7. Let w(d) = d**2 + 10*d - 8. Let h be w(-11). Suppose h*b - 2*b**2 - 12 + 10*b + b**p = 0. Calculate b.
1, 12
Let c(o) be the second derivative of -o**5/5 - 45*o**4 + 2*o**3/3 + 270*o**2 + 624*o. Let c(i) = 0. Calculate i.
-135, -1, 1
Let x = -6182963/13 - -475615. Factor 14/13*a**2 + x*a + 8/13.
2*(a + 2)*(7*a + 2)/13
Suppose -97*s + 108 + 56 = -15*s. Factor 25/4*t**3 - 3/4*t**4 + 3*t - 11*t**s + 0.
-t*(t - 6)*(t - 2)*(3*t - 1)/4
Let k(y) be the second derivative of 1 - 43/40*y**5 + 47*y + 31/60*y**6 + 7/6*y**3 - 2*y**2 - 1/12*y**7 + 13/24*y**4. Suppose k(o) = 0. What is o?
-4/7, 1, 2
Let w(p) = p**3 - 39 + 8*p + 6*p**2 + 3*p**2 + 44. Let x be w(-8). Find a such that -20*a - 7*a**x - 60*a**2 - 30*a**4 - 2*a**5 + 4*a**5 - 65*a**3 = 0.
-2, -1, 0
Let d(r) = 3*r**3 + 2*r**2 - 4*r + 1. Let z be d(1). Let 13/2*w + 1/8*w**z + 169/2 = 0. Calculate w.
-26
Suppose -l = -2*q - 6, 1 = l - 3*q - 6. Find x such that -576*x**2 + 3*x**3 - 3*x**4 - 3*x + 4*x**3 + 563*x**2 + 2*x**l + 18 = 0.
-1, 2, 3
Let z be 25/(-5) + 32/(-3)*-6. Suppose 30*r - 61 = z. Suppose -1/7*k**r + 18/7 + 3*k - 5/7*k**3 - 1/7*k**2 = 0. What is k?
-3, -1, 2
Let o(l) be the first derivative of 5*l**3/3 - 6740*l**2 + 9085520*l - 5026. Factor o(b).
5*(b - 1348)**2
Let y(b) be the first derivative of -b**5/5 + 915*b**4/4 - 69921*b**3 + 208849*b**2/2 + 779. What is d in y(d) = 0?
0, 1, 457
Suppose 4*g + 129 = x, -2*g = -x - 3*x + 54. Let v = 37 + g. What is j in 8*j**5 - 7*j**4 - j**4 - 12*j**5 - v*j**3 = 0?
-1, 0
Let n(x) = -x**2 + 39*x. Let v(w) be the third derivative of 5*w**4/3 - 3*w**2 - 20. Let f(s) = 5*n(s) - 6*v(s). Solve f(j) = 0.
-9, 0
Let n(w) = w**2 + 8*w + 26. Suppose -4*u = 3*t + 19, -u - 2*u = -4*t - 17. Let g be n(t). Factor 4*h + 4*h**5 - 4*h**4 - g*h**3 + 8*h**2 + 3*h**3 - 17 + 13.
4*(h - 1)**3*(h + 1)**2
Let q(j) be the second derivative of 3*j**3 - 1/50*j**5 + 1/1800*j**6 + 0*j**2 + 3/10*j**4 + 0 + 11*j. Let i(u) be the second derivative of q(u). Factor i(w).
(w - 6)**2/5
Let l be (-12)/105*95/114*(-66)/2. Factor -4/7 + l*s - 18/7*s**2.
-2*(s - 1)*(9*s - 2)/7
Let a(s) be the first derivative of s**4/4 - 14*s**3/3 + 7*s**2 - 9*s + 8. Let o be a(13). Factor 29*n**2 + 43*n**3 - n**2 + 7*n**2 - 33*n**3 - 35*n**o - 10*n.
-5*n*(n - 1)*(n + 1)*(7*n - 2)
Let k be (35 + (-3006)/72)/(-1 - 2). Let s(z) be the first derivative of 2*z - 2/3*z**3 + 11 - k*z**4 + 9/2*z**2. Solve s(h) = 0 for h.
-1, -2/9, 1
Let y(o) = o + 8 + 28 - 9 + 6. Let v be y(-9). Find n, given that 9*n**4 - v*n**3 + 19*n**3 - 9*n**2 - 3*n + n + 7*n**5 = 0.
-1, -2/7, 0, 1
Suppose c - 9*k = 5 - 30, -5*c - 2*k + 16 = 0. Let l(j) be the first derivative of 4*j - 12 + 1/3*j**3 + 2*j**c. Let l(m) = 0. What is m?
