 60. Let t(j) = j**2 - j. Let g(b) = l(b) - 6*t(b). Factor g(d).
-5*(d - 2)**2*(d + 3)
Let v = -38025 + 38028. Determine j, given that -6/7 - 2/7*j + 18/7*j**2 - 6/7*j**v - 4/7*j**4 = 0.
-3, -1/2, 1
Let k = 1119 - 1116. Let i(w) be the second derivative of 7*w - 1/6*w**2 + 1/9*w**4 + 0 - 1/6*w**k. Determine a so that i(a) = 0.
-1/4, 1
Let s(h) be the second derivative of -h**5/10 - 17*h**4/3 - 115*h**3 - 900*h**2 - 35*h. Find w such that s(w) = 0.
-15, -4
Suppose -z + 2 = 3*o, -6*z - 8 = -4*z. Let r(y) be the second derivative of -1/12*y**4 - 2*y + 0*y**3 + 0*y**o + 0. Factor r(w).
-w**2
Factor 1/2*k**2 - 25/2 + 0*k.
(k - 5)*(k + 5)/2
Suppose 4 = -27*t + 28*t. Suppose 0*f + 4*f = 3*n - 12, -4*n = f - 35. Find h such that -5*h**2 - t*h + 0*h**2 + h**2 + 0*h**2 + n = 0.
-2, 1
Let s = 43 + -7. Let u = s + -34. Factor 0 + 1/4*c**u + 1/4*c.
c*(c + 1)/4
Let i(j) = -j + 1. Let o be i(1). Suppose 5*g - 2*g - 15 = o. Factor -2*s**5 - 2*s - 3*s**4 - 3 - s + 6*s**3 + 5*s**5 + 6*s**2 - 6*s**g.
-3*(s - 1)**2*(s + 1)**3
Let a(z) be the second derivative of -z**6/135 - 4*z**5/45 + z**4/6 + 4*z**3 - 12*z**2 - 348*z. Suppose a(h) = 0. Calculate h.
-6, 1, 3
Let l(j) = -2*j**4 + j**2 + j + 1. Let f(r) = -11*r**4 - 24*r**3 + 149*r**2 + 30*r - 138. Let v(d) = f(d) - 6*l(d). Suppose v(h) = 0. What is h?
-1, 1, 12
Let t(b) be the third derivative of -5*b**8/168 + 13*b**7/105 + 11*b**6/60 - 13*b**5/30 - b**4/2 - 3*b**2 + 26. Determine g, given that t(g) = 0.
-1, -2/5, 0, 1, 3
Let p(w) = 25*w**2 - 25*w. Let a(l) be the second derivative of l**5/20 + l**4/12 - l**3/6 - 36*l. Let u(o) = -5*a(o) + p(o). Find t, given that u(t) = 0.
0, 2
Let n be -12*15/(-180)*0. Determine t, given that -1/3*t**3 + 4/3 + n*t - t**2 = 0.
-2, 1
Suppose 5*c - 15 = -2*g, -g - 2*c = -4*c + 6. Suppose 0*u + 3*u = g. Suppose 2/5*i**2 - 2/5*i**4 + u + 2/5*i - 2/5*i**3 = 0. Calculate i.
-1, 0, 1
Let q = -2/10151 - -50763/40604. Factor 15/2*c**2 + q + 35/4*c.
5*(c + 1)*(6*c + 1)/4
Factor -14 - 9*o - 6*o**2 - 40 + 9*o**2.
3*(o - 6)*(o + 3)
Let v(n) be the first derivative of 0*n**2 - 1/3*n**3 + 0*n + 2/3*n**6 + 1/5*n**5 - 20 - n**4. Factor v(u).
u**2*(u - 1)*(u + 1)*(4*u + 1)
Let s(j) = -j**3 - 4*j**2 - 3*j + 2. Let h be s(-3). Let r be h/4 + (-15)/(-10). Solve 3*c**3 - c + 4*c**3 + r*c**2 + 4*c**4 + 0*c**2 = 0.
-1, 0, 1/4
Factor 64*a**3 + a**4 - a**4 - 52 - 4*a**4 - 168*a**2 + 160*a.
-4*(a - 13)*(a - 1)**3
Solve 24642/5 + 444/5*a + 2/5*a**2 = 0.
-111
Let p(w) = -7*w**4 + 4*w**3 - 6*w**2 + 16*w + 11. Let g(s) = -s**4 + 2*s + 2. Let k(j) = -6*g(j) + p(j). Let k(m) = 0. Calculate m.
1
Suppose 6*i - 2966 = -2948. Let b(y) be the second derivative of 2*y + 6/5*y**2 + 2/5*y**i + 1/20*y**4 + 0. Factor b(u).
