7. Let n be 2 + b - (1 + -1). Solve -5*q**2 - 18 + 4*q**3 + 17*q**n + 2 = 0 for q.
-2, 1
Let r(p) be the first derivative of -3*p**4/28 + 4*p**3/7 + 15*p**2/14 - 269. Find u, given that r(u) = 0.
-1, 0, 5
Let b be 95/105 + -1 + (-585)/(-189). Let x(g) be the second derivative of 9*g + 0 - 1/36*g**4 + 0*g**2 - 1/120*g**5 + 0*g**b. Suppose x(t) = 0. What is t?
-2, 0
Let p(z) be the second derivative of 0*z**2 + 14/45*z**6 + 0*z**3 + 1/9*z**4 - 1/3*z**5 + 0 + 3*z - 2/21*z**7. Factor p(x).
-4*x**2*(x - 1)**2*(3*x - 1)/3
Let g(f) = -f**3 + f - 1. Let x(p) = 10*p**3 + 68*p**2 - 154*p + 82. Let y(r) = 6*g(r) + x(r). Factor y(s).
4*(s - 1)**2*(s + 19)
Let b(i) be the first derivative of -i**3/3 - 23*i**2/2 - 60*i + 138. Factor b(z).
-(z + 3)*(z + 20)
Let c be (-3 - -3)*3/9. Let g(k) be the second derivative of c*k**5 + 1/28*k**7 - 3*k + 0 - 1/4*k**4 - 1/4*k**3 + 0*k**2 + 1/10*k**6. Factor g(z).
3*z*(z - 1)*(z + 1)**3/2
Let c(n) = n + 25. Let l be c(-22). Let g be (-1)/((0 - 2) + l)*-2. Factor 8/13*j**g + 2/13*j**5 + 2/13*j + 12/13*j**3 + 0 + 8/13*j**4.
2*j*(j + 1)**4/13
Let n(k) be the first derivative of k**5/60 + k**4/6 + k**3/2 - 11*k**2/2 + 19. Let u(s) be the second derivative of n(s). Factor u(q).
(q + 1)*(q + 3)
Let y be (-24)/336 + (-43)/(-14). Let a(l) be the second derivative of -4*l + 0 - 1/42*l**4 + 0*l**y + 1/7*l**2. Let a(b) = 0. Calculate b.
-1, 1
Let d(f) be the first derivative of -5*f**4/4 + 35*f**2/2 - 30*f + 5. Let d(l) = 0. What is l?
-3, 1, 2
Let m = -1247 + 3746/3. Let t(d) be the first derivative of 4/3*d + 4 + 3*d**2 + 7/24*d**4 + m*d**3. Factor t(g).
(g + 2)**2*(7*g + 2)/6
Let o(l) be the third derivative of 1/10*l**5 - 1/240*l**6 + 3*l**2 - 2*l - 7/16*l**4 + 0 - 49/6*l**3. Factor o(g).
-(g - 7)**2*(g + 2)/2
Determine c so that 4/7*c**5 - 68/7*c + 94/7*c**2 - 44/7*c**3 + 16/7 - 2/7*c**4 = 0.
-4, 1/2, 1, 2
Factor 3/4*y**3 + 81/2 + 1/8*y**4 - 27/2*y - 27/8*y**2.
(y - 3)**2*(y + 6)**2/8
Let z(m) be the first derivative of 1/51*m**6 + 3/17*m**4 + 0*m - 4 + 8/85*m**5 + 1/17*m**2 + 8/51*m**3. Determine u, given that z(u) = 0.
-1, 0
Let p = 2922 + -2920. Factor 0 + 1/2*g + 3/2*g**3 - 3/2*g**p - 1/2*g**4.
-g*(g - 1)**3/2
Factor 2/9*j**2 - 2/9*j**3 + 0 + 2/9*j - 2/9*j**4.
-2*j*(j - 1)*(j + 1)**2/9
Let v(u) be the first derivative of 0*u**3 - 8/3*u + 4/3*u**2 - 50 + 1/30*u**5 - 1/6*u**4. Factor v(m).
(m - 2)**3*(m + 2)/6
Let g(k) = -12*k**2 + 4*k + 16. Let o(i) = -i**2 - i. Let v(c) = 6*c**2 + c - 5. Let d(a) = 2*o(a) + v(a). Let h(w) = -8*d(w) - 3*g(w). Factor h(j).
4*(j - 2)*(j + 1)
Let t(a) be the third derivative of -a**8/840 + a**6/45 - 13*a**3/6 + 21*a**2. Let r(l) be the first derivative of t(l). Let r(i) = 0. What is i?
-2, 0, 2
Factor 0*z - 2/13*z**4 + 0*z**2 + 6/13*z**5 + 0 - 4/13*z**3.