-2
Let k = 13544/145 + -2674/29. Factor 0 + 0*o**2 - 33/5*o**4 - k*o**3 + 0*o.
-3*o**3*(11*o + 2)/5
Let z be (-4)/(-2) - (-9 - -1). Let g be ((-920)/300)/(-2) - 2/z. Find c, given that 0 - 1/3*c**2 + g*c = 0.
0, 4
Let w(s) be the second derivative of 0 + 34*s - 1/9*s**4 - 28/9*s**3 + 0*s**2. Factor w(b).
-4*b*(b + 14)/3
Factor 30*i**2 + 135*i + 315/2 - 5/3*i**3 - 5/6*i**4.
-5*(i - 7)*(i + 3)**3/6
Suppose 51 - 51 = -156*w. Let t(g) be the second derivative of w - g + 0*g**2 - 1/28*g**7 + 0*g**6 + 3/20*g**5 - 1/4*g**3 + 0*g**4. Solve t(c) = 0 for c.
-1, 0, 1
Factor 2*l**4 - 42*l - 110*l**3 + 943*l + 1456*l**2 + 681*l + 55*l - 69*l.
2*l*(l - 28)**2*(l + 1)
Factor 36/7*k**2 + 0*k + 0 - 2/7*k**3.
-2*k**2*(k - 18)/7
Let q(z) be the first derivative of -8/7*z**2 + 0*z + 16/21*z**3 - 50 - 1/7*z**4. Factor q(u).
-4*u*(u - 2)**2/7
Let h(t) be the first derivative of t**5/210 + t**4/28 - 4*t**3/21 - 5*t**2/2 - 2*t - 25. Let f(k) be the second derivative of h(k). Factor f(n).
2*(n - 1)*(n + 4)/7
Let x be (5/(-6))/(4/6) - (-8)/(4480/4300). Factor -6 - 3/7*o**2 - x*o.
-3*(o + 1)*(o + 14)/7
Let j(y) be the third derivative of y**6/240 - 19*y**5/40 + 215*y**4/48 - 53*y**3/4 - 212*y**2 + 2*y. Find u, given that j(u) = 0.
1, 3, 53
Let b(p) be the third derivative of -27/8*p**4 - 1/40*p**6 + 0*p**3 + 84*p**2 + 3/5*p**5 + 0*p + 0. Factor b(h).
-3*h*(h - 9)*(h - 3)
Let x(n) be the third derivative of n**8/84 - 46*n**7/35 - 59*n**6/6 + 209*n**5/15 + 123*n**4 - 1168*n**3/3 + 405*n**2 + 3*n + 1. Let x(d) = 0. What is d?
-4, -2, 1, 73
Let s(m) = 953*m - 277320. Let i be s(291). Find b such that -24/5 + 16*b + 58/15*b**2 - 14/15*b**4 - 52/15*b**i = 0.
-3, 2/7, 2
Let m(t) be the first derivative of -t**3/6 - 771*t**2/2 - 594441*t/2 - 3424. Let m(u) = 0. Calculate u.
-771
Let p(y) be the third derivative of -1/110*y**5 + 1/660*y**6 + 1/66*y**4 + 51*y**2 + 0 + 0*y**3 + 2*y. Factor p(g).
2*g*(g - 2)*(g - 1)/11
Let v(i) be the first derivative of -2*i**3/63 - 155*i**2/21 - 44*i/3 + 7089. Let v(k) = 0. What is k?
-154, -1
Let t(j) be the first derivative of -2*j**3/21 + 141*j**2/7 - 1664. Factor t(f).
-2*f*(f - 141)/7
Let u(h) be the second derivative of h**5/10 + 5*h**4/3 - 91*h**3/3 + 80*h**2 + 329*h - 2. Factor u(y).
2*(y - 5)*(y - 1)*(y + 16)
Let w(f) be the second derivative of f**6/30 + f**5/4 + f**4/2 - 2*f - 2291. Factor w(a).
a**2*(a + 2)*(a + 3)
Let i be -9 + ((-1885)/1625)/((-18)/140). Let d(s) be the second derivative of 0*s**2 - 37*s + 0 + i*s**6 + 1/30*s**5 + 0*s**3 + 0*s**4. Factor d(z).
2*z**3*(z + 1)/3
Let q(d) = 3*d - 1. Let w = 30 + -29. Let g be q(w). Find i such that -28*i + 2*i**2 - 1 - 3 - 4*i**g - 11*i**2 = 0.
-2, -2/13
Let j(o) be the third derivative of -o**8/84 + 16*o**7/35 + 152*o**6/15 + 78*o**5 + 603*o**4/2 + 612*o**3 + 89*o**2 + 2*o + 3. Find w, given that j(w) = 0.