3*(u + 2)**2/5
Let i(k) be the second derivative of 5*k**4/12 - 23*k**3/6 + 3*k**2/2 + 28*k. Let l(z) = 10*z**2 - 47*z + 7. Let b(c) = 7*i(c) - 3*l(c). Factor b(p).
5*p*(p - 4)
Find o such that -4*o**4 - 34*o**5 + 65*o**5 - 29*o**5 + 2*o**3 = 0.
0, 1
Factor 0 + 3*a**2 - 1/2*a**3 + 8*a.
-a*(a - 8)*(a + 2)/2
Let x(q) be the second derivative of 0*q**3 - 1/14*q**4 - 3/70*q**5 - 12*q + 0*q**2 + 1/49*q**7 + 0 + 1/35*q**6. Factor x(a).
6*a**2*(a - 1)*(a + 1)**2/7
Factor 6*z**5 - 9*z**5 + 15*z + 6*z**4 + 63*z**3 - 27*z**3 + 42*z**2.
-3*z*(z - 5)*(z + 1)**3
Let z(n) be the third derivative of -n**8/672 - n**7/210 + 3*n**6/40 - 4*n**5/15 + 23*n**4/48 - n**3/2 - n**2 + 43*n. Find r such that z(r) = 0.
-6, 1
Let o(b) = 12*b**2 + 10*b - 26. Let k(a) = -a**2 + 1. Let r(u) = 28*k(u) + 2*o(u). Factor r(d).
-4*(d - 3)*(d - 2)
Let b(i) be the second derivative of -14*i - 6*i**2 + 2*i**3 - 1/4*i**4 + 0. Find p such that b(p) = 0.
2
Let k(x) be the second derivative of 0 + 5/2*x**2 - 5*x - 35/12*x**4 - 5*x**3. Factor k(q).
-5*(q + 1)*(7*q - 1)
Factor 12*w + 36/5*w**2 + 28/5 + 4/5*w**3.
4*(w + 1)**2*(w + 7)/5
Suppose -184 = 6*n + 86. Let j be (-27)/n*15/21. Find w, given that j*w**5 + 3/7*w**3 + 0 + 0*w + 0*w**2 - 6/7*w**4 = 0.
0, 1
Suppose -48*x = -47*x - 15. Suppose -6*v = -33 + x. Find c such that 4/7*c**4 + 0*c + 0 + 2/7*c**2 - 6/7*c**v = 0.
0, 1/2, 1
Let v be (408/28)/((-10)/(-14)). Let z = v - 20. Factor -4/5 + z*k**2 + 2/5*k.
2*(k - 1)*(k + 2)/5
Let n(u) = u**3 + u - 2. Let j(b) = -10*b**3 - 345*b**2 - 6125*b - 5770. Let c(h) = j(h) + 5*n(h). Factor c(x).
-5*(x + 1)*(x + 34)**2
Let b(q) be the third derivative of 0 + 0*q + q**4 - 14*q**2 + 6*q**3 + 1/15*q**5. Factor b(m).
4*(m + 3)**2
Let o = 5 - 3. Let f(s) = 50*s + 17*s**3 - 51 + 85 - 53*s**2 - 46. Let q(j) = -120*j**3 + 372*j**2 - 351*j + 84. Let h(x) = o*q(x) + 15*f(x). Factor h(r).
3*(r - 2)*(r - 1)*(5*r - 2)
Let q(v) be the third derivative of v**8/336 + v**7/105 - v**5/30 - v**4/24 + 114*v**2 - 1. Suppose q(k) = 0. Calculate k.
-1, 0, 1
Let a(r) be the second derivative of r**5/30 - r**4/4 - 6*r**2 + 20*r. Let h(g) be the first derivative of a(g). Factor h(i).
2*i*(i - 3)
Solve -7/5*t + 8/5 - 1/5*t**2 = 0.
-8, 1
Let n(y) be the second derivative of -y**5/120 + 13*y**4/192 - y**3/16 - 12*y**2 + 12*y. Let p(g) be the first derivative of n(g). Factor p(f).
-(f - 3)*(4*f - 1)/8
Let m be (57/2375*10)/((-6)/(-15)). Let -9/5*k**4 + m*k**3 + 0*k**2 + 0*k + 0 + 6/5*k**5 = 0. What is k?
0, 1/2, 1
Let v = -7 - -3. Let o be (1 + 0)*8 + v. Solve 54*l + 29*l**2 + 16 + 24*l**3 + 23*l**2 - 6*l + o*l**4 = 0.
-2, -1
Factor 0 - b**2 - 5/4*b + 1/4*b**3.
b*(b - 5)*(b + 1)/4
Let q(s) = 5*s**3 + 27*s**2 + 13*s - 21. Let k(z) = z**3 + z**2 + 2*z. Let l(i) = -6*k(i) + q(i). Factor l(n).
