7
Let t(y) = -y**3 - 2*y**2 - y - 1. Let i(c) be the third derivative of 0 + 0*c + 13*c**2 + 1/6*c**3. Let n(s) = 4*i(s) + 4*t(s). Factor n(a).
-4*a*(a + 1)**2
Let r = 3 - 1. Factor 3 - 7 + 2*f**3 - 2*f + 2 + r*f**2.
2*(f - 1)*(f + 1)**2
Let x(z) = 2*z**3 + z + 1. Let f(b) = 12*b**3 - 60*b**2 + 180*b + 4. Let a(n) = f(n) - 4*x(n). Determine g so that a(g) = 0.
0, 4, 11
Let q(a) = -25*a**3 + 35*a**2 + 215*a - 155. Suppose -4*k + 17 - 157 = 0. Let p(b) = 2*b**3 - 3*b**2 - 18*b + 13. Let d(v) = k*p(v) - 3*q(v). Factor d(j).
5*(j - 1)**2*(j + 2)
Determine w so that -200 + 590*w - 80 - 2*w**3 + 303*w**2 - 38*w**2 + 5*w**3 + 22*w**3 = 0.
-7, -4, 2/5
Let y(c) be the first derivative of 5*c**7/42 + c**6/6 - 3*c**5/4 - 5*c**4/12 + 5*c**3/3 + 3*c + 17. Let t(u) be the first derivative of y(u). Factor t(g).
5*g*(g - 1)**2*(g + 1)*(g + 2)
Let x(w) be the third derivative of w**5/420 + 7*w**4/24 + 23*w**3/7 + 31*w**2 + 9*w. Factor x(i).
(i + 3)*(i + 46)/7
Let i = 937 + -935. Find g such that -1/2*g**i + 1/2*g + 0 = 0.
0, 1
Determine b so that -4/5*b**4 + 0 - 4/5*b**2 - 16/5*b**3 + 24/5*b = 0.
-3, -2, 0, 1
Let n be (-16)/88 + 10/55. Let q(m) be the third derivative of 0*m + n*m**4 + 0*m**3 + 0 + 1/120*m**5 - m**2. Factor q(o).
o**2/2
Let 11/4*f**3 - 21/2*f**2 - 5/2 - 63/4*f = 0. Calculate f.
-1, -2/11, 5
Let w(k) be the first derivative of 31*k**4/22 - 4*k**3/33 - 96. Solve w(r) = 0 for r.
0, 2/31
Let s(t) be the third derivative of t**7/7560 + t**6/432 + t**5/90 - 7*t**4/12 - 23*t**2. Let z(i) be the second derivative of s(i). Factor z(w).
(w + 1)*(w + 4)/3
Let p = 113 + -104. Suppose 4*i + 4*n - p = n, 4*n = -4. Factor -2/5*m**4 - 4/5*m + 2/5 + 0*m**2 + 4/5*m**i.
-2*(m - 1)**3*(m + 1)/5
Let p(w) be the third derivative of w**7/140 + w**6/8 + 27*w**2. Determine a so that p(a) = 0.
-10, 0
Find o such that -12074 - 3*o**2 - 129*o - 7040 - 1592 + 3831 + 579*o = 0.
75
Suppose -4*z - 3*d = 7, -4*z + 3*d + 23 = -0*z. Suppose 5*k = k + 8. Factor -x**2 - k*x**3 + 6*x + 16 - 12 + x**z.
-2*(x - 2)*(x + 1)**2
Let h be (-9429)/630 + 16 - (-20)/(-24). What is s in 8*s + 12/5 + 3/5*s**2 + h*s**4 - 27/5*s**3 + 3/5*s**5 = 0?
-3, -1, -1/3, 2
Let d = -1269 + 1273. Let n(j) be the first derivative of 0*j**2 + 0*j - 10 + 1/27*j**6 + 2/27*j**3 - 1/18*j**d - 2/45*j**5. Determine x so that n(x) = 0.
-1, 0, 1
Suppose -43*g + 8 = -47*g, -w + 5*g = -12. Find q such that 338/9*q**w - 104/9*q + 8/9 = 0.
2/13
Let n(c) be the first derivative of 3*c**4/4 - 5*c**3 + 6*c**2 - 341. Find m, given that n(m) = 0.
0, 1, 4
Let p(x) be the third derivative of -5*x**7/112 + x**6/16 + 3*x**5/5 - 5*x**4/4 + x**3 - 3*x**2 - 20*x. Solve p(r) = 0 for r.
-2, 2/5, 2
Let s(u) = -2*u**3 - 4*u**2 - 2*u + 3. Let i be s(-2). Factor -5*l + l**5 + 4*l**4 + i*l**2 + 4*l**3 + 11*l**2 - 30*l**2 - 2 + 10*l**2.
