**5. What is u in a(u) = 0?
-2, 1, 3
Let z be 10/2 + (-9 - -7). Suppose -3 + 9 = z*k. Factor 7*c**2 + 15*c**k + 21*c + 15*c**3 + 3*c**4 + 5*c**2 + 6.
3*(c + 1)**3*(c + 2)
Let x = 114 + -108. Suppose -5*q + x = -2*q. Solve -27*c + 4*c**q + 16*c**3 - 16 - 30*c - 7*c = 0 for c.
-2, -1/4, 2
Let a be (-150)/25*9/(-2). Let z = -15 + a. Find t, given that -18*t + 18*t + 15 + z*t - 3*t**2 = 0.
-1, 5
Let m = 274 - 271. Factor 5*p**m + 152*p - 244*p**2 + 185 + 23*p**3 - 121.
4*(p - 8)*(p - 1)*(7*p + 2)
Let u(a) be the first derivative of 1/9*a**6 + 1/3*a**4 + 0*a**3 - 2/5*a**5 - 266 + 0*a**2 + 0*a. Factor u(c).
2*c**3*(c - 2)*(c - 1)/3
Let d(m) be the third derivative of m**5/120 - 43*m**4/24 - 429*m**3/4 - 9074*m**2. Suppose d(y) = 0. What is y?
-13, 99
Let q(n) = -n**2 - n - 1. Let c(l) = 2*l**3 - 471*l**2 + 27849*l + 28325. Let z(x) = c(x) + 3*q(x). Find t such that z(t) = 0.
-1, 119
Let m(g) be the second derivative of -g**4 + 1/90*g**6 + 17/30*g**5 - g - 17/9*g**3 - 15 + 35/6*g**2. Factor m(x).
(x - 1)**2*(x + 1)*(x + 35)/3
What is t in -246 + 58*t - 194*t + 91*t + 120*t**2 + 174*t - 3*t**3 = 0?
-2, 1, 41
Let r(z) be the third derivative of -z**6/18 + 203*z**5/180 + 95*z**4/36 - 11*z**3/6 + z**2 - 17*z - 181. Factor r(o).
-(o - 11)*(o + 1)*(20*o - 3)/3
Let b(v) = -8 - 10*v + 43*v**2 + 79 - 2*v - 37*v**2 - 8*v. Let f(w) = w**2 - 4*w + 14. Let x(m) = -4*b(m) + 22*f(m). Factor x(q).
-2*(q - 2)*(q + 6)
Let f(c) = 11*c**2 - 4446*c + 985674. Let m(x) = -45*x**2 + 17785*x - 3942695. Let a(s) = 25*f(s) + 6*m(s). Find h, given that a(h) = 0.
444
Let k = -80 + 40. Let i = k + 48. Factor -4*m**2 + i*m - 3*m**2 + m**2 + 2*m**2 - 4.
-4*(m - 1)**2
Let w(o) = 32*o - 14. Let d be w(7). Let j = d + -207. Determine k, given that 0*k - 6/5*k**4 - 12/5*k**2 + 0 - 18/5*k**j = 0.
-2, -1, 0
Let t be ((-5445)/(-1452))/(30/16). Factor -1/2*g**2 + t*g + 2 - 1/2*g**3.
-(g - 2)*(g + 1)*(g + 2)/2
Let r(v) = -3*v**3 + 20*v**2 - 11*v + 1. Let c be r(6). Let c*s**2 - 10 + 9*s**2 - 11*s**2 - 5*s = 0. Calculate s.
-1, 2
Let r(g) be the first derivative of -3*g**4/20 + 707*g**3/5 + 4251*g**2/10 + 2127*g/5 - 2943. What is h in r(h) = 0?
-1, 709
Suppose -19*p + 14*p - 15 = 4*i, 3*p + 9 = 4*i. Let w be (-2 + 4 - -2)/2. Factor -8/5*l**w + 2/5*l**4 + i - 16/5*l + 4/5*l**3.
2*l*(l - 2)*(l + 2)**2/5
Let g = 127564/15 + -8500. Let k(q) be the third derivative of -13*q**2 + 0 - 1/150*q**5 + 0*q - 4/15*q**4 - g*q**3. Suppose k(l) = 0. Calculate l.
-8
Let l(f) be the third derivative of -3 + 0*f - 2/9*f**3 + 1/180*f**6 + 35*f**2 + 1/45*f**5 - 1/36*f**4. Factor l(p).
2*(p - 1)*(p + 1)*(p + 2)/3
Let t(w) be the first derivative of 8*w**5/15 - 625*w**4/6 + 104*w**3/3 + 1906. Factor t(q).
