irst derivative of k**6/15 - k**5/5 - 7*k**4/6 - 4*k**3/3 - 2*k + 6. Let j(l) be the first derivative of g(l). Factor j(a).
2*a*(a - 4)*(a + 1)**2
Let o(a) be the first derivative of a**4/2 + 44*a**3/3 + 162. Solve o(q) = 0.
-22, 0
Suppose 0 = 2*b + 3*d - 19, -41 = -5*b - d - 0*d. Determine p so that 18*p - 8*p**2 + 15 + b*p**2 + 3*p**2 = 0.
-5, -1
Let o be (-4)/(-2)*(-4)/(-24). Let f = -2561/3 + 854. Find u such that 1/3*u**3 - o*u**4 + u**2 - 2/3 - f*u = 0.
-1, 1, 2
Let l(i) = 8*i**3 + 33*i**2 - 11*i - 3. Let c(m) = -7*m**3 - 30*m**2 + 9*m + 2. Let w(s) = 3*c(s) + 2*l(s). Factor w(x).
-x*(x + 5)*(5*x - 1)
Let p(s) = 3*s**3 - 2*s**2 + 1. Let z be p(1). Factor 8 + 4*q**2 + 4*q**2 - 6*q**z + 10*q.
2*(q + 1)*(q + 4)
Factor 216*m + 1/2*m**3 - 18*m**2 - 864.
(m - 12)**3/2
Factor w**2 + 6*w**3 - 4*w**3 - 10*w - 3*w**2 - 10 + 4.
2*(w - 3)*(w + 1)**2
Let o(h) = -h**3 - 3*h**2 - h + 4. Let m be o(-2). Let a be (1 - -19)*(-1)/(-2). Solve a*y - m*y**3 + 2*y**2 + 14 - 6 - 2 = 0 for y.
-1, 3
Let d(m) be the first derivative of 2*m**3/57 - 294*m**2/19 + 43218*m/19 - 294. Factor d(h).
2*(h - 147)**2/19
Let j(h) be the third derivative of -h**6/360 - h**5/20 - h**4/9 + 215*h**2. Suppose j(r) = 0. Calculate r.
-8, -1, 0
Let q(p) = 4*p**2 + 30*p + 15. Let u(l) be the third derivative of l**5/60 + 5*l**4/12 + 5*l**3/6 + 12*l**2. Let y(f) = 4*q(f) - 11*u(f). Factor y(z).
5*(z + 1)**2
Suppose 5*v + 8*v**4 - 23*v - 4 - 44*v**2 - 19*v**2 + 41*v**2 = 0. What is v?
-1, -1/2, 2
Let g(c) be the first derivative of c**6/27 - 2*c**5/45 - 5*c**4/18 + 10*c**3/27 + 4*c**2/9 - 8*c/9 + 112. Find a such that g(a) = 0.
-2, -1, 1, 2
Let j(b) be the second derivative of b**4/36 - b**3/2 + 4*b**2/3 + 5*b + 4. Factor j(v).
(v - 8)*(v - 1)/3
Suppose 0*m = 44*m - 264. Let u(d) be the first derivative of -7/18*d**m + 0*d - 1/6*d**4 + 0*d**3 - 5 + 0*d**2 + 3/5*d**5. Determine f so that u(f) = 0.
0, 2/7, 1
Let m(w) = 33*w**5 + 111*w**4 + 237*w**3 + 21*w**2 - 21*w. Let k(n) = -8*n**5 - 28*n**4 - 59*n**3 - 5*n**2 + 5*n. Let s(t) = -21*k(t) - 5*m(t). Factor s(r).
3*r**3*(r + 2)*(r + 9)
Let z(t) be the second derivative of -t**6/10 + 9*t**5/20 + 15*t**4/4 + 17*t**3/2 + 9*t**2 + t - 149. Find r, given that z(r) = 0.
-1, 6
Let r(y) = y**3 - 5*y**2 + 7*y + 15. Let j be r(7). Suppose j*v**2 + 38 - 51*v + 3*v**4 - 15*v**4 - 62 - 75*v**3 = 0. Calculate v.
-8, -1/4, 1
Let h(j) be the third derivative of 0 + 0*j - 1/40*j**6 + 33*j**2 - 1/4*j**5 - 2*j**3 - j**4. Factor h(q).
-3*(q + 1)*(q + 2)**2
Factor 14/9*x**2 + 2*x - 16/9 - 2*x**3 + 2/9*x**4.
2*(x - 8)*(x - 1)**2*(x + 1)/9
Let f(t) be the second derivative of t**8/15120 - t**7/7560 - t**6/1620 - 5*t**3/3 - 15*t. Let v(u) be the second derivative of f(u). Let v(m) = 0. What is m?
