
Let m(s) be the first derivative of -s**4/30 - 2*s**3/5 - 8*s**2/5 - 8*s/3 - 182. Find c, given that m(c) = 0.
-5, -2
Let m = -674/75 + 238/25. Solve -6/5*z - 4/5*z**2 - 2/15*z**3 - m = 0.
-4, -1
Let k(r) be the first derivative of 8 + 6*r**2 + 0*r - 2/3*r**3. Factor k(m).
-2*m*(m - 6)
Factor -164*r**2 + 6724*r - 201*r**3 + 412*r**3 - 210*r**3.
r*(r - 82)**2
Let i(w) = w**2 - 117*w + 3268. Let r be i(46). Solve 12/5 - 14/5*h - r*h**2 = 0.
-2, 3/5
Factor 100*r**2 + 45*r**2 + 2535 + 927*r + 308*r + 6*r**3 + 2*r**3 - 3*r**3.
5*(r + 3)*(r + 13)**2
Let p(i) be the first derivative of 2/9*i + 1/9*i**2 - 11 - 1/18*i**4 - 2/27*i**3. Factor p(b).
-2*(b - 1)*(b + 1)**2/9
Let k(o) = 40*o**2 - 695*o - 630. Let v(g) = 11*g**2 - 174*g - 157. Let l(h) = 4*k(h) - 15*v(h). What is z in l(z) = 0?
-33, -1
Let k(m) be the third derivative of m**7/7560 + m**6/720 + m**5/180 - m**4/4 + 10*m**2. Let w(l) be the second derivative of k(l). Determine x so that w(x) = 0.
-2, -1
Let h(n) be the third derivative of n**6/160 - n**5/40 - 21*n**4/32 - 9*n**3/4 + 532*n**2. Factor h(a).
3*(a - 6)*(a + 1)*(a + 3)/4
Let c(l) be the third derivative of l**5/50 - l**4/12 + 2*l**3/15 + 35*l**2. Factor c(z).
2*(z - 1)*(3*z - 2)/5
Let v(k) = -9*k**3 - 80*k**2 - 1604*k - 4. Let p(l) = -2*l**3 - l - 1. Let u(m) = -4*p(m) + v(m). Factor u(t).
-t*(t + 40)**2
Let f = -477/2 - -239. Let v(y) be the first derivative of -1/2*y**2 - 2 - f*y**3 + 0*y. Factor v(q).
-q*(3*q + 2)/2
Determine d so that -34*d - 96 - 3*d**4 - 28*d + 60*d + 42*d**3 + 84*d**2 - 3*d**5 - 22*d = 0.
-2, 1, 4
Let t(i) be the second derivative of i**8/1680 - i**7/630 - 13*i**4/12 + 15*i. Let y(s) be the third derivative of t(s). Factor y(p).
4*p**2*(p - 1)
Suppose 7*d - 3*d = 12. Determine y so that -3 - 9*y**2 - 168*y - 164*y + 341*y + d*y**3 = 0.
1
Let n(o) be the first derivative of -7*o**5/20 + o**4 - o**3/2 - o**2 - 27*o - 4. Let s(y) be the first derivative of n(y). Factor s(w).
-(w - 1)**2*(7*w + 2)
Suppose 43 = a - 93. Let y = 138 - a. Factor -q**y + 0 + 1/3*q**3 + 2/3*q.
q*(q - 2)*(q - 1)/3
Let g(u) = 2*u**2 + u + 1. Let l(p) = -3*p**4 - 10*p**3 + 37*p**2 + 41*p + 19. Let y(v) = 22*g(v) - 2*l(v). Let y(o) = 0. Calculate o.
-4, -1, -1/3, 2
Let a = -10397 - -72781/7. Suppose -2/7*x**2 + 2/7 + 2/7*x - a*x**3 = 0. Calculate x.
-1, 1
Factor 20 - 8 - 12 + r**3.
r**3
Let -1/5*t**2 + 8/5 - 2/5*t = 0. Calculate t.
-4, 2
Let v(h) = -2*h**2 - 5*h + 6. Let z be v(-3). Let f(u) be the first derivative of -1/2*u**2 - u + 2/3*u**z + 1/2*u**4 + 2 - 1/5*u**5 - 1/6*u**6. Factor f(y).
-(y - 1)**2*(y + 1)**3
Let y(h) be the first derivative of 3*h**5/5 - 201*h**4/4 - h**3 + 201*h**2/2 - 810. Factor y(n).
3*n*(n - 67)*(n - 1)*(n + 1)
Let y be 0/63*(-2)/(6/3). Let y*j + 5/3*j**2 + 0 = 0. Calculate j.
