68. Let j be l(65). Factor -29*i + 4*i**2 - 5*i - k*i + 28 + j*i.
4*(i - 7)*(i - 1)
Suppose 2*u + 2 = 0, -7*u + 8 = 2*n - 11*u. Factor -12*o**3 + 20*o**3 + 8*o**3 + 4*o**4 - 20*o**n.
4*o**2*(o - 1)*(o + 5)
Let p be (-12)/11*22/(-4). Let c(x) be the third derivative of 13*x**2 + 0*x**4 + 0*x + 1/15*x**5 + 0 - 1/24*x**p + 1/210*x**7 + 0*x**3. Factor c(k).
k**2*(k - 4)*(k - 1)
Suppose 0 = -w + 5*p + 96, -10*w + 5*p = -5*w - 400. Suppose u - f = -2*u + 59, 2*f + w = 4*u. Factor 10*t**2 - u + 14*t**2 - 27*t**2 - 24*t.
-3*(t + 1)*(t + 7)
Let g(p) be the first derivative of -2*p - 1/18*p**3 + 1/30*p**5 - 4/3*p**2 - 101 + 1/6*p**4. Suppose g(l) = 0. What is l?
-3, -2, -1, 2
Let g(x) be the first derivative of x**6/360 - 17*x**5/120 + 2*x**4/3 - 4*x**3/3 - 6*x - 59. Let d(n) be the third derivative of g(n). Factor d(m).
(m - 16)*(m - 1)
Let -3/4*y**4 + 1029/4*y**3 + 0 + 258*y**2 + 0*y = 0. What is y?
-1, 0, 344
Let n(o) be the third derivative of -o**4 - 42*o**2 - 6*o**3 + 0*o - 1/15*o**5 + 0. Solve n(s) = 0.
-3
Let f(s) = 23*s**3 - 236*s**2 - 568*s - 64. Let x(i) = 118*i**3 - 1180*i**2 - 2838*i - 320. Let t(z) = 33*f(z) - 6*x(z). Factor t(r).
3*(r - 16)*(r + 2)*(17*r + 2)
Let z(l) be the second derivative of l**4/102 - 466*l**3/51 + 54289*l**2/17 - 97*l - 1. Let z(w) = 0. What is w?
233
Let l = 832 + -922. Let y be 69/(-92)*16/l. Factor 0*m**3 + 2/15*m**4 + 0*m**2 + 0*m - y*m**5 + 0.
-2*m**4*(m - 1)/15
Let t(u) be the first derivative of 2*u**5 + 5*u**4/4 - 15*u**3 - 10*u**2 + 20*u - 149. What is n in t(n) = 0?
-2, -1, 1/2, 2
Let g be 37536/952 - (6/14 - 1). Factor 29*u**2 - 35*u**2 - 5*u**3 + g*u + 16*u**2.
-5*u*(u - 4)*(u + 2)
Let y be (1/3)/(23/276). Factor c**3 - y*c**2 - 8*c**2 + 11*c**2.
c**2*(c - 1)
Factor -1/4*n**4 + 0*n + 931/4*n**2 - 15/2*n**3 + 0.
-n**2*(n - 19)*(n + 49)/4
Let h(c) be the first derivative of 2*c**3/15 - 25*c**2 + 660*c + 12906. Find r, given that h(r) = 0.
15, 110
Let c = -8/481 - -1370/24531. Let a(v) be the first derivative of -c*v**3 + 0*v - 14 + 1/17*v**2. Factor a(t).
-2*t*(t - 1)/17
Let u(i) be the first derivative of 49 + 7/4*i**2 + 1/12*i**3 + 13/4*i. Suppose u(y) = 0. Calculate y.
-13, -1
Let n(b) = -b**5 + b**4 + 4*b**2 - b. Let l(y) = 11*y**5 + 44*y**4 - 135*y**3 - 1544*y**2 + 1606*y. Let h(u) = l(u) + 6*n(u). Find p, given that h(p) = 0.
-8, 0, 1, 5
Find g, given that -16/11*g - 2/11*g**2 + 210/11 = 0.
-15, 7
Let l = 52 - 16. Suppose -2*d = -l + 14. Factor -d*t**2 + t**4 - 2*t**3 + t**4 + 2*t + 9*t**2.
2*t*(t - 1)**2*(t + 1)
Let r(m) be the second derivative of -3*m**7/280 - 37*m**6/480 - m**5/40 + 28*m**4/3 - 24*m. Let n(d) be the third derivative of r(d). Factor n(x).
-3*(x + 2)*(18*x + 1)/2
Let c(d) be the second derivative of 1/21*d**4 + 0 + 0*d**2 + 0*d**3 - 100*d + 4/105*d**6 + 1/14*d**5 + 1/147*d**7. Solve c(h) = 0 for h.
