).
4*(o - 3)*(o + 2)
Let s(q) be the second derivative of -q**7/273 - 4*q**6/195 - q**5/130 + 5*q**4/39 + 4*q**3/39 - 8*q**2/13 - 3*q - 3. Determine o so that s(o) = 0.
-2, 1
Suppose -6*l = -4*l - 6. Factor -3 + 56*a**l - 57*a**3 + 3*a**2 + a + 0*a.
-(a - 3)*(a - 1)*(a + 1)
Let c = -76 + 94. Let b be (-12)/(-28)*12/c. Factor 0*k - 2/7*k**2 - 4/7*k**3 + 0 - b*k**4.
-2*k**2*(k + 1)**2/7
Let t(m) be the first derivative of 0*m - 5/12*m**3 - 1/16*m**4 - 3/4*m**2 - 53. Find o, given that t(o) = 0.
-3, -2, 0
Let u(h) be the first derivative of 3*h**4 - 568*h**3/3 - 792*h**2 - 800*h + 217. Factor u(t).
4*(t - 50)*(t + 2)*(3*t + 2)
Let c be 2888/722 - 38/(-10). Find r such that 21*r + 147/5 + 3/5*r**3 - c*r**2 = 0.
-1, 7
Let p(f) be the first derivative of -2/3*f**3 + 0*f + 1/3*f**4 + 6 - 1/15*f**5 - 7/2*f**2. Let d(c) be the second derivative of p(c). What is l in d(l) = 0?
1
Suppose 0*f - 15 = -3*f. Let y be 84/f - (-1)/5. Determine u so that u**4 - 4*u**3 + y*u**4 - 16*u**5 + 2*u**5 = 0.
0, 2/7, 1
Let x = 6398 - 6396. Let d = -42 + 74. Suppose 6*k + d*k**3 + 24*k**x + 1/2 = 0. Calculate k.
-1/4
Suppose -25*w - 26*w = 9*w - 300. Let -1/4 - 3/2*o**2 + 7/4*o**4 + 5/4*o - 1/2*o**3 - 3/4*o**w = 0. Calculate o.
-1, 1/3, 1
Factor -157*w**3 + 60*w**4 + w**5 - 169*w**3 - 15*w**2 + 211*w**2 + 74*w**3 - 5*w**5.
-4*w**2*(w - 7)**2*(w - 1)
Let m = 56 - 56. Let k(s) be the third derivative of 2/105*s**7 + 0*s**5 - 1/168*s**8 + 4*s**2 + 0 + 0*s + m*s**3 + 0*s**4 - 1/60*s**6. Factor k(l).
-2*l**3*(l - 1)**2
Let a = 80 - 116. Let l = a - -36. Determine m, given that 4/3 - 1/3*m**2 + l*m = 0.
-2, 2
Let o(z) be the second derivative of z**7/105 - z**6/75 - z**5/10 + z**4/6 + 4*z**3/15 - 4*z**2/5 - 17*z. Let o(n) = 0. What is n?
-2, -1, 1, 2
Factor -9/2*y**2 - 9*y - 6 - 3/4*y**3.
-3*(y + 2)**3/4
Suppose 5*h - 2*v = -4, 7 + 3 = h - 4*v. Let i = h - -4. Solve -9*b**2 + b**i + 17*b**2 - 6*b**2 = 0 for b.
0
Factor 30/13*b**2 + 12/13*b**3 + 0 + 16/13*b - 2/13*b**4.
-2*b*(b - 8)*(b + 1)**2/13
Let i(v) = v**3 - 3*v**2 + 3*v + 1. Let c be i(3). Factor -c*b**2 + 0*b**2 - 14*b**3 - 11*b**3.
-5*b**2*(5*b + 2)
Suppose -4*j + 9*j = 0. Let c(a) be the first derivative of j*a - 11/6*a**3 + 3 + 1/2*a**2 + 9/8*a**4. Let c(r) = 0. What is r?
0, 2/9, 1
Let j be (48/28)/(2/7). Suppose -3*r = -0 - j. Factor -6 - 3*p**3 + 2*p**2 + 4*p**r + 3*p + 0*p**2.
-3*(p - 2)*(p - 1)*(p + 1)
Let v be (-60)/40*2/(-6). Solve 5/4*g + v + 1/4*g**3 + g**2 = 0.
-2, -1
Let i(q) be the second derivative of q**8/15680 + q**7/5880 + 2*q**4/3 - 6*q. Let g(l) be the third derivative of i(l). Factor g(u).
3*u**2*(u + 1)/7
Let b = 60 - 58. Factor -2*q - 3*q**3 + 5*q - 2 + b*q**3 + 0*q**3.