-3, -1, 34
Let h(i) be the second derivative of 5/12*i**4 - 125/3*i**3 + 1 + 13*i + 3125/2*i**2. Let h(w) = 0. Calculate w.
25
Let z(o) be the second derivative of -5*o**7/42 - 17*o**6/2 - 49*o**5/2 + 5*o**4/6 + 165*o**3/2 + 245*o**2/2 - 440*o - 1. Factor z(n).
-5*(n - 1)*(n + 1)**3*(n + 49)
Factor 0 + 16*k**3 + 182/5*k**2 + 32/15*k**4 + 338/15*k.
2*k*(k + 1)*(4*k + 13)**2/15
Suppose 9*a + 44 = 31*a. Let 22*p**a - 60*p**2 + 19*p**2 + 60 + 24*p**2 - 40*p = 0. What is p?
2, 6
Let r = 196463/138 + -32740/23. Factor -7/6*j**4 - 13/6*j**2 - 2/3*j - r*j**5 + 0 - 5/2*j**3.
-j*(j + 1)**3*(j + 4)/6
Suppose 245 - 301 = -4*d. Suppose -4*i = 4*o, 2*i - o - d = 4*o. Suppose 0 + 0*b**i + 1/3*b**3 - 1/3*b = 0. Calculate b.
-1, 0, 1
Find s, given that -57*s**4 + 16*s**2 + 0*s + 0 + 7/5*s**5 + 198/5*s**3 = 0.
-2/7, 0, 1, 40
Let n(c) = -68*c**4 - 242*c**3 + 1392*c**2 - 1162*c - 50. Let p(q) = 20*q**4 + 81*q**3 - 464*q**2 + 387*q + 15. Let j(t) = 3*n(t) + 10*p(t). Factor j(k).
-4*k*(k - 12)*(k - 8)*(k - 1)
Suppose -3*m = -10*m - 154. Let l = m - -26. Let -129*u**5 - u**3 + 10*u**l + 134*u**5 + u**3 - 5*u - 10*u**2 = 0. Calculate u.
-1, 0, 1
Let i(z) = z**2 - 8*z + 12. Let s be i(3). Let b be 15/13 + ((-12)/s)/(-4). Factor 0 - b*d**2 + 2/13*d.
-2*d*(d - 1)/13
Let w(y) be the first derivative of 2*y**3/27 + 2144*y**2/9 + 2298368*y/9 - 748. Factor w(b).
2*(b + 1072)**2/9
Let y = 80424/160849 + 1/321698. Solve -1/2*o**2 + 1/2*o**3 + 1/2 - y*o = 0 for o.
-1, 1
Let p(d) = d + 8. Let o be p(-6). Suppose 4*j - 5*g - 32 = 0, -o*g = -j + 2*g + 19. Factor 20*h**4 + 54*h - 84*h**3 + 2*h**5 + 108*h**2 + 26*h**j + 130*h**3.
2*h*(h + 1)*(h + 3)**3
Suppose -34 = 2*l - 4*l + 4*c, -l + 5*c + 32 = 0. Suppose l*p - 52 = 11. Find v such that -p - 363*v + 1 + 369*v + 2*v**2 = 0.
-4, 1
Suppose 20*g - 60 = 40. Let v(m) = 10*m. Let u be v(3). Let -5*t**5 + 10*t**2 - 7 - 1 + g*t**4 - 25*t + u*t**3 - 7 = 0. What is t?
-1, 1, 3
Let a(v) be the first derivative of 2*v**3/15 + 144*v**2/5 + 2176*v/5 + 13462. Let a(q) = 0. What is q?
-136, -8
Let i(b) be the first derivative of 9*b**5/40 - 25*b**4/32 - 37*b**3/4 - 75*b**2/4 - 7*b + 602. Determine g, given that i(g) = 0.
-2, -2/9, 7
Let b(y) be the third derivative of 0*y**4 + 1/840*y**8 + 0*y**5 + 0*y + 0*y**6 + 0 + 80*y**2 + 0*y**3 - 16/525*y**7. Let b(s) = 0. Calculate s.
0, 16
Let z(x) be the second derivative of x**4/6 - 348*x**3 - 1045*x**2 - 5346*x. Factor z(u).
2*(u - 1045)*(u + 1)
Let i(u) be the second derivative of -12*u**7/91 + 287*u**6/195 + 167*u**5/65 - 7*u**4/78 - 6*u**3/13 + 624*u. Determine n so that i(n) = 0.
-1, -1/4, 0, 2/9, 9
Suppose -2*z - 4*w = 8, 20 = 3*z - 3*w - 4. Factor 1225 + 106*j**2 + 130*j**2 + 3596*j + z*j**3 + 