- 13. Suppose 0*a - u = -5*a. Factor -4 + a*b + 3*b - b - b**2 - b.
-(b - 4)*(b - 1)
Determine n, given that -6/7*n**4 + 0 - 8/21*n**5 + 4/21*n**3 + 4/21*n + 6/7*n**2 = 0.
-2, -1, -1/4, 0, 1
Determine z so that 101/2 - 1/4*z**2 - 99/4*z = 0.
-101, 2
Let f(c) be the second derivative of -29*c**6/120 - 259*c**5/80 - 255*c**4/16 - 243*c**3/8 + 27*c**2/4 + 1018*c. Factor f(p).
-(p + 3)**3*(29*p - 2)/4
Let k(i) be the second derivative of 1/11*i**2 - 1/66*i**4 + i - 7 + 1/220*i**5 - 1/66*i**3. Factor k(q).
(q - 2)*(q - 1)*(q + 1)/11
Let t be -5*-3*(-8)/(-20) + -3. Let z be (-88)/(-10) + (-3)/(-15). Find p, given that -p**t - 514 + z*p**2 - 2*p**3 + 502 = 0.
-1, 2
Let -248/9*z**2 - 28*z**4 + 0*z + 166/3*z**3 + 2/9*z**5 + 0 = 0. What is z?
0, 1, 124
Let q(t) be the second derivative of t**4/12 + 25*t**3/6 + 69*t**2/2 - 9*t - 3. Let p be q(-22). Let 0 + 2/3*y**p - 8/3*y**2 + 8/3*y = 0. Calculate y.
0, 2
Let j = -686024/5 + 136667. Let o = j + 538. Solve -16/5*i + 64/5 + o*i**2 = 0 for i.
8
Suppose 11*p = 10*p - 3. Let o be (-5 - -4) + -2*(1 + p). Factor -85*b**o + 25*b**4 + 58*b**2 - b**2 + 23*b**2 - 20*b.
5*b*(b - 2)*(b - 1)*(5*b - 2)
Let 418/7*n - 2/7*n**2 - 416/7 = 0. Calculate n.
1, 208
Let q(g) be the first derivative of -g**4/3 + 22*g**3/3 + 24*g - 12. Let s(b) be the first derivative of q(b). Factor s(z).
-4*z*(z - 11)
Find w such that -48/7*w**4 + 0 + 3/7*w**5 + 135/7*w - 312/7*w**2 + 222/7*w**3 = 0.
0, 1, 5, 9
Let l(f) be the second derivative of f**4/4 + 27*f**3/2 + 269*f + 4. Solve l(p) = 0 for p.
-27, 0
Let c(g) = 89*g**2 + 50*g + 25. Let u(r) be the third derivative of r**5/60 - 5*r**4/24 + 97*r**2. Let p(n) = 3*c(n) - 24*u(n). Factor p(j).
3*(9*j + 5)**2
Determine n, given that -603*n**4 - 3060 - 2057*n + 245*n**3 - 688*n + 300*n**4 + 298*n**4 + 565*n**2 = 0.
-4, -1, 3, 51
Let r(i) be the second derivative of -i**5/130 + 17*i**4/78 - 94*i**3/39 + 168*i**2/13 + 188*i - 6. Suppose r(y) = 0. Calculate y.
4, 6, 7
Let p(x) = 5*x**2 + 23*x + 84. Let t(j) = -2*j**2 + j. Let h(n) = 2*p(n) + 4*t(n). What is d in h(d) = 0?
-21, -4
Let f(z) = -3*z**2 - 98*z - 98. Let p be f(-1). Let g be (-5 - -2*(-15)/(-6))/p. Factor 4/9*k**2 + 2/9*k**3 + g + 2/9*k.
2*k*(k + 1)**2/9
What is x in -113/7*x + 1/7*x**3 - 57/7 - 55/7*x**2 = 0?
-1, 57
Let m(z) = -12*z**3 + 505*z**2 - 21*z - 879. Let w be m(42). Determine s, given that 0 + 27/7*s**2 + 6/7*s + 12/7*s**w = 0.
-2, -1/4, 0
Let u(g) = 18*g + 2*g**2 - 18*g + 15 - 31*g. Let t(q) = 10*q**2 - 185*q + 90. Let r(o) = 6*t(o) - 35*u(o). Solve r(a) = 0 for a.
-3, 1/2
Factor 38/3*h + 2/3*h**2 - 28.
2*(h - 2)*(h + 21)/3
Let m = -15260 + 45787/3. Let s = -7 + 10. Solve -a**4 + 0 + m*a**s + 1/3*a - 5/3*a**2 = 0 for a.