-(n - 21)*(n - 1)*(n + 1)
Suppose 363 + 91*t**2 + 106*t + 129*t**3 + 444*t - 125*t**3 = 0. Calculate t.
-11, -3/4
Suppose 2*i = -f + 3, 8*f - 6 = 10*f. Let k(s) be the second derivative of 1/42*s**4 - 2*s - 1/21*s**i + 1/70*s**5 - 1/7*s**2 + 0. Factor k(t).
2*(t - 1)*(t + 1)**2/7
Let q(o) = 44*o**2 + 155*o + 1600. Let l(t) = -26*t**2 - 77*t - 800. Let v(c) = 10*l(c) + 6*q(c). Factor v(d).
4*(d + 20)**2
Determine o, given that -125*o**2 + 56*o**3 - 32 - 4*o - 54*o**3 + 2*o + 157*o**2 = 0.
-16, -1, 1
Let k(b) be the first derivative of -b**7/2520 - b**6/1080 + b**5/180 + 23*b**3/3 + 21. Let s(d) be the third derivative of k(d). Suppose s(y) = 0. Calculate y.
-2, 0, 1
Let n(q) be the third derivative of -27*q**2 + 0 - 1/420*q**7 + 1/30*q**5 + 0*q**3 - 1/80*q**6 + 0*q + 1/840*q**8 - 1/60*q**4. Determine k so that n(k) = 0.
-2, 0, 1/4, 1, 2
Let b(i) be the first derivative of -i**4/30 - 2*i**3/9 + i**2/15 + 2*i/3 - 466. Let b(t) = 0. What is t?
-5, -1, 1
Let a(n) = 2*n**4 + 2*n**3 + 75*n**2 - 45*n + 17. Let c(m) = m**4 + m**3 + 25*m**2 - 15*m + 6. Let p(f) = 6*a(f) - 17*c(f). Determine b, given that p(b) = 0.
-3, 0, 1
Let o = 828 - 86939/105. Let z(u) be the second derivative of 0*u**2 - 2*u + 1/14*u**4 + 0*u**5 + 0 + 2/21*u**3 - o*u**6. Solve z(x) = 0 for x.
-1, 0, 2
Factor 1/4*l**2 - 17/2*l + 0.
l*(l - 34)/4
Suppose 0 = -5*r + 6 + 4. Let v be 9/r + (-21)/14. Find q such that 3*q**v - 3 - 3*q - q**2 - 2*q**2 + 2*q**2 + 4*q**2 = 0.
-1, 1
Let w(i) be the first derivative of i**4/4 - i**3 - 9*i**2/2 + 27*i + 37. Solve w(p) = 0 for p.
-3, 3
Let b = -12151/11 + 1105. Factor -8/11*d**3 + 10/11*d**2 + 2/11*d**4 - b*d + 0.
2*d*(d - 2)*(d - 1)**2/11
Suppose 4*r - 4*k = 12, -6 = -4*r + 2*r - 5*k. Find g such that -16*g**3 + 1015*g + g**r + 20*g**2 - 995*g = 0.
-2/3, 0, 2
Suppose 0 = -a - 4*g + 15, -3*a = -2*a - g. Let -8/9*j**a - 8/9 - 32/9*j**2 + 8/9*j**4 - 28/9*j + 4/9*j**5 = 0. Calculate j.
-1, 2
Let j be -6 + 9 - (-29310)/27. Let r = j - 1087. Let 2/9*w**4 + 4*w**2 + 40/9*w + 16/9 + r*w**3 = 0. What is w?
-2, -1
Let z(w) be the third derivative of 2*w**7/105 + 17*w**6/30 + 31*w**5/5 + 175*w**4/6 + 196*w**3/3 + 40*w**2 + 1. Solve z(q) = 0.
-7, -2, -1
Let r be (6/(-8))/((90/(-192))/15). Let x be (-6)/(-4)*2/r. Factor 1/8*i**3 + 1/8*i**2 + 0*i - x*i**4 + 0 - 1/8*i**5.
-i**2*(i - 1)*(i + 1)**2/8
Factor r**4 + 10 + 8*r**3 - 23*r + 10*r**2 + 31*r**4 - r**5 - 36*r**4.
-(r - 1)**3*(r + 2)*(r + 5)
Suppose -3*q - 535 = -4*t, -576 = -5*t - 5*q + 119. Let o = 275/2 - t. Determine w, given that o*w - 3/4 - 3/4*w**2 = 0.
1
Let i(q) be the second derivative of q**4/6 - q**3/33 - 5*q. Factor i(h).
2*h*(11*h - 1)/11
Let y(b) be the second derivative of 20*b + 1/90*b**6 - 1/18*b**3 - 1/126*b**7 - 1/18*b**4 + 0 + 1/6*b**2 +