-1, 0, 2
Let i(t) be the second derivative of t**8/840 + t**7/210 - t**6/60 - t**5/15 + t**4/3 + 8*t**3/3 - 21*t. Let d(g) be the second derivative of i(g). Factor d(w).
2*(w - 1)**2*(w + 2)**2
Let x be 6 + 18/(-6) + (3 - 104/20). Factor -x*z + 2/5*z**3 - 1/5*z**4 + 3/5*z**2 - 4/5.
-(z - 2)**2*(z + 1)**2/5
Suppose -3*c - 12 = -2*m, -m - 4*c = -6*m + 23. Suppose -3 = -h - 1. Factor -2*q**m - q**4 - 2*q**3 + 4*q**h + 0*q**3 - 8*q**2.
-q**2*(q + 2)**2
Let j = 117 - 111. Let i(x) be the second derivative of 3*x + 0*x**2 + 1/30*x**j + 0*x**3 + 1/12*x**4 + 1/10*x**5 + 0. Let i(o) = 0. Calculate o.
-1, 0
Let d = 19 + -16. Determine k so that 37*k**3 - 39*k**d + k**5 + k**5 = 0.
-1, 0, 1
Let j be (-13 + 13)/((1 - 2)*3). Factor 0 - 2/23*t**3 - 6/23*t**4 + 0*t**2 + j*t + 8/23*t**5.
2*t**3*(t - 1)*(4*t + 1)/23
Let x(i) be the second derivative of -i**6/285 + i**4/19 + 8*i**3/57 + 3*i**2/19 + 16*i - 1. Factor x(c).
-2*(c - 3)*(c + 1)**3/19
Let h(b) be the second derivative of -2*b**6/15 - 9*b**5/5 - 14*b**4/3 - 14*b + 10. Factor h(k).
-4*k**2*(k + 2)*(k + 7)
Let f = -38 + 93. Let p(h) = -3*h. Let r be p(-1). Suppose -55*x + f*x + 10*x**2 - 5*x**r = 0. Calculate x.
0, 2
Let m(k) = -2*k**3 + 37*k**2 - 25*k + 5. Let l(y) = 3*y**3 - 56*y**2 + 37*y - 8. Let r(d) = 5*l(d) + 8*m(d). Factor r(h).
-h*(h - 15)*(h - 1)
Suppose 3*j + 2*j - 32 = -4*s, 0 = -4*s - 2*j + 20. Let g be (s + (-72)/21)/(8/(-56)). Determine o, given that -2*o**g + 0 + 0*o - 4/5*o**2 = 0.
-2/5, 0
Let y(n) = n**2 + 9*n + 66. Let x(t) = 4*t**2 + 29*t + 198. Let m(f) = 6*x(f) - 21*y(f). Determine p, given that m(p) = 0.
-6, 11
Let c(v) = -4*v**2 - 15*v - 53. Let l(x) = -15*x**2 - 45*x - 160. Let p(a) = 10*c(a) - 3*l(a). Factor p(j).
5*(j - 5)*(j + 2)
Suppose -3*z = 3*u, -5*z + z - 16 = 0. Let o(m) be the first derivative of -4 + 3/2*m**u - 3*m**2 + 0*m - m**3 + 3/5*m**5. Factor o(x).
3*x*(x - 1)*(x + 1)*(x + 2)
Let w(p) be the first derivative of -3/16*p**4 - 51 + 0*p**2 - 3/4*p**3 + 0*p. Factor w(j).
-3*j**2*(j + 3)/4
Let n = -15/544 - -2281/3808. Find q such that -4/7*q**3 + 10/7*q**2 - n*q + 0 = 0.
0, 1/2, 2
Suppose -6 + 6 = 2*x. Let o(g) be the second derivative of 0*g**4 - 1/210*g**7 + 0*g**2 - 5*g - 1/30*g**3 + 0*g**6 + 1/50*g**5 + x. Factor o(i).
-i*(i - 1)**2*(i + 1)**2/5
Determine a, given that 0*a**5 - 21*a**2 + 3*a**5 + 27*a**3 + 7*a - 13*a**4 - a - 2*a**4 = 0.
0, 1, 2
Let n(c) be the second derivative of c**7/7 - 4*c**6/15 - 43*c**5/10 - 28*c**4/3 - 20*c**3/3 + 9*c. Determine t, given that n(t) = 0.
-2, -1, -2/3, 0, 5
Let m(f) be the third derivative of f**7/42 + f**6/4 + f**5/4 - 65*f**4/12 - 20*f**3 - 262*f**2. Find v, given that m(v) = 0.
-4, -3, -1, 2
Let o(l) be the third derivative of -3*l**6/40 + 7*l**5/20 - l**4/4 - 5*l**2 + 2. Factor o(c).