0, 1/3, 1
Let u = 1784 + -1782. Let i(r) be the third derivative of 0 + 17*r**u + 3/2*r**3 + 0*r + 1/60*r**5 - 1/4*r**4. Factor i(f).
(f - 3)**2
Let s(u) be the third derivative of u**6/840 - u**5/20 - 289*u**4/168 - 31*u**3/2 + 5210*u**2. Factor s(l).
(l - 31)*(l + 3)*(l + 7)/7
Suppose 3*y + 13 = 5*d, -4*d - 7 = -2*y - 17. Let m(z) be the third derivative of 17*z**d + 0 - 1/30*z**3 - 1/300*z**5 + 1/60*z**4 + 0*z. Factor m(r).
-(r - 1)**2/5
Let n = 700 + -698. Factor -8 + 61*o + 9 + 26 + 15*o + 38*o**n - 6*o**3 + 5.
-2*(o - 8)*(o + 1)*(3*o + 2)
Factor -2/9*r**2 + 0 + 160/9*r.
-2*r*(r - 80)/9
Let f(s) be the second derivative of 45*s + 0 + 1/24*s**4 + 0*s**3 + 0*s**2 + 1/60*s**6 - 1/20*s**5. Factor f(j).
j**2*(j - 1)**2/2
Let u(t) be the first derivative of 3*t**5/20 + 7*t**4/8 + t**3/3 - 15*t**2/4 + 9*t/4 - 1347. Factor u(d).
(d - 1)*(d + 3)**2*(3*d - 1)/4
Let s(r) be the third derivative of -3*r**8/56 - 103*r**7/140 - 51*r**6/80 + 963*r**5/40 + 1223*r**4/16 + 75*r**3 + 9931*r**2. Solve s(x) = 0.
-25/4, -4, -1, -1/3, 3
Let y be 4/10 + 5 + (-72)/30. Let -2*p**2 - 3*p**5 + 12*p**3 + y*p**4 + 0*p**5 + 0*p**5 - 10*p**2 = 0. What is p?
-2, 0, 1, 2
Let i(j) be the second derivative of 0*j**3 - 4*j**2 + 1/2*j**4 + 1/10*j**5 + 0 + 20*j. Determine t so that i(t) = 0.
-2, 1
Solve -2814*c - 5938947 - 1/3*c**2 = 0.
-4221
Suppose 7*z = 12*z + 64*z. Let b(u) be the third derivative of 0*u + z + 2/945*u**7 - 12*u**2 + 1/9*u**5 + 7/270*u**6 + 0*u**3 + 1/6*u**4. Factor b(m).
4*m*(m + 1)*(m + 3)**2/9
Suppose 5*s + 5 = 0, -5*f + 20 = -7*s + 2*s. Let c(h) be the first derivative of -6 + 5/3*h**f + 25*h - 15*h**2. What is r in c(r) = 0?
1, 5
Let l be (-5 + (-9)/(-2))*-10. Find n such that -508*n**3 + 407*n + 140*n**4 + 416*n - 12*n**l - 1023*n + 580*n**2 = 0.
0, 2/3, 1, 5
Let a(l) be the first derivative of 196*l**3/3 + 994*l**2 + 5041*l + 1675. Factor a(i).
(14*i + 71)**2
Suppose -329 = -249*u + 556 + 360. Let q(j) be the third derivative of 0*j + 0 + 22*j**2 - 1/50*j**u + 1/40*j**4 + 1/200*j**6 + 0*j**3. Factor q(g).
3*g*(g - 1)**2/5
Let b = 245 - 241. Factor -p**4 - 8*p**4 + 4*p**3 + 0*p**3 - 41*p**b.
-2*p**3*(25*p - 2)
Let p(u) = -2*u**3 - 817*u**2 + 168103*u + 511704. Let z(l) = -5*l**3 - 1632*l**2 + 336210*l + 1023407. Let b(o) = -7*p(o) + 3*z(o). Factor b(r).
-(r - 413)**2*(r + 3)
Suppose -7*n + 3 = -6*n. Let m be (-26)/(-13)*n/((-6)/(-5)). Solve -957*x**4 - 88*x**3 + 8*x**m + 865*x**4 + 20*x**5 + 32*x**2 = 0 for x.
-1, 0, 2/7, 4
Let b(a) be the first derivative of -a**3/3 + 12*a**2 - 144*a + 2159. Let b(g) = 0. Calculate g.
12
Let c be (-85423)/42 - (-2)/(-4). Let n = -2034 - c. Factor 8/21*b + n + 2/21*b**2.