-(q - 1)**2*(q + 2)
Solve -306/5*b**2 - 154/5*b**4 - 8/5 - 88/5*b - 76*b**3 = 0.
-1, -2/7, -2/11
Let j be (-226 - -227)*(-1 - (-25)/7). Solve -22/7*b**4 - 4/7*b**3 - j*b**5 + 0 + 0*b + 0*b**2 = 0 for b.
-1, -2/9, 0
Factor 3 + 1/8*c**2 + 5/4*c.
(c + 4)*(c + 6)/8
Let t(x) = 15*x**2 - 2*x - 1. Let q be t(-1). Suppose -d = -4*w + 4 - 0, q = -2*w + 5*d. Let -r**2 + r**4 + 2 - w + 2*r**2 + 2*r**3 = 0. Calculate r.
-1, 0
Let v(c) be the first derivative of -5*c**4 + 15/2*c**2 - 4 - 5/3*c**3 + 0*c. Find x such that v(x) = 0.
-1, 0, 3/4
Let m(w) be the second derivative of w**4/8 - 4*w**3 + 48*w**2 + 53*w + 1. Factor m(g).
3*(g - 8)**2/2
Let b = 1588/3 + -529. Let m(x) be the third derivative of b*x**4 + 2*x**2 + 0*x - 1/30*x**5 - 4/3*x**3 + 0. Factor m(u).
-2*(u - 2)**2
Let v = 2022 + -2022. Let p(r) be the third derivative of -1/200*r**6 + 0*r - 11*r**2 + 0*r**4 + v + 0*r**3 + 1/50*r**5. Factor p(g).
-3*g**2*(g - 2)/5
Let p(s) be the third derivative of -s**7/420 - s**6/45 - s**5/20 - 5*s**3/6 - s**2. Let a(x) be the first derivative of p(x). Factor a(r).
-2*r*(r + 1)*(r + 3)
Let i(h) be the first derivative of 12*h**5/5 + 28*h**4 + 256*h**3/3 + 32*h**2 - 192*h - 291. Factor i(f).
4*(f + 2)**2*(f + 6)*(3*f - 2)
Suppose -4*c = i - 0*c - 3, 4*i + 4*c - 12 = 0. Let -37 + 43 - i*x**3 + 6*x**3 - 9*x = 0. What is x?
-2, 1
Let f(u) be the second derivative of -u**6/75 + u**5/25 + u**4/6 - 2*u**3/5 - 41*u. Factor f(p).
-2*p*(p - 3)*(p - 1)*(p + 2)/5
Let u(h) be the third derivative of h**8/168 - h**7/105 - h**6/6 - 4*h**5/15 + 55*h**2. Factor u(a).
2*a**2*(a - 4)*(a + 1)*(a + 2)
Let m(y) be the third derivative of y**7/1260 + y**6/360 - y**5/360 - y**4/72 - 5*y**2 + 17. Factor m(h).
h*(h - 1)*(h + 1)*(h + 2)/6
Let q(l) = -8*l**3 - 176*l**2 - 115*l + 53. Let u(c) = -9*c**3 - 178*c**2 - 115*c + 54. Let w(d) = 6*q(d) - 7*u(d). Suppose w(m) = 0. Calculate m.
-12, -1, 1/3
Let n(r) be the third derivative of -r**5/20 - 5*r**4/8 - 2*r**3 + 332*r**2. Let n(c) = 0. What is c?
-4, -1
Let q(n) be the second derivative of 4*n**6/15 + 23*n**5/20 + 7*n**4/6 + 60*n - 2. Find u such that q(u) = 0.
-2, -7/8, 0
Let z(i) = i**3 + i**2 - 4*i. Let u(r) = r**3 + 2*r**2 - 5*r - 1. Let k be (-4 - -2)*-1 - (-3 - 0). Let f(j) = k*z(j) - 4*u(j). Let f(d) = 0. Calculate d.
-1, 2
Suppose 5*u**2 - 7579 + 17238 - 7269 + 14522 + 25408 - 920*u = 0. Calculate u.
92
Let y be 2 - ((-313)/(-132) + (-2)/8). Let v = 16/11 + y. Factor 4/3*g - 1/3*g**2 - v.
-(g - 2)**2/3
Let p(d) be the second derivative of -d**6/60 - d**5/40 + d**4/8 + 5*d**3/12 + d**2/2 - 76*d. Let p(c) = 0. Calculate c.
-1, 2
Let y = 2141 + -2105. Factor y*d + 12*d**2 + 36 + 4/3*d**3.
4*(d + 3)**3/3
Factor -86/9*d**3 - 5488/9 - 2/9*d**4 - 140*d**2 - 6664/9*d.