2*q**2*(q - 156)*(4*q - 1)/3
Let k(l) be the first derivative of -l**5/120 - l**4/8 - 2*l**3/3 - 85*l**2/2 - 110. Let n(j) be the second derivative of k(j). Let n(u) = 0. What is u?
-4, -2
Let z(t) be the third derivative of 0*t + 1/25*t**5 + 4*t**2 - 5 - 1/40*t**4 + 1/200*t**6 - 2/5*t**3. Factor z(i).
3*(i - 1)*(i + 1)*(i + 4)/5
Let m(s) be the third derivative of -s**6/120 + 19*s**5/20 + 39*s**4/8 + 59*s**3/6 + 1036*s**2. Solve m(g) = 0.
-1, 59
Let a(r) = 72*r + 867. Let z be a(-12). Factor -3/5*x**z - 27/5 - 21/5*x**2 + 51/5*x.
-3*(x - 1)**2*(x + 9)/5
Let m(t) be the third derivative of -t**7/70 - 13*t**6/5 - 153*t**5/10 - 38*t**4 - 101*t**3/2 + 3882*t**2. Factor m(f).
-3*(f + 1)**3*(f + 101)
Let d = -5225 + 36579/7. Factor -4/7*r**2 + 2*r**3 - 2*r + d.
2*(r - 1)*(r + 1)*(7*r - 2)/7
Let a(t) be the first derivative of -t**4/18 - 1226*t**3/27 + 8361. Factor a(c).
-2*c**2*(c + 613)/9
Factor 24*o**5 + 71*o**4 - 400*o**2 - 320*o**3 + 5*o**4 - 28*o**5.
-4*o**2*(o - 10)**2*(o + 1)
Let v = -862/45 + 6941/360. Let t(s) be the first derivative of -2*s + 1/6*s**3 + s**2 - 15 - v*s**4. Suppose t(b) = 0. Calculate b.
-2, 1, 2
Suppose w + u - 3*u + 2 = 0, 2*w = -4*u + 4. Suppose w = 3*q - 3 - 6. Factor 24*y**q - 216 + 34*y**4 + 216*y - 108*y**2 + 54 - 36*y**4.
-2*(y - 3)**4
Suppose -57 = 5*h + 4*j, -749*h = -747*h + 5*j + 84. Factor 4 - 1/9*w**h - 16/3*w + 13/9*w**2.
-(w - 6)**2*(w - 1)/9
Let i = 1195 + -702. Let g = 495 - i. Factor 18*u**2 + g*u + 63*u**4 + 109/2*u**3 + 0 + 49/2*u**5.
u*(u + 1)**2*(7*u + 2)**2/2
Let v(c) be the second derivative of 1/20*c**5 - 1/12*c**4 + 5*c + 0*c**2 + 3 - 1/3*c**3. Factor v(t).
t*(t - 2)*(t + 1)
Let i(v) = 9*v**2 + 2*v - 2. Let o be i(-2). Let r be (-4)/(-10) - 0 - (-48)/o. Factor 2*j**r - 8/5 - 6/5*j**3 + 8/5*j.
-2*(j - 2)*(j + 1)*(3*j - 2)/5
Let k = -13 + -82. Let z = k + 119. Let 8*v**3 + 16*v**2 + 24 - z - 4*v - 8 - 8*v**4 - 4*v**5 = 0. What is v?
-2, -1, 1
Let n(m) = -10*m**2 - 114*m**3 + 109*m**3 - 7*m + 1 + 6*m**2 + 6*m. Let o be n(-1). Factor -9/7*j**2 - 6/7*j**o + 3/7*j**4 + 24/7*j - 12/7.
3*(j - 2)*(j - 1)**2*(j + 2)/7
Let s be (1 + 0)*(-9 + 108/9). Factor -1127*j**3 - 1170*j**s + 3*j**4 + 42*j**2 + 2270*j**3.
3*j**2*(j - 7)*(j - 2)
Let j(s) = -49*s**2 + 70*s + 171. Let t(h) = 45*h**2 - 69*h - 174. Let q(m) = -12*j(m) - 13*t(m). What is p in q(p) = 0?
-14, -5
Factor 169/4*n**4 + 16 - 216*n - 351*n**3 + 781*n**2.
(n - 4)**2*(13*n - 2)**2/4
Let l(w) be the second derivative of w**5/5 + 287*w**4/3 + 41470*w**3/3 + 40898*w**2 - 699*w. Factor l(x).
4*(x + 1)*(x + 143)**2
Suppose 2*h - 4*x = 20, -65*h - 3*x = -70*h + 22. Find j, given that -8 - 16*j**4 + 5*j**3 - 14*j - h*j**2 + 3*j**3 + j**2 - 16*j**4 + 35*j**4 = 0.