-3*c*(c - 2)*(3*c - 1)
Let c(i) = -i**4 - i**3 + i - 1. Let r(m) = 4*m**4 - 4*m**3 + 11*m**2 - 8*m + 3. Let s(f) = -6*c(f) - 2*r(f). Find n such that s(n) = 0.
0, 1, 5
Let f(w) = w**2 + 9*w + 2. Let n be f(-10). Suppose n - 4 = 4*a. Factor -5*c**2 + 9*c**2 + a - 2.
4*c**2
Suppose -3*k + 20 = 11. Factor -4*x**k + 12*x - 8*x**2 + 1 + 2 - 3.
-4*x*(x - 1)*(x + 3)
Let y = -16 + 18. Suppose 5*f - 8 - y = 0. Factor 5*o**2 + 9 - o**f + 10 - 23 + 4*o**3 - 4*o.
4*(o - 1)*(o + 1)**2
Suppose 8*s = s - 259. Let y = s - -39. Find r such that -4/3 - y*r - 2/3*r**2 = 0.
-2, -1
Let j(k) be the third derivative of k**5/15 - k**4/3 - 6*k**2 + 2. Factor j(x).
4*x*(x - 2)
Let o = 12 - 7. Let v be 2/o*(8 - 12/4). Factor 2 - v*l + 1/2*l**2.
(l - 2)**2/2
Let m(r) be the third derivative of 0*r**4 + 0*r + 0*r**5 + 0*r**3 - 1/840*r**8 - 3*r**2 - 1/300*r**6 + 0 - 2/525*r**7. Factor m(q).
-2*q**3*(q + 1)**2/5
Let h(g) be the first derivative of 0*g + 56 + 1/7*g**2 + 0*g**3 - 1/14*g**4. Let h(q) = 0. Calculate q.
-1, 0, 1
Let r(i) be the third derivative of -i**8/20160 + i**7/3780 - i**6/2160 - i**4/8 - 2*i**2. Let u(x) be the second derivative of r(x). Factor u(m).
-m*(m - 1)**2/3
Let u(p) = 2*p - 2. Let b be u(2). Suppose 0 = 3*w - 5*s - 1, 4*w - 10 = -0*w - b*s. Let -8 - w*a + 11*a + 2 - 3*a**3 + 0*a**3 = 0. What is a?
-2, 1
Let z be 0*(4/(-24)*-3)/1. Suppose -10 = -3*d + 2*d - 4*a, -2 = -4*d + 3*a. Determine n, given that -3*n + n**3 + n**2 - 3 + d*n**2 + 2*n**3 + z*n**3 = 0.
-1, 1
Let i(c) be the third derivative of -c**6/840 - 2*c**5/105 + 19*c**4/168 - 5*c**3/21 + 14*c**2 - 12. Determine n, given that i(n) = 0.
-10, 1
Let w(n) = n**2 + 7*n + 5. Let r be w(-6). Let x be ((-7)/28)/(-2 - r). What is k in 0*k**2 - x*k**3 + 0 - 1/4*k**4 + 0*k = 0?
-1, 0
Solve -4 - 33/4*d - 1/4*d**3 - 9/2*d**2 = 0.
-16, -1
Let j be 28/6 - (206 - 202). Suppose j*l**2 + 0 - 1/6*l**3 - 1/2*l = 0. What is l?
0, 1, 3
Let w(c) be the second derivative of -c**3/3 + 4*c**2 + 4*c. Let o be w(3). Factor -2 - 10 + 4*a**o - 20*a + 4*a**3 - 6*a**2 - 2*a**2.
4*(a - 3)*(a + 1)**2
Let o(n) be the second derivative of -n**7/21 - 8*n**6/15 - 11*n**5/5 - 4*n**4 - 3*n**3 - 35*n - 4. Factor o(v).
-2*v*(v + 1)**2*(v + 3)**2
Let t(r) be the first derivative of 1/8*r**2 + 1/16*r**4 + 0*r - 17 - 1/6*r**3. Solve t(u) = 0.
0, 1
Let m(s) be the third derivative of 1/20*s**5 + 7/480*s**6 - 1/12*s**3 + 2*s**2 + 0*s + 1/32*s**4 + 0. Factor m(i).
(i + 1)**2*(7*i - 2)/4
Solve 14/3*b**4 - 64/3*b**2 - 2/3*b**5 - 4*b**3 + 0 + 64/3*b = 0.
-2, 0, 1, 4
Let s = 1359/1561 + -3/223. Let l(y) be the first derivative of -2/7*y**2 - s*y + 2/21*y**3 - 7. Factor l(b).
2*(b - 3)*(b + 1)/7
Let d(x) be the first derivative of -x**3/15 + 7*x**2/5 + 3*x - 96