2*z**3*(z - 1)*(3*z + 2)/13
Let b(s) be the second derivative of -s**4/18 - 25*s**3/9 + 26*s**2/3 - s + 9. Find c, given that b(c) = 0.
-26, 1
Solve -3*t**3 - 35*t**2 - 39*t**2 + 60*t**2 - 13*t + 6 = 0.
-3, -2, 1/3
Factor 0 - 1/4*x**2 + 5/2*x.
-x*(x - 10)/4
Let o be (-9)/12 - (-39)/4. Suppose 0*r + 3*r - o = 0. Factor -2*x + x**2 + r*x**3 + 0*x**3 + 0*x.
x*(x + 1)*(3*x - 2)
Suppose 2*i - 3*n - 13 = 0, -5*n - 23 = -4*i - 0*i. Let p = 3 - 1. Factor 4*t + 10*t**2 + 4*t**4 + 4*t**2 + p*t**2 + 12*t**3 - 4*t**i.
4*t*(t + 1)**3
Let w(u) = -2*u + 36. Let m be w(17). What is c in -12*c**2 - 12*c**3 + 10 - 1 + 0*c**3 + 33*c + 36*c**m = 0?
-1/2, 3
Let v(m) be the first derivative of -1/60*m**5 + 1/6*m**3 + 2 + 4*m + 1/18*m**4 + 0*m**2. Let k(o) be the first derivative of v(o). Factor k(c).
-c*(c - 3)*(c + 1)/3
Let y(s) be the first derivative of 4*s**3/3 + 47*s**2/10 - 22*s/5 - 8. Factor y(q).
(4*q + 11)*(5*q - 2)/5
Let h(v) be the third derivative of -7*v**4/24 - 34*v**3/3 + 39*v**2. Let y be h(-10). Factor 2/3*q + 2/3*q**y - 4/3.
2*(q - 1)*(q + 2)/3
Let f(w) = 11*w**4 + 46*w**3 + 30*w**2 - 34*w - 53. Let u(z) = 21*z**4 + 91*z**3 + 60*z**2 - 69*z - 103. Let j(b) = 11*f(b) - 6*u(b). Factor j(m).
-5*(m - 1)*(m + 1)**2*(m + 7)
Let b(u) be the first derivative of u**3/3 - 35*u**2/2 + 34*u + 87. Factor b(f).
(f - 34)*(f - 1)
Let w(k) be the third derivative of -2*k**6/15 - 4*k**5/5 + 5*k**4/2 - 8*k**3/3 - 36*k**2. What is s in w(s) = 0?
-4, 1/2
Let u(r) be the third derivative of r**7/2520 - r**6/90 + 2*r**5/15 + r**4/2 - 14*r**2. Let k(t) be the second derivative of u(t). Solve k(v) = 0 for v.
4
Let t(s) be the second derivative of 1 - 5*s + 1/30*s**4 + 2/15*s**3 + 0*s**2. Factor t(w).
2*w*(w + 2)/5
Let n(p) be the second derivative of p**7/1120 - p**5/40 - p**3/3 - 5*p. Let k(t) be the second derivative of n(t). Find x, given that k(x) = 0.
-2, 0, 2
Let x be 4/(-1 + 4/2). Suppose k + 2*m = 2, -k + m - 1 = -3. Factor 1/3*q**x + 1/3 - 4/3*q**3 + 2*q**k - 4/3*q.
(q - 1)**4/3
Let q = -149963/4 + 37491. Factor 3/4 + 1/4*k - q*k**3 - 3/4*k**2.
-(k - 1)*(k + 1)*(k + 3)/4
Let g be (2 - 1)/(72/18). Let p(x) be the second derivative of -g*x**2 - 1/24*x**3 + 7*x + 0 + 1/48*x**4. Factor p(m).
(m - 2)*(m + 1)/4
Factor 1/9*b**3 + 14/9*b**2 + 65/9*b + 100/9.
(b + 4)*(b + 5)**2/9
Let d(z) be the third derivative of 1/12*z**4 + 2*z**2 - 1/30*z**5 + 0 + 0*z**3 + 0*z. Factor d(y).
-2*y*(y - 1)
Factor -1/10*d**3 - 3*d**2 + 256/5 - 96/5*d.
-(d - 2)*(d + 16)**2/10
Suppose 155 = 2*l + 5. Let o = l + -73. Factor 5/4*f**o - 1 + 2*f.
(f + 2)*(5*f - 2)/4
Suppose -1 = 2*b - 7, -3*w + 3*b + 33 = 0. Suppose -4*a + w = 3*c, -4*a + 5*c = 7 - 37. Factor 1 + a*t**3 - t**3 - 1 + 6*t**2 + 2*t.