2*(b + 2)**2/21
Let r(c) be the first derivative of c**6/720 - c**5/80 + 10*c**3/3 + 5*c**2/2 - 269. Let l(d) be the third derivative of r(d). Factor l(o).
o*(o - 3)/2
Let h(j) be the first derivative of -2*j**3/9 + 450*j**2 - 303750*j - 334. Factor h(b).
-2*(b - 675)**2/3
Let c(a) be the second derivative of 35*a**4/18 - 55*a**3/2 - 75*a**2/2 + 2*a + 409. Solve c(b) = 0 for b.
-3/7, 15/2
Let 2993*w**3 - 44452*w**2 + 44800 - 166*w**4 + 4499*w**3 - 182*w**4 - 8640*w + 1144*w**3 + 4*w**5 = 0. What is w?
-1, 1, 7, 40
Let t(o) be the third derivative of 4*o**3 + 1/6*o**5 + 1/120*o**6 + 0*o - 74*o**2 + 0 + 7/6*o**4. Find z, given that t(z) = 0.
-6, -2
Suppose -4*r + 96 = 5*s + 83, -6 = -2*r - 2*s. Factor 4*a**r - 16/5*a**3 + 4/5*a**4 + 0 - 8/5*a.
4*a*(a - 2)*(a - 1)**2/5
Let g(d) be the second derivative of -d**7/3780 + 11*d**6/1080 + d**5/15 + d**4/2 - d**2/2 - 2*d - 15. Let q(w) be the third derivative of g(w). Factor q(n).
-2*(n - 12)*(n + 1)/3
Suppose 9*p - 187 - 83 = 0. Factor 9 + 23 - 7*w**4 - 34*w**2 - 30*w + 10*w**4 - w**4 + p*w**3.
2*(w - 1)**2*(w + 1)*(w + 16)
Let s(v) = 1017*v**2 - 25*v + 31. Let z(i) = 185*i**2 - 5*i + 6. Let y(n) = 2*s(n) - 11*z(n). Factor y(p).
-(p - 4)*(p - 1)
Let l be 696/448 + (6/4)/((-392)/112). Let b(s) be the first derivative of 1/2*s**3 - l*s**4 + 31 + 9/4*s**2 - 3/2*s. Suppose b(h) = 0. What is h?
-1, 1/3, 1
Let p be 202106/43785 - 2/45. Suppose p - 1732/7*i**3 + 1760/7*i**4 + 272/7*i + 152/7*i**2 - 484/7*i**5 = 0. What is i?
-2/11, 1, 2
Let x(f) be the second derivative of f**5/30 - 25*f**4/2 + 1875*f**3 - 43*f**2/2 + 54*f. Let j(d) be the first derivative of x(d). Factor j(i).
2*(i - 75)**2
Determine x, given that -8/7*x**2 - 2/7*x**3 + 36/7 + 6/7*x = 0.
-3, 2
Suppose -4*b = 2*w + 4, 13*b - 12*b + 11 = 2*w. Factor -11*z + 0*z**2 + 9*z**2 - 6*z**2 - w*z**2.
-z*(z + 11)
Suppose b - 8 = -6. Let p(i) = 5*i**3 - i**2 - 2*i + 1. Let w be p(b). Suppose -4*z**2 - w*z - 4*z - 18*z + 7*z - 144 = 0. What is z?
-6
Let m(p) be the third derivative of p**7/1260 - 13*p**6/20 - 237*p**5/20 - 357*p**4/4 - 1431*p**3/4 - 7*p**2 - 90. Solve m(s) = 0.
-3, 477
Let f(p) be the first derivative of p**3/12 - 63*p**2/8 + 14049. Factor f(y).
y*(y - 63)/4
Suppose -4*f + 301 = 5*s, -s - 44 = -f + 4*s. Find i, given that -75*i**2 - f*i**2 - i**3 + 8 + 136*i**2 + i = 0.
-8, -1, 1
Determine s so that 10652*s + 1134355*s**2 - 132603*s**3 + 1621*s**4 + 348*s - 417973*s**3 + 1144*s**4 + 164201*s**3 - 5*s**5 - 1512500 = 0.
-1, 2, 275
Let t(g) be the second derivative of -g**9/1512 - g**8/280 - g**7/210 + 83*g**3/3 + 21*g + 1. Let z(r) be the second derivative of t(r). Factor z(c).
-2*c**3*(c + 1)*(c + 2)
Suppose -30*l = -2*l - 112. Factor r**3 - r**2 - 2*r + 2*r**2 - l*r**2 + 2*r**2 + 0*r**3.
r*(r - 2)*(r + 1)
Let b(y) be the first derivative of -y**3 - 513*y**2/2 + 1566*y - 6724. Factor b(s).
-3*(s - 3)*(s + 1