)
Let r(s) be the second derivative of s**6/10 + 279*s**5/10 - 238*s**4 + 291*s**3 + 5157*s**2/2 - 10*s. Factor r(c).
3*(c - 3)**2*(c + 1)*(c + 191)
Let p(o) be the first derivative of 4*o**5/15 - 723*o**4 + 8668*o**3/3 - 12998*o**2/3 + 2888*o - 5242. Factor p(t).
4*(t - 2166)*(t - 1)**3/3
Factor -7427*p + 8232*p + 4*p**2 + p**2.
5*p*(p + 161)
Suppose -2*y + 85 = 3*y. Let v = 222 - 147. Solve y*l**2 - 3*l - 14*l**2 + 360 + 72 + v*l = 0.
-12
Let c be 12/(-22) + 1575/1980. Let q(n) be the second derivative of 5/3*n**4 - c*n**5 + 0 - 10/3*n**3 + 0*n**2 - 11*n. Find r, given that q(r) = 0.
0, 2
Suppose -49*g - 107*g = -52*g - 520. Let r(w) be the second derivative of 2/15*w**4 + 0 - 9*w + 0*w**2 + 1/10*w**g - 1/15*w**3. Factor r(v).
2*v*(v + 1)*(5*v - 1)/5
Let x = 633 + -617. Suppose -108*o**3 - 135*o + 15*o**4 + x*o**5 + 119*o + 17*o**4 + 76*o**2 = 0. What is o?
-4, 0, 1/2, 1
Factor 0 + 0*f - 2/23*f**3 - 2/23*f**2 + 2/23*f**5 + 2/23*f**4.
2*f**2*(f - 1)*(f + 1)**2/23
Let u be (-475)/(-76) + 3/(-8) + (-1)/(-8). Let t(c) be the first derivative of -3*c**4 - 3 - u*c**2 - 3/5*c**5 - 3*c - 6*c**3. Let t(a) = 0. Calculate a.
-1
Let c(n) = n**2 + 5. Let v be c(4). Let w be 3 - (v/6)/(-7). Suppose 0 - i - i**3 - 3/2*i**4 + w*i**2 = 0. Calculate i.
-2, 0, 1/3, 1
Let s(x) be the second derivative of 0 - 116*x - 1/135*x**6 + 17/45*x**5 + 0*x**2 + 512/27*x**3 - 160/27*x**4. Factor s(n).
-2*n*(n - 16)**2*(n - 2)/9
Let q(l) be the second derivative of 11 - 1/20*l**5 + 3*l - l**3 - 7/12*l**4 + 0*l**2. Solve q(d) = 0.
-6, -1, 0
Factor 192 - 70*p + 36*p**2 + 18*p**2 - 52*p**2.
2*(p - 32)*(p - 3)
Suppose -3*a - 128 = -19*a. Let r be (a + -5)*2/3. Determine f, given that -1/3*f**r + 1/3 + 0*f = 0.
-1, 1
Let v(z) be the first derivative of 2*z**5/5 - 81*z**4/2 - 168*z**3 - 4*z**2 + 672*z + 2879. Factor v(o).
2*(o - 84)*(o - 1)*(o + 2)**2
Let g(w) = -w**4 + 2*w**3 - 5*w**2 + 6*w. Let n(m) = m**3 - 10*m + 13. Let v be n(2). Let f(b) = b**3 - 2*b. Let r(k) = v*g(k) + 2*f(k). Solve r(q) = 0 for q.
0, 1, 2
Suppose -96 = -4*p + p. Suppose 3*y = -0*o - 13*o - 13, -3*o = -5*y + 3. Solve 0 + y*q - p*q**2 - 1/2*q**4 - 8*q**3 = 0 for q.
-8, 0
Let x = -1146 - -1145. Let v be 101/(-1818) - x/2. Factor v*z**3 - 4/9*z + 1/9*z**4 - 4/9 + 1/3*z**2.
(z - 1)*(z + 1)*(z + 2)**2/9
Let b = 175 - 173. Factor -2*m**3 - 17 - 24*m**b - 15 - 5*m + 2*m**4 + 61*m.
2*(m - 2)**2*(m - 1)*(m + 4)
Let b(z) = 25*z**2 + 610*z + 1870. Let p(g) = 6*g**2 - 1. Let w(x) = -b(x) + 5*p(x). Factor w(t).
5*(t - 125)*(t + 3)
Let r be 5 + (4 - (-3 + 8) - 1). Suppose -89*m**3 + 250 - 40*m**2 + 25*m + 33*m**3 + 29*m**r + 32*m**3 = 0. What is m?
-2, 5
Suppose -44 + 28 = 4*l. Let q be 5 - (329/63 + l/18). Suppose q + 3/5*m + 1/5*m**2 = 0. Calculate m.