2*t*(t + 1)*(2*t + 1)
Factor 1/2*d + 1/6*d**2 + 0.
d*(d + 3)/6
Let x(g) be the third derivative of 1/48*g**4 + 0*g - 1/120*g**5 + 0 - 1/240*g**6 + 0*g**3 + 1/420*g**7 - 13*g**2. Factor x(v).
v*(v - 1)**2*(v + 1)/2
Let v = -62 - -68. Let t(n) = 3*n**2 - 18*n + 2. Let r be t(v). Suppose -15/2*q**r - 6 - 12*q - 3/2*q**3 = 0. What is q?
-2, -1
Let t = 3236 - 3236. Factor 9/2*o - 3/2*o**3 + t*o**2 - 3.
-3*(o - 1)**2*(o + 2)/2
Let a(m) be the first derivative of -m**2/2 - 2*m - 11. Let q be a(-2). Factor q - 1/4*c**2 - 1/2*c.
-c*(c + 2)/4
Let q(r) be the first derivative of 0*r + 17 + 10*r**2 + 0*r**3 - 5/4*r**4. Factor q(g).
-5*g*(g - 2)*(g + 2)
Let l(h) be the first derivative of -6 + 1/12*h**3 - 1/120*h**5 - 1/2*h**2 + 0*h**4 + 0*h. Let z(r) be the second derivative of l(r). Factor z(j).
-(j - 1)*(j + 1)/2
Let l(c) be the third derivative of c**6/540 + c**5/90 - c**4/12 + 5*c**3/27 - 26*c**2 + 2. Let l(a) = 0. Calculate a.
-5, 1
Let g(s) be the first derivative of s**6/1080 - s**5/360 + 6*s**3 + 10. Let i(t) be the third derivative of g(t). Factor i(f).
f*(f - 1)/3
Let w = 5397 - 43175/8. Determine d so that 1/2 - 1/4*d**4 - w*d**5 - 7/8*d - 1/4*d**2 + d**3 = 0.
-4, -1, 1
Suppose -99*o + 101*o - 1338 = 0. Let p = o - 4671/7. Find j such that 18/7 + 2/7*j**2 + p*j = 0.
-3
Let p(b) be the first derivative of -b**6/8 - 3*b**5/2 - 99*b**4/16 - 10*b**3 - 6*b**2 + 353. Solve p(s) = 0.
-4, -1, 0
Factor 2*m**2 + 6*m**2 + 10*m - 3*m**3 - 7*m**3 - 2*m**4 - 6*m**2.
-2*m*(m - 1)*(m + 1)*(m + 5)
Let u = -20286/5 - -81149/20. Determine x, given that -3 + 7/4*x - u*x**2 = 0.
3, 4
Let m = -56 - -35. Let s be (-3)/2 - m/6. Factor 6/7*o**s + 4/7*o + 2/7*o**3 + 0.
2*o*(o + 1)*(o + 2)/7
Let y = -258 - -255. Let r be (y - 57/(-21)) + 32/14. Factor 2/5*l**r + 0 - 6/5*l.
2*l*(l - 3)/5
Let z(d) = -4*d + 26. Let c be z(6). Let w be 14/c + 6/(-2). Factor 2/7*p**w + 22/7*p + 2/7*p**3 - 8/7 - 18/7*p**2.
2*(p - 1)**3*(p + 4)/7
Let z = 12253 + -12251. Factor -32/7*a - 4/7 + 36/7*a**z.
4*(a - 1)*(9*a + 1)/7
Let j(d) be the first derivative of d**6/2 - 3*d**5/5 - 3*d**4/4 + d**3 + 67. Determine w so that j(w) = 0.
-1, 0, 1
Let r = -4063/4 + 1018. Factor -r*k - 1/4 - 7/4*k**3 - 15/4*k**2.
-(k + 1)**2*(7*k + 1)/4
Let h(r) be the second derivative of -1/30*r**5 + 1/6*r**4 - 1/3*r**3 + 5*r + 0 + 5/2*r**2. Let p(w) be the first derivative of h(w). Factor p(o).
-2*(o - 1)**2
Let z = 113 - 109. Factor -4*n**2 + 3*n**5 - 8*n**3 - 5*n**5 + 10*n + 42 - 46 + 8*n**z.
-2*(n - 2)*(n - 1)**3*(n + 1)
Let u be -1 + 5 + -1 + 1. Factor 3*a**4 + 5*a**3 - 6*a**4 + u*a**4 - 6*a**3.
a**3*(a - 1)
Let k(w) = -6*w**3 + 51*w**2 + 25*w + 21. Let c be k(9). Factor -15/4*h + 7/4*h**2 + 9/4 - 1/4*h**c.
-(h - 3)**2*(h - 1)/4
Let r(p) be the first derivative of -p