0
Let h(l) = l**3 + 12*l**2 - 14*l - 11. Let o be h(-13). Let f(m) be the first derivative of -21/4*m**4 - o*m - 61/6*m**3 - 7*m**2 - 9/10*m**5 + 4. Factor f(p).
-(p + 2)**2*(3*p + 1)**2/2
Let p(k) = -k**2 - 9*k + 32. Let h be p(-14). Let i = h + 40. What is s in -1/2 + 3/2*s + i*s**2 = 0?
-1, 1/4
Factor -2/7*j**3 + 4/7 + 4/7*j - 3/7*j**2 + 1/7*j**4.
(j - 2)**2*(j + 1)**2/7
Let s(q) be the second derivative of -q**8/8400 + q**7/4200 + q**6/1800 - q**5/600 + q**3/2 - 8*q. Let o(l) be the second derivative of s(l). Factor o(g).
-g*(g - 1)**2*(g + 1)/5
Let c(y) be the first derivative of y**7/280 - y**6/60 - y**5/40 + y**4/4 + 19*y**3/3 - 10. Let u(j) be the third derivative of c(j). Factor u(g).
3*(g - 2)*(g - 1)*(g + 1)
Let o(f) be the first derivative of -f**5/12 + 5*f**4/12 + 19*f**2/2 + 34. Let j(y) be the second derivative of o(y). Factor j(p).
-5*p*(p - 2)
Let b = -16 - -19. Suppose 20 = 5*y - 0. Suppose 17*g + y + 0*g**4 + 6*g**b - 5*g + 13*g**2 + g**4 + 0 = 0. Calculate g.
-2, -1
Let m(b) be the first derivative of -b**7/147 + 2*b**6/105 + 2*b**5/105 - 51*b**2/2 - 38. Let i(n) be the second derivative of m(n). Let i(d) = 0. Calculate d.
-2/5, 0, 2
Let t(z) = 5*z**2 - 12*z + 20. Let g(i) = 11*i**2 - 25*i + 41. Let s = 61 + -65. Let l(o) = s*g(o) + 9*t(o). Find j such that l(j) = 0.
4
Let q(x) be the third derivative of 0*x**5 + 1/200*x**6 + 1/175*x**7 + 0*x + 0*x**3 - 3/560*x**8 + 0 + 0*x**4 + 16*x**2. Find b such that q(b) = 0.
-1/3, 0, 1
Let f be 4/(24/(-238)) - 7/(-42). Let u = 41 + f. Factor u*y**3 + 0 + 1/4*y**2 + 9/4*y**4 + 0*y.
y**2*(3*y + 1)**2/4
Let w(g) = -3*g - 118. Let u be w(-40). Factor 14/11*a**3 - 2/11*a**4 + 40/11*a - 36/11*a**u - 16/11.
-2*(a - 2)**3*(a - 1)/11
Factor -10*v**2 - 32 - 48*v + 12*v**2 - 16*v - 224 - 6*v**2.
-4*(v + 8)**2
Let g = 13 + -7. Let k = g - 3. Factor 23*s**5 + 14*s**4 - 15*s**5 + 4*s + 4*s**k - 4*s - 2*s**2.
2*s**2*(s + 1)**2*(4*s - 1)
Suppose 6*u + 29 = 137. Suppose -3 = -7*a + u. Find h such that 4/3*h**a - 4*h**4 - 4/3*h**5 - 16/3 + 28/3*h**2 + 0*h = 0.
-2, -1, 1
Factor 135/7*h - 1/7*h**3 + 6/7*h**2 + 400/7.
-(h - 16)*(h + 5)**2/7
Determine m so that -16*m**5 - 200*m**3 + 644024 + 116*m**4 - 644024 + 100*m**2 = 0.
0, 1, 5/4, 5
Let i(r) be the first derivative of 0*r - 1/6*r**4 + 4/9*r**3 - 1/3*r**2 + 20. Factor i(g).
-2*g*(g - 1)**2/3
Let l(h) be the second derivative of 0*h**2 - 1/63*h**7 - 8*h - 1/18*h**4 + 0 + 0*h**3 - 1/10*h**5 - 1/15*h**6. Let l(p) = 0. What is p?
-1, 0
Factor 4/3*j + 1/3*j**4 + 0 + 8/3*j**2 + 5/3*j**3.
j*(j + 1)*(j + 2)**2/3
Let g be 34/(-7) + 445/89. Let f(a) be the first derivative of 4/35*a**5 + 0*a**4 + 4 + 0*a + 1/21*a**6 - 4/21*a**3 - g*a**2. Determine v, given that f(v) = 0.
-1, 0, 1
Let h(x) be the second derivative of x**6/45 + x**5/5 - 4*x**4/9 - 2*x**3/3 + 7*x**2/3 - x. Suppose h(q) = 0. Calculate q.
