calculate c.
0, 2/7
Let v(t) = -3*t**3 - 148*t**2 + 417*t - 318. Let y(b) = 8*b**3 + 444*b**2 - 1256*b + 947. Let r(l) = 11*v(l) + 4*y(l). Solve r(u) = 0.
1, 2, 145
Suppose -348 - 3108 = -8*k. Factor 216*x**2 - 4218 + 5*x**4 + 1626 + 60*x**3 - x**4 - k*x.
4*(x - 3)*(x + 6)**3
Let h(k) = k**2 + k - 1. Let d = -3 - -4. Let i(z) be the second derivative of z**4/6 + 5*z**3/6 + 563*z - 2. Let s(g) = d*i(g) - 3*h(g). Factor s(c).
-(c - 3)*(c + 1)
Let m(l) = -14*l**4 - 49*l**3 - 48*l**2 + 36*l. Let h(t) = 40*t**4 + 146*t**3 + 144*t**2 - 108*t. Let q(c) = -4*h(c) - 11*m(c). Find f, given that q(f) = 0.
-6, -2, 0, 1/2
Let u(c) be the second derivative of -c**5 + 0*c**2 + 0*c**4 + 2/21*c**7 + 0*c**6 + 3*c + 8/3*c**3 - 16. Find q such that u(q) = 0.
-2, -1, 0, 1, 2
Factor -150*w + 1553*w**2 + 3 - 363 + 216*w - 1554*w**2.
-(w - 60)*(w - 6)
Let z = 3 + -2. Suppose 2*p + 5*h + 1 = 3*p, -p = 5*h - z. Suppose 10*j - p + 6*j + 2*j**3 + 9 + 10*j**2 + 0 = 0. What is j?
-2, -1
Let m be (12/5)/((-75)/(-1250)*2). Let w(l) be the first derivative of 0*l - 1/5*l**3 + 3/25*l**5 + 0*l**4 - 