d).
d*(d - 1)**2*(d + 1)
Let d(b) = -10 + b**2 - 2*b**3 - 11*b + 4*b**3 - 3*b**3 + 12*b**2. Let f be d(12). Find z such that 2/5*z**f + 10 + 4*z = 0.
-5
Let p(m) be the third derivative of -m**5/150 + m**4 - 116*m**3/15 + 9*m**2 + 10. Solve p(b) = 0 for b.
2, 58
Let r(n) be the second derivative of 0 - 8/15*n**5 + 0*n**2 + 2/3*n**4 - 8*n - 7/6*n**3 + 7/90*n**6. Let o(g) be the second derivative of r(g). Factor o(k).
4*(k - 2)*(7*k - 2)
Let h = -12099/5 - -2420. Find c, given that 0*c - h*c**2 + 4/5 = 0.
-2, 2
Let g = -69 - -73. Determine a, given that -7*a - 4*a**3 - g*a**4 - a**2 + 11*a + 5*a**2 = 0.
-1, 0, 1
Factor -305/3*j**2 - 300*j - 5/3*j**4 + 30*j**3 - 500/3.
-5*(j - 10)**2*(j + 1)**2/3
Let k = -14 - -16. Suppose 4*s - 2 = 3*s - 4*u, 4*u = 5*s - 10. Factor -4 + 0 + 13*f**k + 25*f + 2*f**s - 6.
5*(f + 2)*(3*f - 1)
Let m(z) be the first derivative of z**4/6 - 14*z**3/9 - 42. Determine x so that m(x) = 0.
0, 7
Let b be 28/(-6)*(113 + -127). Factor 6*q**3 - b - 109/3*q**2 + 84*q - 1/3*q**4.
-(q - 7)**2*(q - 2)**2/3
Let x(g) be the third derivative of -g**6/24 + g**5/12 + 35*g**4/12 - 20*g**3 - 62*g**2. Suppose x(l) = 0. What is l?
-4, 2, 3
Let v(k) be the second derivative of k**5/10 + 2*k**4/3 - 13*k. Suppose v(o) = 0. What is o?
-4, 0
Let m(y) = -y**3 + 7*y**2 + y - 39. Let h be m(6). Let n(g) be the third derivative of 0*g - 9*g**2 + 1/120*g**5 + 1/8*g**4 + 3/4*g**h + 0. Factor n(c).
(c + 3)**2/2
Suppose 5*m - 4 = k + 33, -4*m + 5*k = -38. Suppose 3*h**5 - h**5 - h**2 - 2 + 9*h**4 - 3*h + 6*h**2 + 6*h**3 + m*h**3 = 0. What is h?
-2, -1, 1/2
Let c = 56 + -54. Let u(s) = -8*s**3 - 10*s**2 + 7*s - 9. Let d(y) = -y**3 - y**2 + y - 1. Let t(q) = c*u(q) - 18*d(q). Factor t(w).
2*w*(w - 2)*(w + 1)
Suppose -4*w - 28 = -l - 35, -w - l = 7. Factor -3/8*i - 3/8*i**2 + w.
-3*i*(i + 1)/8
Suppose -7 = 30*x - 31*x. Solve -9*c**3 - x*c**3 + 2*c**5 + 12*c**3 + 2*c = 0 for c.
-1, 0, 1
What is j in -2/3*j**4 + 8/3*j**3 - 136/3*j + 70/3 + 20*j**2 = 0?
-5, 1, 7
Let m(k) = 16*k**4 - 8*k**2 + 4. Let l(b) = 4*b**4 - 5*b**4 + b**3 - 1 - b + b**2 + 0*b**4. Let p(x) = 12*l(x) + m(x). Let p(a) = 0. What is a?
-2, -1, 1
Let x = -170 - -174. Determine g, given that g**4 + 4*g**3 + 4*g - 16*g**4 - 24*g**2 + 8 + 23*g**x = 0.
-2, -1/2, 1
Let k(q) be the second derivative of -5*q**4/6 - 5*q**3/6 + 5*q**2/2 - 10*q. Let i(g) = g**3 - g + 1. Let u(w) = 5*i(w) - k(w). What is l in u(l) = 0?
-2, 0
Let v(c) be the second derivative of c**6/225 + 3*c**5/25 + 9*c**4/10 - 362*c. Suppose v(p) = 0. What is p?
-9, 0
Let d = 4 - 2. Let w be 9 + 92/(-12) + -1. Factor 0*p + 1/3 - w*p**d.
-(p - 1)*(p + 1)/3
Let d(o) be the third derivative of o**7/42 + 35*o**6/12 + 1153*o**5/12 - 525*o**4 + 1080*o**3 + 26*o**2 + 5*o. Let d(y) = 0. What is y?