-7, -1, 1
Let h(w) be the first derivative of w**5/20 - 35*w**4/8 + 132*w**3 - 1296*w**2 - 6912*w + 277. Let h(z) = 0. Calculate z.
-2, 24
Let h(s) be the third derivative of -s**5/15 + 2*s**4 + 56*s**3/3 + 274*s**2. Let h(c) = 0. What is c?
-2, 14
Let y = -36 - -30. Let f(s) = s**3 + 7*s**2 + 11*s + 30. Let o be f(y). Let -1/8*n**3 - 1/8*n**2 + 1/4*n + o = 0. Calculate n.
-2, 0, 1
Let v be (-20 - 544/(-18)) + 0 + -8. Suppose -v*n**2 - 8/9 + 28/9*n = 0. Calculate n.
2/5, 1
Let 38/3*q**3 + 52/3*q**2 - 10/3*q - 8 = 0. What is q?
-1, 12/19
Suppose 8*v = 3*v + 25. Determine c so that -3*c - 4*c + 4*c**v + 7*c**3 + 2 - 13*c**4 + 0*c**2 + 11*c**2 - 4*c = 0.
-1, 1/4, 1, 2
Let g(p) = -p**2 + 33*p - 11. Let m(h) = 6*h - 2. Let z(q) = -2*g(q) + 11*m(q). What is a in z(a) = 0?
0
Let t(y) be the third derivative of -1/3*y**3 + 0 - 1/24*y**4 - 4*y**2 + 0*y + 1/60*y**5. Factor t(j).
(j - 2)*(j + 1)
Let p(i) be the third derivative of -i**7/350 - 9*i**6/200 - 3*i**5/10 - 11*i**4/10 - 12*i**3/5 + 11*i**2. Solve p(x) = 0.
-3, -2
Let r = -97 + 103. Let -4*h**3 + 2*h**2 - 16*h + r*h**2 + 12*h = 0. Calculate h.
0, 1
Let g be (-11)/(-28) - (247/(-52))/(-19). Factor -g*o**2 - 16/7 - 8/7*o.
-(o + 4)**2/7
Let z(d) be the second derivative of d**2 + 0 + 1/6*d**4 + 2/3*d**3 + 13*d. Factor z(i).
2*(i + 1)**2
Factor -61*z**4 + 56*z**4 + 40*z - 3*z**2 - 10*z**3 + 23*z**2.
-5*z*(z - 2)*(z + 2)**2
Let t(a) = 5*a**2 + 6*a + 1. Let i(c) = -6*c**2 - 7*c - 1. Let b = -15 + 12. Let o(r) = b*t(r) - 2*i(r). Solve o(y) = 0 for y.
-1, -1/3
Let a = 1279 - 1273. Let q(z) be the first derivative of z**2 + 12 - 1/9*z**a - 1/3*z**4 - 4/9*z**3 + 2/5*z**5 - 2/3*z. Suppose q(p) = 0. What is p?
-1, 1
Factor 0*c + 0*c**2 + 2*c**3 + 0 + 2/9*c**5 + 20/9*c**4.
2*c**3*(c + 1)*(c + 9)/9
Suppose -l + 14 = 5*o + 2*l, o + l - 2 = 0. Factor -6*u**2 - o*u - 2*u**2 + 4*u**2 + 0*u**2.
-4*u*(u + 1)
Suppose 3*k + v - 6 = 0, -5*k + 2*v = -284 + 263. Suppose 2/7*m**k + 4/7*m**2 + 0 + 0*m = 0. Calculate m.
-2, 0
Let f(j) be the second derivative of -5*j**4/12 - 5*j**3/2 - 2*j + 1. Factor f(d).
-5*d*(d + 3)
Let y(w) = 6*w**3 + 7*w**2 - 4*w + 5. Let c(s) = -5*s**3 - 6*s**2 + 3*s - 4. Let q(g) = -5*c(g) - 4*y(g). What is m in q(m) = 0?
-1, 0
Let d(o) = o**3 - 3*o**2 + 4*o - 1. Let q be d(3). Let k(l) = -4*l + 11. Let c be k(2). Solve -33*u**c + 33*u**2 - 17 - 4*u + u + q + 9*u**4 = 0.
-1/3, 1, 2
Let t(q) be the second derivative of -q**6/72 - 5*q**3/2 - 10*q. Let s(y) be the second derivative of t(y). Solve s(u) = 0 for u.
0
Suppose -16 = -4*t, -l - 6*t + t = -17. Let u be (6/45)/(l/(-5)). Factor 8/9*w - u*w**4 + 0 + 0*w**2 