 - 5 - 1. Suppose -x*j - j = -6. Suppose -j*b**3 + 10*b**2 - 3*b - 12*b**2 + 3*b**3 = 0. Calculate b.
-1, 0, 3
Let j(m) be the second derivative of 0*m**2 + 0 + 2/3*m**4 - 105*m + 4/3*m**3 + 1/10*m**5. Factor j(f).
2*f*(f + 2)**2
Let u(h) be the first derivative of -h**7/840 + h**6/180 + h**5/30 - h**4/3 + 59*h**3/3 + 22. Let k(v) be the third derivative of u(v). Factor k(d).
-(d - 2)**2*(d + 2)
Let n(m) be the third derivative of m**8/3024 - m**7/90 + 137*m**6/1080 - 59*m**5/108 + 43*m**4/36 - 40*m**3/27 - 2*m**2 - m - 449. Factor n(p).
(p - 10)*(p - 8)*(p - 1)**3/9
Let v be (43 + (-18768)/460)*(-28)/(-22). What is w in 12/5*w + v*w**2 + 2/5*w**3 + 0 = 0?
-6, -1, 0
Let w(b) be the third derivative of b**6/12 - 79*b**5/5 + 125*b**4/4 + 94*b**3/3 - 10*b**2 + 303. Find i, given that w(i) = 0.
-1/5, 1, 94
Suppose 4*s - 61 = -0*s + 3*x, -2*s - 5*x = -11. Let j = s - 9. Factor -545*r**4 + 3*r**3 + 3*r**5 + 0*r**5 + 551*r**j.
3*r**3*(r + 1)**2
Find g, given that -44/9*g + 2/9*g**2 - 46/9 = 0.
-1, 23
Factor 19 - 147 + 8*o**2 - 3*o + 183*o + 0*o**2 - 160.
4*(o + 24)*(2*o - 3)
Let p be 53 + -531*125/1575. Factor 240/7 - 256/7*m - 4/7*m**3 + p*m**2.
-4*(m - 15)*(m - 2)**2/7
Let d(b) = -346*b + 8655. Let n be d(25). Let r(s) be the first derivative of -4/3*s**3 + 0*s + 4*s**4 + 0*s**2 + 31 + 4*s**n. Find u, given that r(u) = 0.
-1, 0, 1/5
Determine p so that 44/9*p**3 - 2/9*p**4 + 106/3*p**2 + 56*p + 0 = 0.
-3, 0, 28
Let g = -271 - -273. Factor 2048 + 106*n + 5*n - n**2 + 3*n**g + 17*n + 0*n**2.
2*(n + 32)**2
Suppose 3*l = 3*b - 21, 2*b - l + 5 = 7*b. Solve 5*w**b + 9*w**2 - 10*w - 12 - 81*w**4 + 10*w**3 - 81*w**4 + 160*w**4 = 0 for w.
-1, 1, 6
Factor 15/4*x - 17/2 + 1/4*x**2.
(x - 2)*(x + 17)/4
Let a = 15903 + -15902. Let i(m) be the first derivative of 0*m**2 + 20*m + a - 5/3*m**3. Factor i(h).
-5*(h - 2)*(h + 2)
Let c = -59 + 113. Determine r, given that -c*r**2 - 36*r**3 + 4*r + 30 + 35*r - 24*r**4 - 14*r**3 + 9*r**5 - 46*r**3 = 0.
-1, 2/3, 5
Let q(u) = 120*u - 30837. Let l be q(257). Determine o, given that -16/19*o**2 - 32/19 + 40/19*o + 2/19*o**l = 0.
2, 4
Let y = -2/407 + 22397/2442. Let x(k) be the second derivative of 0 - 4*k - 65/12*k**4 - y*k**3 - 5*k**2 - k**5. Suppose x(f) = 0. What is f?
-2, -1, -1/4
Let a(p) be the second derivative of 1/360*p**6 + 5/24*p**4 + 7/180*p**5 + 2*p + 8*p**2 + 1/2*p**3 + 0. Let u(h) be the first derivative of a(h). Factor u(q).
(q + 1)*(q + 3)**2/3
Suppose -5*t - 5 = -2*k, 13 + 12 = 5*k. Let i(s) = 8*s + 16. Let j(y) = -y**2. Let b(g) = t*j(g) - i(g). Suppose b(d) = 0. Calculate d.
-4
Let r(j) = j**4 - j**2 - 1. Let l(q) = 24*q**3 - 25*q + 0*q**2 + 26*q**4 + q + 19*q**2 - 6 + 14*q**2 - 38*q**4. Let k(d) = l(d) + 15*r(d). Solve k(v) = 0 for v.