-2, -1, 4/3
Suppose -3*c + 5*n = -2 - 5, 2*n = 2. Factor -2*w**c + 7*w - 27*w**3 - 7*w - 12*w**2 + 14*w**5 - 5*w**5 + 4*w.
w*(w - 2)*(w + 1)**2*(9*w - 2)
Let d(g) be the third derivative of g**10/50400 - g**9/2880 - g**8/840 - g**5/30 + 5*g**3/2 + 145*g**2. Let l(z) be the third derivative of d(z). Factor l(w).
3*w**2*(w - 8)*(w + 1)
Let b(k) be the third derivative of -k**5/300 - 311*k**4/120 + 313*k**3/15 - 1850*k**2 - 2*k + 1. Factor b(i).
-(i - 2)*(i + 313)/5
Let j(f) = -f**3 + 22*f**2 - 75. Let v be j(22). Let x be (-1 - 1*-1)*v/(-150). Solve 7/3*o**2 - 2/3*o + x = 0 for o.
0, 2/7
Let z(n) be the first derivative of n**4/30 - 7*n**3/15 - 8*n**2/5 - 119*n - 252. Let v(d) be the first derivative of z(d). Solve v(p) = 0 for p.
-1, 8
Let h(j) be the second derivative of j**5/40 + 9*j**4/4 - 517*j**3/4 + 2299*j**2 + j + 6484. Determine i so that h(i) = 0.
-76, 11
Let z(g) be the first derivative of -g**4/22 + 4*g**3/11 + 21*g**2 + 1960*g/11 - 353. Suppose z(m) = 0. What is m?
-7, 20
Suppose 12*d + 6534 = -2298. Let w = 738 + d. Determine i so that 8/7*i - 10/7 + 2/7*i**w = 0.
-5, 1
Let d(x) = 1819*x**2 + 7272*x - 14. Let g be d(-4). Find y, given that -2/5*y**g - 168/5*y - 3528/5 = 0.
-42
Let p be (376/40 + -11)/((-9)/60). Determine t, given that 4*t**3 - 4/3*t**5 - p*t + 16/3*t**4 - 40/3*t**2 + 0 = 0.
-1, 0, 2, 4
Let p(b) = -20*b**3 - 3471*b**2 + 13301*b + 3564. Let u(i) = -620*i**3 - 107600*i**2 + 412330*i + 110480. Let n(y) = -185*p(y) + 6*u(y). Factor n(w).
-5*(w - 4)*(w + 177)*(4*w + 1)
Suppose -2*h = 44 - 48. Suppose -3*t = -4*o - 30, -5*t + o = h*o - 50. Let t*n**3 - 7*n**3 - 19*n**2 + 4*n**2 + 12*n = 0. What is n?
0, 1, 4
Factor 2677298/9 + 4628/9*x + 2/9*x**2.
2*(x + 1157)**2/9
Let z be 5 - (-2 - -3) - -6. Suppose -z*o + 16 = -2*o. Determine u so that -7*u**3 + u + 5*u**4 + 4 + 0*u**2 + 3*u**5 - 9*u**o - u + 4*u = 0.
-2, -1, -2/3, 1
Let r be ((-15)/10 + 1)/(-2). Let l(y) be the first derivative of r*y**3 + 0*y + 3/16*y**4 + 0*y**2 - 14. Factor l(s).
3*s**2*(s + 1)/4
Let s be (3795/110)/((-42)/(-2)) + (-1)/7. Suppose -4*c - 3*z = -57, -z + 0 - 1 = 0. Factor c*y + 75/2 + s*y**2.
3*(y + 5)**2/2
Let z(y) be the third derivative of 0*y + 63*y**2 + 0*y**3 + 1/6*y**6 + 0 - 1/12*y**5 + 1/14*y**7 - 5/12*y**4. Factor z(o).
5*o*(o + 1)**2*(3*o - 2)
Let m(f) be the third derivative of f**6/200 - 216*f**5/25 + 185757*f**4/40 + 187489*f**3/5 - 4844*f**2. Let m(j) = 0. What is j?
-2, 433
Let j(n) be the first derivative of 28 + 26/5*n**2 + 12/5*n**3 + 16/5*n. Find x, given that j(x) = 0.
-1, -4/9
Factor 28*q - 11/3*q**3 - 1/3*q**4 + 0 - 16/3*q**2.
-q*(q - 2)*(q + 6)*(q + 7)/3
Let k = -2899078/5 + 579818. Solve k + 92/5*f + 44/5*f**5 + 312/5*f**3 + 248/5*f**2 + 188/5*f**4 = 0 for f.
-1, -3/11
Factor 2/5*g**2 - 44*g + 218/5.
2*(g - 109)*(g - 1)/5
Let s(f) be the third deri