u**2 - l = 0.
-3
Let r(c) = 8*c**4 + 20*c**3 + 20*c**2 + 12*c + 4. Let b(p) = -p**4 - p**3 - p - 1. Let y(i) = 4*b(i) + r(i). Determine d, given that y(d) = 0.
-2, -1, 0
Let l(m) be the first derivative of m**3/3 + m**2 + m + 14. Let k(w) = w + 1. Let r(i) = k(i) - l(i). Factor r(p).
-p*(p + 1)
Suppose 0 = 9*i - 23 - 4. Let q(x) be the second derivative of 0*x**2 - 1/6*x**4 + 4*x - 1/3*x**6 + 0 - 4/5*x**5 + 2/3*x**i. Factor q(n).
-2*n*(n + 1)**2*(5*n - 2)
Suppose -5*k + 2 = -6*k. Let f be ((-12)/(-30))/(k/(-20)). Factor 86*t - 2*t**f - 2*t + 20*t**3 - 72*t**2 + 24*t - 54.
-2*(t - 3)**3*(t - 1)
Factor -2/3*q**3 - 46/3 + 30*q - 14*q**2.
-2*(q - 1)**2*(q + 23)/3
Let c(p) = 48*p**2 - 543*p + 1695. Let y = 47 - 49. Let f(h) = -3*h**2 + 34*h - 106. Let b(a) = y*c(a) - 33*f(a). Factor b(x).
3*(x - 6)**2
Let x be (-66)/(-56) - (-9)/(-21). Let p(w) be the first derivative of x*w**2 - 11 + w + 1/6*w**3. Factor p(g).
(g + 1)*(g + 2)/2
Let p(g) be the first derivative of g**6/6 + 24*g**5/5 + 89*g**4/4 - 646*g**3/3 + 462*g**2 - 392*g + 133. Suppose p(k) = 0. What is k?
-14, 1, 2
Let z(f) be the first derivative of -f**5/210 + 4*f**4/21 - 64*f**3/21 - 11*f**2/2 - 26. Let p(c) be the second derivative of z(c). Factor p(h).
-2*(h - 8)**2/7
Suppose 1/2*q**2 + 11/2*q - 6 = 0. What is q?
-12, 1
Let g be 5/(0/2 - -1). Suppose 0 = -f - 5*p + 13, p = 240*f - 237*f - 7. Suppose g*j + 7/3*j**2 + 1/3*j**f + 3 = 0. Calculate j.
-3, -1
Factor 69*g - g**3 - 20*g**2 - 108*g + 83*g.
-g*(g - 2)*(g + 22)
Let b(c) be the third derivative of c**8/80640 + c**7/20160 - c**6/1440 - 3*c**5/20 + 3*c**2. Let x(o) be the third derivative of b(o). Factor x(j).
(j - 1)*(j + 2)/4
Suppose -3*m + 2*z + 110 = m, -z + 35 = m. Let n be (-2)/3 + 620/m. Suppose 4*l**3 - n*l + 2*l**2 + 12 - 2*l**2 + 4*l**2 = 0. Calculate l.
-3, 1
Let b(w) be the second derivative of -2*w**6/15 + 12*w**5/5 + 5*w**4 - 52*w**3/3 - 2*w + 396. Factor b(a).
-4*a*(a - 13)*(a - 1)*(a + 2)
Let o(c) = -c**3 - 4*c**2 + 14. Let u be o(-3). Let q(y) be the first derivative of -y**4 + 0*y**2 - 5 - 2/5*y**u + 0*y + 1/3*y**6 + 0*y**3. Factor q(t).
2*t**3*(t - 2)*(t + 1)
Factor 18 - 69 - 5*q**2 - 83 + 33 + 360*q - 254.
-5*(q - 71)*(q - 1)
Suppose 2*g + 23 - 1 = 0. Let n = g - -13. Suppose 2*c**3 + 84 + n*c**4 - 84 - 4*c**2 = 0. Calculate c.
-2, 0, 1
Let v(i) be the first derivative of i**5/4 - 10*i**3/3 - i + 2. Let y(s) be the first derivative of v(s). Factor y(u).
5*u*(u - 2)*(u + 2)
Let t(n) be the first derivative of n**6/5 + 8*n**5/25 - 19*n**4/10 - 16*n**3/15 + 12*n**2/5 + 56. Let t(r) = 0. Calculate r.
-3, -1, 0, 2/3, 2
Let p(i) be the third derivative of -5/6*i**6 + 19/6*i**4 + 8/3*i**5 + 0 - 33*i**2 + 4/3*i**3 + 0*i. Factor p(c).
-4*(c - 2)*(5*c + 1)**2
Factor 17/4 - 9/2*t + 1/4*t**2.