-7, -1, 1
Let n(c) be the first derivative of -2*c**3/7 + 72*c**2/7 - 102*c - 3003. Factor n(z).
-6*(z - 17)*(z - 7)/7
Let s(t) be the second derivative of 3*t**5/20 - 25*t**4/2 + 369*t**3/2 - 1948*t. Factor s(k).
3*k*(k - 41)*(k - 9)
Factor -9/8*p**3 + 0 + 0*p + 3/4*p**2.
-3*p**2*(3*p - 2)/8
Let w(s) = -s**4 + 33*s**3 - 256*s**2 + 630*s + 895. Let r(y) = y**4 - 32*y**3 + 255*y**2 - 628*y - 896. Let t(x) = -5*r(x) - 4*w(x). Let t(f) = 0. What is f?
-1, 9, 10
Let h = 236213 + -236213. Let z**2 + 1/2*z**3 + h + 0*z = 0. What is z?
-2, 0
Let f be -6 - ((-1)/7 - (-1235)/(-224)). Let s = 1/32 - f. Factor 0 + 0*a - s*a**3 + 0*a**2 + 3/8*a**4.
3*a**3*(a - 1)/8
Let i(b) be the third derivative of 1/525*b**7 - 63*b**2 - 9/5*b**4 + 9/25*b**5 - 1/25*b**6 + 27/5*b**3 + 0 + 0*b. Factor i(g).
2*(g - 3)**4/5
Let u be (-70)/(-24)*1062/3717. Find p, given that 8/3*p - u - 1/2*p**2 = 0.
1/3, 5
Let k(s) = 25*s**3 + 135*s**2 - 600*s + 325. Let f(u) = -12*u**3 - 65*u**2 + 300*u - 163. Let j(v) = -5*f(v) - 3*k(v). Factor j(t).
-5*(t - 2)*(t + 8)*(3*t - 2)
Let w(m) be the first derivative of m**3 - 525*m**2/2 + 1548*m + 6053. Suppose w(h) = 0. What is h?
3, 172
Suppose 37*f + 28 = 33*f. Let x(n) = -n - 2. Let t be x(f). Suppose 46*p**5 - 51*p**5 + t - 25*p - 50*p**3 + 19*p**2 + 31*p**2 + 25*p**4 = 0. What is p?
1
Factor -87 - 83/4*y + 1/4*y**2.
(y - 87)*(y + 4)/4
Let p(m) = 2*m**3 + m**2 - 4*m + 2. Let n(b) = -44*b**3 + 285*b**2 - 410*b - 41. Let u(c) = n(c) - 2*p(c). Factor u(a).
-(a - 3)**2*(48*a + 5)
Let d(t) be the third derivative of -t**7/560 - 13*t**6/320 - 3*t**5/8 - 7*t**4/4 - 4*t**3 + 18*t**2 + 82. Factor d(c).
-3*(c + 1)*(c + 4)**3/8
Factor 17*x**2 + 22*x**2 + 30*x - 25906*x**4 + 25903*x**4 + 6*x**3.
-3*x*(x - 5)*(x + 1)*(x + 2)
Let y(t) be the third derivative of -t**9/211680 - t**8/10080 + t**7/2205 + 7*t**5/12 + 24*t**2. Let c(h) be the third derivative of y(h). Factor c(i).
-2*i*(i - 1)*(i + 8)/7
Let s(a) be the second derivative of -1/90*a**4 + 1/45*a**3 + 1 - 81*a + 4/3*a**2. Factor s(r).
-2*(r - 5)*(r + 4)/15
Let s(u) be the second derivative of -5*u**7/84 + u**6/6 + 5*u**5/2 + 5*u**4 + 219*u - 6. Factor s(k).
-5*k**2*(k - 6)*(k + 2)**2/2
Suppose 16*r - 210 = 37*r. Let u be (6/r)/(-3) + 1007/665. Factor 3/7*j**5 + 12/7*j**3 - 6/7*j**2 + u*j**4 - 6/7 - 15/7*j.
3*(j - 1)*(j + 1)**3*(j + 2)/7
Let j(q) be the second derivative of 3*q**5/160 - 9*q**4/4 - 223*q**3/16 - 225*q**2/8 - 5684*q. Let j(i) = 0. What is i?
-2, -1, 75
Factor -839523/2 + 3/8*u**3 + 418968*u + 6345/8*u**2.
3*(u - 1)*(u + 1058)**2/8
Let x(z) = 7*z**2 + 2*z - 1. Let y(g) = 16*g**2 + 5*g - 3. Let t(h) = 7*x(h) - 3*y(h). Let o(r) = -5*r**2 + 35*r - 34. Let m(s) = -o(s) - 2*t(s). Factor m(u).