-3, 0
Let x(l) = 6*l**2 - 20*l - 1. Let n be x(4). Let a be -16 + n + -3*22/(-42). What is z in -2/7*z**2 + a*z + 0 = 0?
0, 2
Suppose -32*s = 25*s. Let r(n) be the second derivative of s - 16*n - 1/3*n**3 - 1/15*n**6 + 3/40*n**5 + 1/84*n**7 + 1/6*n**4 + 0*n**2. Factor r(u).
u*(u - 2)**2*(u - 1)*(u + 1)/2
Let c(g) be the third derivative of -g**7/70 + 3*g**6/40 + 7*g**5/20 - 15*g**4/8 - 9*g**3 - 997*g**2. Factor c(u).
-3*(u - 3)**2*(u + 1)*(u + 2)
Let c(w) be the second derivative of -w**4/8 - 11*w**3/4 + 675*w**2 + 2*w + 1497. Determine k, given that c(k) = 0.
-36, 25
Let n(k) be the second derivative of 5 - 1176/5*k**5 + 1652/9*k**4 + 343/9*k**7 + 16*k**2 - 656/9*k**3 + k + 4459/45*k**6. Factor n(w).
2*(w + 3)*(7*w - 2)**4/3
Let o = 5166 - 5164. Let g(v) be the first derivative of 1/6*v**3 + 0*v**2 - o*v + 14. Factor g(x).
(x - 2)*(x + 2)/2
What is n in -33/2*n - 1/4*n**2 - 189/4 = 0?
-63, -3
Let i(t) = 2*t**4 + 2*t**3 + 2*t**2 - t + 1. Let h(r) = 3*r**4 + 35*r**3 - 220*r**2 - 258*r + 2. Let l(p) = -h(p) + 2*i(p). Factor l(j).
j*(j - 16)**2*(j + 1)
Let n = -1011074 - -399374462/395. Let j = n - -1/79. Determine m, given that -j*m**2 - 6*m - 15 = 0.
-5
Let t(m) be the second derivative of 41*m + 1/150*m**6 + 1/10*m**3 + 2 + 1/60*m**4 - 1/5*m**2 - 3/100*m**5. Factor t(l).
(l - 2)*(l - 1)**2*(l + 1)/5
Let c = -331 - -326. Let y(z) = -13*z**4 + 2*z**3 + 3*z**2 - 3*z + 3. Let h(t) = t**2 - t + 1. Let x(m) = c*y(m) + 15*h(m). Factor x(a).
5*a**3*(13*a - 2)
Suppose 167*x + r + 8 = 170*x, -4*x - 5*r + 36 = 0. Let o(a) be the first derivative of 16*a**2 + 42 + 20/3*a**3 + a**x + 16*a. Factor o(h).
4*(h + 1)*(h + 2)**2
Suppose 3*z + 2*j - 118 = -9, z = 5*j + 25. Find b such that z*b**2 + 185*b**5 - 96*b**4 - 200*b**5 + b**4 + 75*b**3 = 0.
-7, -1/3, 0, 1
Let 2/13*y**2 - 88 - 568/13*y = 0. What is y?
-2, 286
Factor -1/8*k**4 - 11043/8 - 927/2*k**2 - 209/4*k**3 - 5535/4*k.
-(k + 3)**3*(k + 409)/8
Let a(y) = -y**3 + 20*y**2 - 1979*y + 44509. Let h be a(22). Find n such that 16/5 - 44/5*n**h - 192/5*n + 36*n**2 = 0.
1/11, 2
Let l(m) be the first derivative of -28/3*m**3 + 25*m**2 + 56 + 1/2*m**4 - 24*m. Suppose l(k) = 0. Calculate k.
1, 12
Factor 14*p - 1/4*p**3 - 5/4*p**2 + 15.
-(p - 6)*(p + 1)*(p + 10)/4
Let p(s) be the second derivative of -5*s + 0*s**3 + 1 + 3/5*s**5 + 0*s**2 + 1/4*s**4. Suppose p(r) = 0. Calculate r.
-1/4, 0
Let r = 1007/235 + -192/47. Let k(x) be the second derivative of 11*x - 2/3*x**3 + 0 + 1/3*x**2 - 1/9*x**6 + 2/9*x**4 + r*x**5. What is f in k(f) = 0?
-1, 1/5, 1
Let s = -1901/963 + 235/107. Factor s*y**3 + 2/3*y**2 - 16/9 - 4/3*y.
2*(y - 2)*(y + 1)*(y + 4)/9
Let o(c) = c**4 + c + 6. Let x(q) = -q**4 + 75*q**3 - 486*q**2 + 2*q + 2604. Let d(w) = 2*o(w) - x(w). Find r such that d(r) = 0.