(t - 17)*(t - 1)/4
Let m(g) = 3*g**3 + 11*g**2 + 34*g + 22. Let z(f) = -13*f**3 - 43*f**2 - 137*f - 89. Let b(p) = 9*m(p) + 2*z(p). Factor b(s).
(s + 1)*(s + 2)*(s + 10)
Determine q, given that 8/3*q + 2/3*q**5 - 10/3*q**3 + 0*q**2 + 0 + 0*q**4 = 0.
-2, -1, 0, 1, 2
Let n(z) = -z**2 - z. Let m(x) = -5*x**2 - 4*x. Let k be 0 + (-1 - (-15)/(-5)). Let o(a) = k*n(a) + m(a). Factor o(q).
-q**2
Suppose 3*r - 28 = u + 15, -5*u - 85 = -5*r. Suppose -1 = -2*f + 15. Solve 2 + f*q + 2*q**2 - r*q + q = 0.
1
Let t be -1 + (2 + 1)/(-3) + 8. Suppose -5*j = -3*j - t. Factor 0 + 0*g - 1/2*g**2 - 1/2*g**j.
-g**2*(g + 1)/2
Find g such that -2*g**5 + 58*g + 6*g + 19*g**2 - 60*g**3 + 13*g**2 + 106*g**4 - 138*g**4 - 2*g**5 = 0.
-4, -1, 0, 1
Let d(f) be the first derivative of -3*f**4/32 - 3*f**3/2 - 33*f**2/16 + 102. Factor d(m).
-3*m*(m + 1)*(m + 11)/8
Let w(v) be the first derivative of 1/7*v**2 + 15/14*v**4 - 21 + 0*v - 16/21*v**6 - 16/35*v**5 + 16/21*v**3. Suppose w(l) = 0. Calculate l.
-1, -1/4, 0, 1
Let c(u) = -2*u**4 - 2*u**2 - u + 1. Let t(f) = -7*f**4 + 39*f**3 - 36*f**2 + 14*f - 2. Let v(b) = -6*c(b) - 3*t(b). Factor v(o).
3*o*(o - 2)*(o - 1)*(11*o - 6)
Let a(n) = -2*n**3 - 9*n**2 - 4*n - 11. Let c be a(-5). Suppose -18*w = -w - c. Factor 0*h**w + 4/3*h**4 + 0*h**3 + 0 - 4/3*h**5 + 0*h.
-4*h**4*(h - 1)/3
Let x(p) = -p**3 - 10*p**2 - 9*p. Suppose 3*w = -0*a + 5*a + 19, -4*a - 18 = -w. Let h(q) = -q**3 - q**2. Let r(n) = w*h(n) - x(n). Factor r(y).
3*y*(y + 1)*(y + 3)
Factor 56/15*i + 2/15*i**2 + 392/15.
2*(i + 14)**2/15
Let i(o) be the first derivative of o**6/3 + 22*o**5/5 + 9*o**4 - 4*o**3/3 - 19*o**2 - 18*o - 224. Factor i(h).
2*(h - 1)*(h + 1)**3*(h + 9)
Suppose 9*q - 42 = -24. Find r such that -2/7*r + 4/7*r**q + 0 - 2/7*r**3 = 0.
0, 1
Suppose 0 = -9*n + 40*n - 93. Factor 0*y + 2/7*y**n - 6/7*y**2 + 8/7.
2*(y - 2)**2*(y + 1)/7
Let x(l) be the second derivative of 0 + 2*l**2 + 0*l**4 + 0*l**3 + 3*l + 1/300*l**5. Let b(u) be the first derivative of x(u). Find q, given that b(q) = 0.
0
Let l(h) be the third derivative of -2*h**7/105 + 4*h**6/15 - 4*h**5/5 - 3*h**2 - 3. Factor l(t).
-4*t**2*(t - 6)*(t - 2)
Let p(d) = -33*d + 170. Let y be p(5). Factor 12/5*a**3 + 0 + 8/5*a**4 + 2/5*a**y + 8/5*a**2 + 2/5*a.
2*a*(a + 1)**4/5
Let k(j) be the third derivative of -27*j**6/220 + 39*j**5/110 - 10*j**4/33 + 4*j**3/33 - j**2 + 2. Factor k(a).
-2*(a - 1)*(9*a - 2)**2/11
Solve 480 + 264*m + 3/2*m**3 + 42*m**2 = 0 for m.
-20, -4
Factor 1/2*y**2 + 45 - 91/2*y.
(y - 90)*(y - 1)/2
Let u = 11114 - 11110. Find f, given that 3/2*f**u - 9/2*f**3 + 0*f**2 + 0 + 6*f = 0.
-1, 0, 2
Let z(a) be the first derivative of -a**3 - 96*a**2 - 3072*a - 64. Find y such that z(y) = 0.