-36, 1
Let d(m) be the first derivative of m**5 + 15*m**4/2 - 40*m**3/3 - 15*m**2 + 35*m - 101. Factor d(b).
5*(b - 1)**2*(b + 1)*(b + 7)
Let i(c) = 3*c - 6*c - 5*c + c**2 + 4 - 2. Let l be i(8). Factor 0*x**3 - 2*x**2 - 7*x**2 - x**3 + 8*x**l.
-x**2*(x + 1)
Suppose 0 = -3*s - c + 1, 3 = 5*s - 0*c + 3*c. Suppose -g = -s*g - 4. Determine m so that 3*m**3 + 35*m**g + 7*m**2 - 38*m**4 - 4*m**2 - 3*m = 0.
-1, 0, 1
Let g be (-1 + -1)*2*(-188)/16. Let 20 + 4*q**2 - 67*q + q**2 + g*q = 0. What is q?
2
Factor 15*d + 25/2 + 5/2*d**2.
5*(d + 1)*(d + 5)/2
Suppose 4*v + 24 = -5*i, -4*i = -6*v - 31 - 5. Factor 0*w**3 + 0 + 0*w + 10/9*w**4 - 2/9*w**5 + i*w**2.
-2*w**4*(w - 5)/9
Let m = 4 + 7. Let u = m - 13. Let j(d) = -5*d**4 + 3*d**2 - 2*d. Let w(i) = -6*i**4 - i**3 + 3*i**2 - 2*i. Let t(r) = u*w(r) + 3*j(r). Factor t(s).
-s*(s - 1)*(s + 1)*(3*s - 2)
Let j(c) = 5*c**4 + 28*c**3 + 41*c**2 + 22*c. Let p(n) = 4*n**4 + 27*n**3 + 42*n**2 + 22*n. Let s(w) = 3*j(w) - 4*p(w). Solve s(v) = 0 for v.
-22, -1, 0
Suppose 4 = 5*f - 5*p + 34, 4*f + 5*p = 30. Factor f*u - 6/5*u**5 + 9/5*u**4 + 6/5*u**3 + 0 + 0*u**2.
-3*u**3*(u - 2)*(2*u + 1)/5
Let u be 4/(-10)*(-16 + 1). Suppose u - 1 = 5*h. Determine n so that -h - 3*n + 1 + 3*n**2 - 6 = 0.
-1, 2
Let k(w) = -6*w**2 + 346*w - 122. Let t(p) = p**2 + 2*p + 2. Let z(c) = -2*k(c) - 28*t(c). Factor z(g).
-4*(g + 47)*(4*g - 1)
Let t(g) be the first derivative of -g**3/36 - 5*g**2/6 + 7*g/4 + 18. What is s in t(s) = 0?
-21, 1
Let y(z) = -z**3 + 54*z**2 + 48*z + 387. Let k be y(55). Determine u, given that 0*u - 2/3*u**4 + 0 - 4/3*u**k - 2*u**3 = 0.
-2, -1, 0
Suppose -40/9*a**2 + 4/9*a**3 - 148/9*a - 104/9 = 0. Calculate a.
-2, -1, 13
Suppose 4 = f + 4*z, 5*f + 3*z - z + 16 = 0. Let w be 0*-2*(-1)/f. Suppose w - 8/3*o**2 + 0*o - 4/3*o**3 + 4/3*o**4 = 0. What is o?
-1, 0, 2
Factor -1/4*u**3 + 5/4*u**2 + 1/4*u - 5/4.
-(u - 5)*(u - 1)*(u + 1)/4
Let q be 2/28 - 16875/(-8750). Factor 5/3*p + 8/3*p**q - 50/3 + 1/3*p**3.
(p - 2)*(p + 5)**2/3
Suppose -57 = -11*o + 163. Factor -7*j + 4*j - 14*j + o - 3*j + 50*j**3 - 95*j**2.
5*(j - 2)*(2*j + 1)*(5*j - 2)
Let z = -103 - -106. Find t, given that -t**2 - 3*t - 2*t + 54*t**z + t - 56*t**4 + 7*t**2 = 0.
-2/7, 0, 1/4, 1
Factor -1575*a**3 - 208*a + 1737*a**3 + 95*a**2 + 24 + 319*a**2.
2*(a + 3)*(9*a - 2)**2
Let t(p) be the first derivative of 49 - 10/3*p**3 - 35/2*p**2 + 5/4*p**4 - 20*p. Suppose t(d) = 0. Calculate d.
-1, 4
Suppose 20 = g - 4*b, 13*b + 20 = 2*g + 10*b. Let p(l) be the first derivative of -6*l**3 - 2*l**2 - 22/5*l**5 + 0*l - 2 - l**6 - 15/2*l**g. Factor p(w).
-2*w*(w + 1)**3*(3*w + 2)
Let f(u) be the first derivative of 2*u**3/39 - 5*u**2/13 + 12*u/13 - 169. Let f(n) = 0. Calculate n.