(l - 1)*(l + 1)**3*(l + 2)
Suppose -21 = 2*n - 3*i - 24, -4*n + 2*i + 10 = 0. Factor -n*v**3 + 0 - 25/3*v**2 + 2*v.
-v*(v + 3)*(9*v - 2)/3
Let v(o) be the first derivative of -o**4/3 + 8*o**3 - 72*o**2 - 2*o - 1. Let x(i) be the first derivative of v(i). Factor x(j).
-4*(j - 6)**2
Let y(i) be the third derivative of -i**5/20 - i**4/6 - 2*i**3/9 - 12*i**2 + 5. Factor y(g).
-(3*g + 2)**2/3
Let m(p) be the third derivative of 0 - 14*p**2 + 0*p**5 + 0*p - 1/14*p**4 + 1/840*p**6 - 8/21*p**3. Factor m(q).
(q - 4)*(q + 2)**2/7
Let u be -4 - (-3 - 4)*1. Let 3*m - 6*m**u + 4 - m**4 + 0*m**3 - m**2 - 2 + 3*m**3 = 0. Calculate m.
-2, -1, 1
Suppose -4 = 2*z + 5*m + 6, 0 = 5*z - 3*m - 37. Suppose z*c - 16*c = -22. Factor -4/7*t - 2/7*t**c - 2/7.
-2*(t + 1)**2/7
Let g(j) = 8*j - 93. Let b be g(12). Let f(l) be the first derivative of b*l + 1/9*l**3 + 12 - l**2. Find q, given that f(q) = 0.
3
Let f = -5/193 - -208/579. Let y(m) be the second derivative of 0 + 0*m**2 + 2*m + 3/20*m**5 + f*m**4 - 1/42*m**7 - 1/15*m**6 - 2/3*m**3. Factor y(i).
-i*(i - 1)**2*(i + 2)**2
Let k be (-15)/(540/(-8)) + (-5)/(-45). Solve 0 - k*v + 1/6*v**2 = 0 for v.
0, 2
Let w(o) be the first derivative of -o**6 + 27*o**5/10 + 15*o**4/4 - 19*o**3/2 - 9*o**2 + 6*o - 69. Solve w(n) = 0 for n.
-1, 1/4, 2
Let j(f) be the second derivative of f**5 + 595*f**4/12 + 725*f**3 - 1125*f**2/2 + 94*f. Let j(i) = 0. Calculate i.
-15, 1/4
Suppose -50*z + 38*z = -24. Solve 0 + 2/15*i - 2/15*i**z = 0.
0, 1
Determine q, given that 24*q**2 + 19*q**3 + 4*q**5 - 4*q**3 + q**5 - 36*q**4 - 9*q + q**5 + 6*q**5 - 6 = 0.
-1/2, 1, 2
Let y(z) be the third derivative of -z**5/60 + z**4/6 + 7*z**3/2 - 306*z**2. Let y(f) = 0. What is f?
-3, 7
Find k such that -11*k**4 + 35*k**2 - k**4 + 3*k**5 + 3*k - 23*k**2 + 9*k**3 - 15*k = 0.
-1, 0, 1, 2
Let j(d) be the first derivative of d**5 + 5*d**4/4 - 20*d**3/3 - 10*d**2 + 186. Factor j(v).
5*v*(v - 2)*(v + 1)*(v + 2)
Suppose 15 = 2*m - w, m + 4*w = 3*m - 30. Let i(c) = 2*c**4 - 9*c**3 - 9*c**2 + 2*c - 5. Let d(y) = y**4 + y - 1. Let q(x) = m*d(x) - i(x). Factor q(v).
3*v*(v + 1)**3
Let j be -1 + 3 + 0/(-4). Suppose 5*c + g = 40, c - 2 + 5 = j*g. Factor 2*y**2 + y**3 - c*y**4 + y**3 + 5*y**4 - 2*y.
-2*y*(y - 1)**2*(y + 1)
Let b(v) be the third derivative of 0*v**3 - 1/840*v**8 + 0 + 0*v - 2/75*v**5 - 4/525*v**7 - 1/60*v**4 + 11*v**2 - 1/50*v**6. Factor b(q).
-2*q*(q + 1)**4/5
Let n(c) be the first derivative of 3/22*c**4 + 0*c + 2/55*c**5 - 17 - 4/11*c**2 + 0*c**3. Factor n(k).
2*k*(k - 1)*(k + 2)**2/11
Let z = -1779/116 - -655/29. Factor -t**2 + z*t - 7/4.