-32
Let d be (-9002)/(-630) - 14 - (-1 + 8/9). Determine b so that d*b**2 + 0 - 2/5*b = 0.
0, 1
Let l(j) be the third derivative of j**6/480 + 2*j**5/15 + 31*j**4/96 + j**2 + 27. Factor l(v).
v*(v + 1)*(v + 31)/4
Solve -18*g + 3/2*g**2 + 48 = 0 for g.
4, 8
Solve 39*d**2 + 48 + 116*d - 28*d**2 + 65*d**2 + 4*d**4 - 2*d**4 + 14*d**2 + 24*d**3 = 0.
-6, -4, -1
Let x(v) = -7*v**2 - 4*v + 9. Let k(t) = t**2 - 3*t - 4. Let j be k(5). Let n(r) = -13*r**2 - 7*r + 17. Let o(h) = j*n(h) - 11*x(h). What is b in o(b) = 0?
-1, 3
Find z, given that 30 + 6*z**2 - 37*z**3 + 40*z**3 - 21*z - 18*z**2 = 0.
-2, 1, 5
Let y(m) be the third derivative of m**10/30240 - m**9/5040 + m**8/3360 - m**4/4 + 17*m**2. Let a(w) be the second derivative of y(w). Factor a(z).
z**3*(z - 2)*(z - 1)
Determine t so that -5/2*t**4 - 55*t**3 + 55*t + 60*t**2 - 115/2 = 0.
-23, -1, 1
Let g(d) be the first derivative of -d**8/3920 + d**6/420 - d**4/56 - 8*d**3/3 + 4. Let x(y) be the third derivative of g(y). Determine l, given that x(l) = 0.
-1, 1
Factor 0 + 8*j - 4/3*j**4 - 4/3*j**2 - 16/3*j**3.
-4*j*(j - 1)*(j + 2)*(j + 3)/3
Let k(s) be the third derivative of -s**6/24 + 7*s**5/3 + 145*s**4/24 + 100*s**2. Factor k(o).
-5*o*(o - 29)*(o + 1)
Let a = 10 + -82. Let o be (-1)/((-2)/(-4)) + a/(-27). Factor 1/3*d + o*d**2 - 1/3.
(d + 1)*(2*d - 1)/3
Let m(w) be the second derivative of w**6/24 - 43*w**5/16 + 25*w**4/6 + 35*w**3/2 - 478*w. Factor m(g).
5*g*(g - 42)*(g - 2)*(g + 1)/4
Let t be (2/(-4)*(3 + -3))/(-2). Solve t*g + 0*g + 9 - 6*g - 3*g**2 = 0.
-3, 1
Factor 2/3*l**2 - 6*l + 12.
2*(l - 6)*(l - 3)/3
Factor 0*p - 10*p**3 + 0*p + 3*p**3 + 12*p**3 - 90*p**2.
5*p**2*(p - 18)
Suppose 65 = -2*j + 191. Factor 245 - 5*d**3 + j*d**2 + 57*d - 372*d + 18*d**2 - 6*d**2.
-5*(d - 7)**2*(d - 1)
Let s(a) = -3*a**2 + 273*a + 10. Let z(c) = -3*c**2 + 270*c + 12. Let w(y) = -6*s(y) + 5*z(y). Suppose w(x) = 0. What is x?
0, 96
Let s(z) be the first derivative of z**6/1800 - z**4/30 + 2*z**3 - 12. Let n(i) be the third derivative of s(i). Let n(b) = 0. Calculate b.
-2, 2
Suppose -165*j + 159*j = -12. Let g(o) be the first derivative of 1 + 0*o + 3/2*o**j + o**3. Factor g(l).
3*l*(l + 1)
Suppose 0 = -3*k - a - 37, -2*a = -0*k - 2*k - 38. Let d be k/35 - (-51)/15. Factor -20*m**2 + 5*m**3 - 20*m + 10*m**d + 9 - 9.
5*m*(m - 2)*(3*m + 2)
Let x(j) be the first derivative of -135*j**4/4 - 43*j**3 - 20*j**2 - 4*j + 282. Suppose x(s) = 0. Calculate s.
-2/5, -1/3, -2/9
Suppose 2*j + 3*x = -11, 2*j + 3*x + 17 = 3*j. Let f be (-3 + (-21)/(-6))*j - -2. Determine i, given that 0 + 0*i + 3/2*i**4 + 0*i**2 + 3/2*i**f = 0.
-1, 0
Let t(c) be the second derivative of c**7/21 - c**6/3 + 9*c**5/10 - 7*c**4/6 + 2*c**3/3 + 4*c + 26. What is m in t(m) = 0?
0, 1, 2
Let h(d) = 8*d**4 + 40