-2*(d + 1)*(d + 14)**3/9
Let j(o) be the second derivative of 0 + 0*o**3 - 1/90*o**5 + 1/27*o**4 + 0*o**2 - 10*o. Factor j(h).
-2*h**2*(h - 2)/9
Let a be (-6)/24 + (-1)/(-4). Suppose -5*u + 20 = -a*u. Let 2*d**2 + 2/3*d + 2*d**3 + 2/3*d**u + 0 = 0. Calculate d.
-1, 0
Let u be (-66 - -57) + (-94)/(-10). Suppose 0 - 4/5*y - u*y**2 = 0. Calculate y.
-2, 0
Let q(z) = -4*z**3 - 9*z**2 + 21*z - 22*z + 11 + 5*z**3. Let m be q(9). Factor -i**2 + 2*i**m - i**3 - i**3 + 3*i**3.
i**2*(i + 1)
Let c(v) = 5*v**2 - 2*v - 1. Let i(q) = -112*q**2 + 52*q + 32. Let o(b) = 44*c(b) + 2*i(b). Find r, given that o(r) = 0.
-1, 5
Let q(h) be the second derivative of -h**7/5670 - h**6/1620 - h**5/1080 + 5*h**4/4 - 8*h. Let w(y) be the third derivative of q(y). What is p in w(p) = 0?
-1/2
Let v = 7/10 - -561/70. What is s in -1/7*s**4 + 15/7*s**3 + 3*s - v*s**2 + 14 = 0?
-1, 2, 7
Let g(m) be the second derivative of m**5/20 - m**4/2 + 7*m**3/6 - 3*m**2 + 7*m. Let p be g(5). Find l, given that -65*l - p*l**2 + 65*l + 4*l**3 = 0.
0, 1
Let y(b) be the third derivative of 0*b + 3/55*b**5 - 4/165*b**6 - 2/33*b**4 + 1/33*b**3 + 0 - 18*b**2 + 1/231*b**7. Find d such that y(d) = 0.
1/5, 1
Suppose -3*t = 3*p - 27, -t = 4*p + t - 34. Solve 3 + 0*o**3 - 4*o**3 - p*o**2 - 3 = 0 for o.
-2, 0
Factor 0 + 1/4*k**3 - 1/2*k**2 + 1/4*k.
k*(k - 1)**2/4
Let h be ((-176)/(-330))/(48/60). Solve 2/9*b**3 + 14/9*b + 10/9*b**2 + h = 0 for b.
-3, -1
Let r(v) be the second derivative of v**9/189 - v**8/168 + v**7/504 - 13*v**4/6 - v. Let c(f) be the third derivative of r(f). Factor c(o).
5*o**2*(4*o - 1)**2
Let y(h) be the third derivative of -2*h**7/21 - 4*h**6/15 - h**5/15 + h**4/3 - 146*h**2. Solve y(r) = 0 for r.
-1, 0, 2/5
Let y(o) be the third derivative of 25*o**8/336 + 4*o**7/21 + o**6/20 - 2*o**5/15 + o**4/24 - o**2 + 195*o. Suppose y(i) = 0. Calculate i.
-1, 0, 1/5
Let o(h) be the second derivative of -h**7/210 + 2*h**6/75 + h**5/25 - 11*h**4/30 - h**3/10 + 9*h**2/5 - h - 3. Determine q, given that o(q) = 0.
-2, -1, 1, 3
Let z(a) be the first derivative of -a**3/9 + 2*a**2/3 - a + 91. Factor z(c).
-(c - 3)*(c - 1)/3
Let j be -14 + 11 - 1969/(-657). Let d = 1979/2628 + j. Solve 3*i**3 - 3/2*i**2 + 27/4 - 9*i + d*i**4 = 0 for i.
-3, 1
Let a = 377 + -1507/4. Factor 1/4*m**2 - a*m**4 - 1/4*m**5 + 0 + 1/4*m**3 + 0*m.
-m**2*(m - 1)*(m + 1)**2/4
Let w be -324 + (-3 - 2*9/(-6)). Let a = -321 - w. Factor 2/9*x**5 + 0*x**a + 0*x + 2/3*x**4 + 0 - 8/9*x**2.
2*x**2*(x - 1)*(x + 2)**2/9
Let j(n) be the third derivative of -30*n**2 + 1/40*n**5 + 0*n + 0*n**3 + 1/240*n**6 + 0 + 1/24*n**4. Find b such that j(b) = 0.
-2, -1, 0
Let v(f) be the second derivative of f**7/252 - f**6/180 - f**5/60 + f**4/36 + f**3/36 - f**2/12 - 570*f. Determine s so that v(s) = 0.
-1, 1
Let v(q) = 5*q**3 + 105*q**2 + 225*q + 5. Let s(l) =