-(t - 7)*(4*t - 1)/4
Let q(s) = 3*s**3 - 2*s**2 + s + 4. Let k be q(3). Let o be (2 - k/36)*8. Find x, given that -o - 2/9*x**2 + 2/3*x = 0.
1, 2
Suppose 0 = 4*x - 12, 4*q + 8 - 35 = -5*x. What is g in -90*g**2 + 7*g - q*g**3 - g**3 + 102*g**2 + 9*g = 0?
-1, 0, 4
Let d be ((2/(-6))/((-9)/(-72)))/(-1). Let q(w) be the first derivative of 1 + 0*w + d*w**3 - 4*w**2 - 1/2*w**4. Factor q(z).
-2*z*(z - 2)**2
Let z(l) be the second derivative of l**4/9 - 428*l**3/9 + 22898*l**2/3 + 239*l. What is t in z(t) = 0?
107
Let i(c) = -c**3 + 24*c**2 - 42*c - 37. Let r be i(22). Let v(n) = n**3 - 9*n**2 + 13*n + 9. Let y be v(r). Factor 2/9*d + 2/9*d**y + 0.
2*d*(d + 1)/9
Suppose -56 - 59 = -23*r. Let y(x) be the second derivative of 2/15*x**3 + 2*x - 2/25*x**r + 0*x**2 + 0 + 1/30*x**4 - 1/25*x**6. Let y(b) = 0. What is b?
-1, 0, 2/3
Let u(a) be the second derivative of -a**7/56 + a**6/40 + 63*a**5/80 - 45*a**4/16 + 389*a. Factor u(g).
-3*g**2*(g - 3)**2*(g + 5)/4
Let w = 2176 + -2174. Let n(c) = c**2 - 2*c - 3. Let o be n(3). Suppose -2*t**w - 8/3*t**3 + o + 2/3*t = 0. Calculate t.
-1, 0, 1/4
Let h(w) = -w + 8. Let p be h(10). Let u be (-48)/(-28) - p/7. Solve -12*k + 3*k - 2*k**2 - 4 - k**2 - u = 0.
-2, -1
Let u = 152 - 299/2. Find v such that 25/2*v**2 + u*v**3 + 0 + 10*v = 0.
-4, -1, 0
Let p be -1*(2554/(-34) + 4/34). Let a = 677/9 - p. Determine r so that -8/9*r + a + 2/3*r**2 = 0.
1/3, 1
Let l = 338 - 336. Factor 0 + m**l - 1/2*m - 5/8*m**3 + 1/8*m**4.
m*(m - 2)**2*(m - 1)/8
Let v(i) = -2*i**3 + 2*i**2 + 4*i + 3. Let b(c) = 3*c**3 - 4*c**2 - 7*c - 5. Let y(f) = 4*f + 31. Let l be y(-9). Let o(r) = l*v(r) - 3*b(r). Factor o(m).
m*(m + 1)**2
Let m(u) be the first derivative of u**5 - 270*u**4 + 59390*u**3/3 - 57780*u**2 + 57245*u + 713. Factor m(n).
5*(n - 107)**2*(n - 1)**2
Suppose -101 = -14*g - 1921. Let k be ((-20)/(-4) - 10)*4/g. Let k*a**4 + 4/13*a**3 + 8/13 - 8/13*a - 6/13*a**2 = 0. What is a?
-2, 1
Let l(r) be the second derivative of r**5/80 + r**4/6 - 19*r**3/24 + 5*r**2/4 - 47*r. Factor l(s).
(s - 1)**2*(s + 10)/4
Let n(t) be the second derivative of -1/63*t**7 + 4/9*t**4 + 10*t + 7/9*t**3 - 2/45*t**6 + 1/15*t**5 + 2/3*t**2 + 0. Determine u, given that n(u) = 0.
-1, 2
Let j(a) = 9*a - 18. Let h be j(9). Let o = 321/5 - h. Factor 2/5*t**5 - 4/5*t - o*t**3 + 2/5*t**4 - 2*t**2 + 0.
2*t*(t - 2)*(t + 1)**3/5
Let g be ((-12)/(-24))/(1/8). Let h(n) be the third derivative of 0*n + 0*n**3 - 5*n**2 + 0 - 1/5*n**5 + 1/8*n**g. Factor h(w).
-3*w*(4*w - 1)
Determine s so that -336/5*s**2 + 1024/5 - 2/5*s**4 + 46/5*s**3 + 128*s = 0.
-1, 8
Let g(l) be the third derivative of -l**9/423360 - l**8/70560 - 2*l**5/15 + 17*l**2. Let x(s) be the third derivative of g(s). Determine u, given that x(u) = 0.
-2, 0
Let p(r) be the first derivative of -r**6/36 + 4*r**5/15 + 5*r**4/4 + 16*r**3/9 + 11*r**2/1