-2, 3, 12
Let r(j) be the first derivative of -j**5/300 + 7*j**4/60 - 49*j**3/30 - 41*j**2/2 - j - 12. Let x(o) be the second derivative of r(o). Factor x(t).
-(t - 7)**2/5
Let s = -348 + 384. Solve -111*v + 117*v + 80 + 5*v**2 + 43*v + s*v = 0.
-16, -1
Let w = -106950 - -746797/7. Let q = 265 + w. Factor 2/7*a - q*a**3 - 2/7*a**2 + 2/7.
-2*(a - 1)*(a + 1)**2/7
Let a(f) be the third derivative of -5/24*f**3 + 0 + 1/120*f**5 + 0*f - 199*f**2 - 3/32*f**4. Factor a(k).
(k - 5)*(2*k + 1)/4
Let n be (16/(-36))/((-22)/33). Let p(w) be the second derivative of 0 + 9*w + 1/30*w**6 - 1/5*w**5 - n*w**3 + 1/2*w**2 + 1/2*w**4. Solve p(s) = 0 for s.
1
Let s(h) = -2 - 32*h + 54*h + 5 - 31*h. Let m(r) = -r**2 + 2*r. Let p(k) = 2*m(k) + s(k). Let p(d) = 0. What is d?
-3, 1/2
Suppose 57 + 9*z**4 + 22*z**4 + 63 + 4*z**3 + 44*z - 27*z**4 - 76*z**2 = 0. Calculate z.
-5, -1, 2, 3
Let a = 28553 + -85657/3. Factor 10/9*q + 1/3*q**2 - a*q**3 + 1/9*q**4 + 0.
q*(q - 5)*(q - 2)*(q + 1)/9
Suppose -8*n + 35 = -31 + 42. Let m(r) be the third derivative of -3/70*r**7 - 2*r**n + 0 - 23/20*r**5 + 0*r + 2*r**4 + 16*r**2 + 7/20*r**6. Solve m(l) = 0.
2/3, 1, 2
Factor -774*j**2 + 2644*j - 2*j**3 - 7*j**3 + 13*j**3 - 554*j**2 - 1320 + 0*j**3.
4*(j - 330)*(j - 1)**2
Let n(d) = -3*d**3 + 14*d**2 + 6*d - 2. Let r be n(5). Let -5*u + 5*u - 4*u**2 + 19 - r = 0. What is u?
-2, 2
Let b(i) be the second derivative of 0 + 1/13*i**2 + 64*i + 2/39*i**3 + 1/78*i**4. What is o in b(o) = 0?
-1
Factor 13*m**4 - m**5 - 200*m**3 - 47*m**3 + 235*m**3.
-m**3*(m - 12)*(m - 1)
Let s(l) be the first derivative of 49*l**6/12 + 4627*l**5/10 + 14319*l**4 + 122228*l**3/3 - 42044*l**2 + 12696*l - 1105. Solve s(n) = 0.
-46, -3, 2/7
Let d be (-6)/(-3) - (-2)/9. Let r = 8401729/9 - 933525. Solve -d*y - 8/9 + 8/9*y**3 - r*y**2 = 0.
-1, -1/2, 2
Let s(j) be the second derivative of -j**4/4 - 3*j**3/2 + 3*j**2/2 + 2*j. Let z(b) = 25 + 25 + 29 + 22 - 100. Let v(l) = s(l) - 9*z(l). Factor v(r).
-3*(r + 1)*(r + 2)
Suppose 0 - 858/7*j**4 + 208/7*j**2 - 359/7*j**3 + 1089/7*j**5 + 64/7*j = 0. What is j?
-1/3, 0, 8/11
Let b = 2540 + -2536. Suppose 0*f = 5*f - 10. Factor -3 + 61*i**f - b*i - 60*i**2 + 6.
(i - 3)*(i - 1)
Let y(r) = -2*r**3 + 18*r**2 - r. Let u(v) = 3*v + 55. Let i be u(-20). Let z(a) = a**3 - 8*a**2 + a. Let g(b) = i*z(b) - 2*y(b). Solve g(m) = 0 for m.
0, 1, 3
Let v(s) = -2*s**2 + 9*s - 5. Let z be v(4). Let l(o) = o + 3. Let a be l(z). Determine n so that -103*n**2 - 102*n**2 + 8 - 12*n + 209*n**a = 0.
1, 2
Let j = -186 - -192. Let n be 0/(112/84*j/(-4)). Factor 0 + 2/7*m**2 + n*m - 2/7*m**3.
-2*m**2*(m - 1)/7
Let j be 20*380/5520 - (-7)/(-161). Solve 4/3*c**2 + 1/6*c - 1/6*c**3 - j = 0.
-1, 1, 8
Let a(o) be the second derivative 