2, 3
Suppose s + 4*s - 20 = 0. Let -4 + s - n**2 + 4*n - 3*n = 0. Calculate n.
0, 1
Let r(p) be the first derivative of 8*p**6/3 + 84*p**5/5 + 41*p**4 + 148*p**3/3 + 30*p**2 + 8*p - 13. What is u in r(u) = 0?
-2, -1, -1/4
Suppose 52/5*f**2 + 12/5 - 46/5*f - 14/5*f**3 - 4/5*f**4 = 0. Calculate f.
-6, 1/2, 1
Let g be 12/(-12 + 6) - (-1 + -13). Let 32*b**3 + 9*b**5 - 8*b**4 + 16*b**4 + g*b**4 - 5*b**5 + 16*b**2 = 0. What is b?
-2, -1, 0
Let k(d) be the first derivative of -d**3/3 - 3*d**2/2 + 47. Suppose k(b) = 0. What is b?
-3, 0
Let o(r) = r**3 - r**2 - 4*r - 1. Let t be o(3). Suppose -g + t = -j - 2*j, -j + 4*g = 20. Let -6*k**2 - 4/3*k + j - 14/3*k**3 = 0. What is k?
-1, -2/7, 0
Let m(o) = -o**3 - 6*o**2 - 5*o + 3. Let s be m(-5). Factor -s - 2*p**2 + 1 + 6*p - 5 + 3.
-2*(p - 2)*(p - 1)
Let w = -101 - -106. Let b(d) be the first derivative of d**2 + 0*d - 2*d**3 + 3/2*d**4 - 2 - 2/5*d**w. Suppose b(k) = 0. What is k?
0, 1
Let d(s) = -s**2 - 20*s - 19. Let p(l) = 2*l**2 + l - 1. Let r(k) = -d(k) + p(k). Solve r(y) = 0 for y.
-6, -1
Solve 9*u - 3/2*u**2 - 15/2 = 0.
1, 5
Let b(q) be the first derivative of q**5/150 - q**3/15 - 9*q**2/2 - 28. Let s(d) be the second derivative of b(d). Suppose s(v) = 0. Calculate v.
-1, 1
Suppose a + 5 = 7. Find l such that 0 - 2/3*l**a - 2/3*l = 0.
-1, 0
Let l(a) be the first derivative of -a**4/10 + a**2/5 + 80. Factor l(c).
-2*c*(c - 1)*(c + 1)/5
Let l(v) be the first derivative of -4*v**3/3 + 7*v**2/4 + v/2 - 17. What is r in l(r) = 0?
-1/8, 1
Let w(y) = -y**3 - 128*y**2 + 251*y - 122. Let n(m) = m**3 + 260*m**2 - 503*m + 242. Let r(u) = 2*n(u) + 5*w(u). Factor r(l).
-3*(l - 1)**2*(l + 42)
Let l be 2/(-4)*(-20)/(1 + 4). Let h = -1 - -14. Factor h*y**2 - 15*y**l + 0*y + y + 1.
-(y - 1)*(2*y + 1)
Suppose 3*f = -4*o + 32 + 18, -5*f = o - 4. Solve o*d**2 - 38/3*d + 2/3*d**4 - 6*d**3 + 4 = 0.
1, 6
Suppose 0 = -3*q - p - 8 - 4, -5*p = 4*q + 16. Let z be ((-12)/21)/(q/14). Factor h**2 - h**3 + h**z + 2*h**3 + h**3.
2*h**2*(h + 1)
Find p, given that 12*p**2 + 14*p**2 - 390*p - 8607 - 31*p**2 + 1002 = 0.
-39
Let a(b) be the third derivative of -7*b**2 + 1/4*b**5 + 0 + 0*b**3 - 1/12*b**4 + 0*b. Let a(r) = 0. Calculate r.
0, 2/15
Let o(s) be the first derivative of 4 + 0*s**3 - 1/36*s**4 + 0*s**2 + 2*s. Let j(d) be the first derivative of o(d). Let j(q) = 0. What is q?
0
Let m(j) = 5*j + 20. Let r be m(0). Let l = 41/2 - r. Factor -5/4*h - 9/4*h**2 - l*h**4 - 7/4*h**3 - 1/4.
-(h + 1)**3*(2*h + 1)/4
Let z(v) be the third derivative of v**7/210 + v**6/20 + v**5/15 - v**4/4 - 5*v**3/6 + 7*v**2 - 12. Suppose z(i) = 0. Calculate i.
-5, -1, 1
Suppose 1 - 1/4*w**3 + 0*w - 3/4*w**2 = 0. Calculate w.
-2, 1
Let u(q) be the first derivative of 4 - q**2 + 10/21*q**3 + 6/7*q - 1/14*q**4. F