-2, -1, 0
Let d(g) be the first derivative of -g**6/6 - 19*g**5/10 - 7*g**4/2 + 77*g**3/3 + 195*g**2/2 + 225*g/2 + 5558. Let d(m) = 0. Calculate m.
-5, -3/2, -1, 3
What is j in 421*j + 279*j + 2*j**2 + 298*j + 934*j + 466578 = 0?
-483
Suppose 0 = n + 3*g + 12, 12 = n + n - 3*g. Let w = -683/8 - -687/8. Factor w*p**2 + n*p + 0.
p**2/2
Let j(r) be the second derivative of -r**5/10 - 61*r**4/14 - 362*r**3/21 - 48*r**2/7 - 5563*r. Determine g, given that j(g) = 0.
-24, -2, -1/7
Let q(b) be the first derivative of 5*b**6/6 - 5*b**4 - 1449. Determine x, given that q(x) = 0.
-2, 0, 2
Let -636/7 - 92/7*m**2 - 2/7*m**3 + 730/7*m = 0. What is m?
-53, 1, 6
Suppose 5*g + q = 26, 93*g - 96*g + 2*q = -13. Let w(u) be the first derivative of -3/11*u**4 + 1/11*u**2 + 7/55*u**g + 0*u + 1/11*u**3 + 4. Factor w(o).
o*(o - 1)**2*(7*o + 2)/11
Let 68/11*c - 2/11*c**2 + 304/11 = 0. Calculate c.
-4, 38
Let x = 968 - 966. Let d(m) = 4*m**2 + 33*m - 23. Let u be d(-9). Factor -4/3 - 4/3*f**3 - u*f - 4*f**x.
-4*(f + 1)**3/3
Factor -25 + 1418*b + 706*b**2 + 5281*b**3 + 411 + 324 - 5283*b**3.
-2*(b - 355)*(b + 1)**2
Let z(n) be the first derivative of -n**5 - 15*n**3 + 0*n**2 - 15/2*n**4 + 46 + 0*n. Let z(a) = 0. Calculate a.
-3, 0
Let o be ((-1 + 5 - 3) + 9)*9/234. Let m(b) be the first derivative of -o*b**4 + 19 + 22/39*b**3 + 1/13*b**2 - 4/13*b. Let m(k) = 0. Calculate k.
-2/5, 1/2, 1
Determine u, given that -182/3*u**2 - 2/3*u**3 + 752/3*u - 760/3 = 0.
-95, 2
Let f(h) = 157*h + 12 - 10 - 151*h + 16. Let q be f(-3). Factor q*n + 12/7*n**2 + 0 - 4/7*n**4 - 8/7*n**3.
-4*n**2*(n - 1)*(n + 3)/7
Let r(t) be the third derivative of 2/9*t**4 + 0*t - 2/45*t**5 + 0 - 157*t**2 + 0*t**3 + 1/360*t**6. Factor r(n).
n*(n - 4)**2/3
Let o(b) = -59*b**2 - 531*b + 3. Let h be o(-9). Suppose 0 + 9/8*q**h - 69/8*q**2 + 21/4*q = 0. What is q?
0, 2/3, 7
Let 98/5*y - 2/5*y**3 - 42/5*y**2 + 138/5 = 0. Calculate y.
-23, -1, 3
Solve -85*h**2 - 16*h**3 + 38*h**3 + 72*h**2 + 11*h**3 + 3*h**4 + 66*h**2 - h**5 + 24*h = 0 for h.
-3, -1, 0, 8
Let h(n) be the first derivative of -n**3/3 + 48*n**2 + 97*n - 1386. Factor h(b).
-(b - 97)*(b + 1)
Let y(b) = -27*b**2 - 107*b + 856. Let h(g) = 21*g**2 + 105*g - 852. Let z(c) = -4*h(c) - 3*y(c). Factor z(d).
-3*(d - 7)*(d + 40)
Let i = 146 - 137. Factor -2*d**2 - 60*d - 54 + i*d**3 + 15*d + 23*d**2 - 3*d**4.
-3*(d - 3)**2*(d + 1)*(d + 2)
Suppose 26*a - 81 = -a. Let 6*j**a + 5*j**4 - 7*j + 7*j - 7*j**4 = 0. Calculate j.
0, 3
Let q = 18027 - 18025. Let r(v) be the first derivative of -1/15*v**5 - 4/3*v**4 + 24*v**q - 27*v + 28 - 46/9*v**3. Find m such that r(m) = 0.
-9, 1
Let l(j) be the third derivative of 7/36*j**4 + 0 - 4*j - 1/180*j**5 + 2*j**2 - 49/18*j**3. Factor l(g).