3*(u - 10)*(u - 1)
Suppose 1205*g - 89*g - 3177 = -945. Factor 0 + 2/7*m**3 + 4/7*m**g + 0*m.
2*m**2*(m + 2)/7
Let a(i) be the third derivative of i**8/672 - 9*i**7/140 - 59*i**6/120 - 91*i**5/60 - 41*i**4/16 - 31*i**3/12 - 409*i**2 + 2*i. Find n, given that a(n) = 0.
-1, 31
Suppose 49/9*k**3 - 53/3*k - 154/9*k**2 - 4 = 0. What is k?
-3/7, 4
Let y = 10319 + -10319. Let s(n) be the third derivative of 21*n**2 - 7/12*n**4 - 8/3*n**3 + y*n + 1/30*n**5 + 0. Solve s(w) = 0.
-1, 8
Let o(c) be the first derivative of 41*c**4 - 80*c - 2/3*c**6 - 4*c**5 + 136*c**2 - 332/3*c**3 - 136. Factor o(d).
-4*(d - 2)*(d - 1)**3*(d + 10)
Let y = 1095886/238235 - 1/47647. Determine v, given that 47/5*v**2 + 1/5*v**4 + 5*v**3 + y*v + 0 = 0.
-23, -1, 0
Let w(y) = 32*y**2 - 531*y - 1764. Let j(q) = 5*q**2 - 89*q - 294. Let m(u) = -39*j(u) + 6*w(u). Find i, given that m(i) = 0.
-3, 98
Let j(x) be the first derivative of x**6/6 + 33*x**5/5 + 141*x**4/2 + 64*x**3/3 - 768*x**2 + 5439. Find b, given that j(b) = 0.
-16, -3, 0, 2
Let x(m) be the first derivative of m**4 + 8*m**3/3 - 26*m**2 + 40*m - 596. Factor x(p).
4*(p - 2)*(p - 1)*(p + 5)
Factor 41728/9*n**2 + 237568/9*n + 184/9*n**4 - 2/9*n**5 + 262144/9 - 5384/9*n**3.
-2*(n - 32)**3*(n + 2)**2/9
Let g(r) = 3*r + 15*r**2 + 28 - 43*r**2 + 5*r**2 + 16*r**2. Let o(w) = 15*w**2 - 5*w - 55. Let p(t) = 5*g(t) + 2*o(t). Factor p(u).
-5*(u - 3)*(u + 2)
Let w(t) be the second derivative of t**4/84 + 25*t**3/21 - 52*t**2/7 - 2087*t. Let w(n) = 0. Calculate n.
-52, 2
Let m(u) be the third derivative of u**6/40 + 27*u**5/10 - u**4/8 - 27*u**3 + 561*u**2. Factor m(v).
3*(v - 1)*(v + 1)*(v + 54)
Find m, given that -2/9*m**2 - 868/9 - 146/3*m = 0.
-217, -2
Let y(s) be the first derivative of 32*s - 20/3*s**3 - 4*s**2 - 16 - s**4. Suppose y(h) = 0. What is h?
-4, -2, 1
Suppose 4*p - 2*r = 12 + 2, 2 = -2*r. Let b be 640/(-60) - (-24)/4 - (0 + -7). Let -3*z**3 + p*z - 5/3*z**2 + b*z**4 - 2/3 = 0. Calculate z.
-1, 2/7, 1
Let v be (-3)/(-2)*120/90. Find o such that -7*o**2 - 4 - 21*o**2 + 10*o**2 + 4*o**3 + 14*o + 6*o**3 - v*o**4 = 0.
1, 2
Let p(r) = r**3 - 20*r**2 - 71*r - 156. Let t(m) = 6*m**3 - 100*m**2 - 339*m - 780. Let l(d) = 11*p(d) - 2*t(d). Solve l(b) = 0.
-13, -4, -3
Suppose -23*v = -160 - 47. What is w in -43*w**5 + v*w**3 - 29*w**4 + 17*w**4 + 46*w**5 = 0?
0, 1, 3
Let m(o) be the third derivative of -o**6/200 + 13*o**5/30 + 91*o**4/30 + 92*o**3/15 - 616*o**2. Find x such that m(x) = 0.
-2, -2/3, 46
Let c(f) be the second derivative of -f**6/270 + 2*f**5/9 - 19*f**4/18 - 7*f**3 - 14*f - 9. Let z(u) be the second derivative of c(u). Let z(b) = 0. What is b?
1, 19
Let t(l) be the first derivative of -l**6/45 - 2*l**5/25 + l**4/30 + 14*l**3/45 - 8*l/15 + 2850. Find c such that t(c) = 0.
-2, -1, 1
Let z(r) be t