-(g - 7)**2/3
Factor 63/5*m**2 - 17*m + 36/5 + 1/5*m**4 - 3*m**3.
(m - 9)*(m - 4)*(m - 1)**2/5
Let k(o) be the first derivative of o**6/10 - 102*o**5/25 - 21*o**4/4 + 1887. What is g in k(g) = 0?
-1, 0, 35
Let n(u) be the second derivative of -u**5/50 - 13*u**4/5 - 676*u**3/5 - 17576*u**2/5 - 4534*u. Factor n(k).
-2*(k + 26)**3/5
Let c(b) be the second derivative of 5/3*b**3 + 0 - 1/4*b**5 + 0*b**2 + 5/12*b**4 + 159*b. Find s such that c(s) = 0.
-1, 0, 2
Let l be (-10)/4*32/56*(-7)/2. Solve -1/3*q**l + q**3 + 0 + 8/3*q**2 + 4/3*q - 2/3*q**4 = 0 for q.
-2, -1, 0, 2
Let i(b) be the second derivative of -b**6/30 + 7*b**5/5 - 57*b**4/4 - 350*b**3/3 + 2450*b**2 - 2542*b + 1. Suppose i(g) = 0. Calculate g.
-5, 5, 14
Suppose -2*v = -4*v + 8. Let s = -1447 + 1458. Let 11 + 2*l - s - 5*l**2 + 4*l**2 - 2*l**3 + l**v = 0. Calculate l.
-1, 0, 1, 2
Let r(z) = -5 - 10 - 11 + 3 - 2*z. Let y be r(-14). Find a such that 13*a - a - 5 - 2*a - y*a**2 = 0.
1
Let b(h) be the second derivative of h**3/6 - 3*h**2/2 - 24*h. Let g be b(3). Factor -2*p**5 + g*p**2 + p**5 + 2*p**4 - 2*p**2 + 0*p + p.
-p*(p - 1)**3*(p + 1)
Let l be (-71877)/342 + -2 + (-13)/(-6). Let a be (-80)/30*5/(l/9). Factor -4/7*r**3 + 0 - a*r + 8/7*r**2.
-4*r*(r - 1)**2/7
Factor -2/13*t**2 - 96/13 + 38/13*t.
-2*(t - 16)*(t - 3)/13
Suppose 56*w - 97*w - 225 = 343*w - 1761. Find g, given that 14/11*g**w - 36/11*g + 0 - 14/11*g**2 + 38/11*g**3 - 2/11*g**5 = 0.
-2, -1, 0, 1, 9
Let b(f) be the first derivative of -5*f**4/4 + 50*f**3/3 + 40*f**2 - 800*f + 6810. Factor b(h).
-5*(h - 10)*(h - 4)*(h + 4)
Factor 7*a + 5*a**2 + 17*a - 136*a**3 + 69*a**2 + 308*a**3 - 150*a**3.
2*a*(a + 3)*(11*a + 4)
Let z(p) be the second derivative of -p**4/30 - 39*p**3/5 - 46*p**2 - 1113*p. Factor z(t).
-2*(t + 2)*(t + 115)/5
Factor 54*g - 2/3*g**2 + 0.
-2*g*(g - 81)/3
Solve -574*h - 4*h**3 + 65*h - 477*h**2 - 471 - 400*h + h**3 - 36*h = 0 for h.
-157, -1
Factor 246*m + 504*m + 6*m**2 + 2*m**2 - 324*m - 5*m**2.
3*m*(m + 142)
Let u be (-1 - (-24)/(-8)) + 6. Let j(r) = r**2 - 15*r + 29. Let k be j(u). Find h such that -6/7*h - 12/7*h**2 + 6/7*h**k + 9/7*h**4 + 3/7 = 0.
-1, 1/3, 1
Let i(f) be the second derivative of 0*f**2 - 2 - 1/147*f**7 + 0*f**3 + 16*f + 4/35*f**5 + 0*f**4 - 2/105*f**6. Suppose i(d) = 0. What is d?
-4, 0, 2
Let a(s) = 10*s**3 - 37*s**2 + 17*s - 8. Let i(j) = 2*j**3 - 4*j**2 - j. Let n(v) = a(v) - 6*i(v). Let n(f) = 0. What is f?
-8, 1/2, 1
Let b(r) be the first derivative of 2*r**3/33 - 267*r**2/11 + 532*r/11 + 4035. Factor b(t).
2*(t - 266)*(t - 1)/11
Let u be ((-36)/(-5))/((-61)/(-9455)). Let r = 2235/2 - u. Factor 0 - r*n**2 + 9/2*n.
-3*n*(n - 3)/2
Factor 1886/15*d + 944/15 + 188/3*d**2 - 2