- 1)**2*(v + 1)**2
Let m(l) be the third derivative of -1/48*l**4 + 1/240*l**5 + 0*l**3 + 0*l - 5*l**2 + 1. Determine i, given that m(i) = 0.
0, 2
Suppose 3/4*i**5 - i**2 + 17/8*i**4 + 0 + 7/8*i**3 - 1/2*i = 0. What is i?
-2, -1, -1/2, 0, 2/3
Let 63*d**4 - 23*d**4 - 44*d**4 = 0. What is d?
0
Let 22*m - 144*m + 412 + 211*m - 4*m**2 + 325*m + 6*m**2 = 0. Calculate m.
-206, -1
Let s(d) be the first derivative of 2*d**5/75 + 3*d**4/10 - 2*d**3/45 - 3*d**2/5 - 391. Let s(o) = 0. What is o?
-9, -1, 0, 1
Suppose 16 = 7*m + 114. Let s be 5 - 8/m - 5. Factor 0 + s*v + 2/7*v**2.
2*v*(v + 2)/7
Let c = -6118/3 + 2040. Factor -4/9*u + c*u**2 - 2/9*u**3 + 0.
-2*u*(u - 2)*(u - 1)/9
Suppose -3 = -s, -2*b - 5*s + 8 + 7 = 0. Let r = -73 + 73. Factor 0*p**2 + 1/3*p**3 + 1/3*p**5 + 2/3*p**4 + b*p + r.
p**3*(p + 1)**2/3
Factor 116*x + 22*x - 4*x**2 - 3666 - 5550 - 522*x.
-4*(x + 48)**2
Let k(j) be the first derivative of 9 + 4/3*j**3 + 0*j - 1/2*j**2. Find h, given that k(h) = 0.
0, 1/4
Suppose 5/2*c**2 + 5/2*c**3 + 0 - 5/2*c**4 - 3*c + 1/2*c**5 = 0. Calculate c.
-1, 0, 1, 2, 3
Let p(t) be the third derivative of t**6/24 + 5*t**5/6 + 35*t**4/6 + 20*t**3 + 709*t**2. Determine x, given that p(x) = 0.
-6, -2
Let m(p) be the second derivative of -5/6*p**3 + 5/4*p**4 + 0 + 11*p - 5*p**2 - 1/6*p**6 + 1/4*p**5. Factor m(s).
-5*(s - 2)*(s - 1)*(s + 1)**2
Let o = -41 - -63. Let k(c) = 2*c - 6. Let z be k(13). Solve -o*u - 2*u**2 + 0*u**2 + 4 + z*u = 0.
-2, 1
Factor -11/4*p + 0 - 1/4*p**2.
-p*(p + 11)/4
Let y(f) be the first derivative of f**6/720 - f**5/120 + f**4/72 + 9*f**2/2 + 18. Let s(k) be the second derivative of y(k). Suppose s(c) = 0. Calculate c.
0, 1, 2
Factor 62/11 + 12/11*c**2 + 74/11*c.
2*(c + 1)*(6*c + 31)/11
Solve -143*l**2 + 66*l + 48 - 3*l**3 + 304*l**2 - 146*l**2 = 0.
-2, -1, 8
Let q(d) be the third derivative of d**8/560 - d**6/200 - 18*d**2. Solve q(w) = 0.
-1, 0, 1
Let r = -887 - -891. Let b be 3/(-6) - (-22)/12. Find n, given that 0*n - 2/3 + 0*n**3 - 2/3*n**r + b*n**2 = 0.
-1, 1
Let x(f) be the first derivative of f**4/16 - 5*f**3/12 + f**2/2 - 13. Factor x(c).
c*(c - 4)*(c - 1)/4
Let d(p) = -13*p**3 - 4*p**2 - 4*p + 9. Let q(i) = -2*i**3 - 1. Let t(o) = 3*d(o) - 21*q(o). Let t(f) = 0. Calculate f.
-2, 2, 4
Suppose 3*r - 7*r + 96 = 0. Let f(s) = 3*s + 12. Let i be f(-3). Suppose -r + 18*k**2 + 57*k**i + 42*k - 18*k**4 - 92*k - 34*k - 3*k**4 = 0. What is k?
-1, -2/7, 2
Factor 0*g**2 - 57/2*g**4 - 43/6*g**3 + 0*g + 2/3*g**5 + 0.
g**3*(g - 43)*(4*g + 1)/6
Let m = 377/3 + -733/6. Factor -1/2*p**2 - m*p - 3.
-(p + 1)*(p + 6)/2
Let q be (0 + (-4)/6)*-171. Let w = -453/4 + q. Factor -h**2 + w*h**3 + 1/4*h + 0.
h*(h - 1)*(3*h - 1)/4
Let i = -15897/20 + 795. Let c(k) be the third derivative of 0*k - i*k**6 - 1/70*k**7 - 3/2*k**3 + 0 + k**2 - 3/5*k**5 - 5/4*k**4. Factor c(b).
-3*(b + 1)**3*(b + 3)
Let x(v) be the third derivative of v**6/180 + v**5/20 + v**4/24 - 2*v**3/9 + 37*v**2. Find h such that x(h) = 0.
-4, -1, 1/2
Let w be (-96)/(-42)*(-28)/(-40). Solve -6/5*f + w - 2/5*f**2 = 0 for f.
-4, 1
Factor -57228*u + 57073*u - 10*u**2 + 21 + 59.
-5*(u + 16)*(2*u - 1)
Suppose -3*f = -5*f + 28. Suppose 4*i = 3*w - f, -2*i + 4 = w + 3*w. Factor 8*t**4 - 5*t**4 + t + 3*t**w - t + 6*t**3.
3*t**2*(t + 1)**2
Let z be (19 + -35)/(6/3) + 11. Suppose -2/9*b**z + 0 - 4/9*b**2 + 2/3*b = 0. What is b?
-3, 0, 1
Let b(f) = 3*f**4 - 2*f**3 - 3*f**2 + 2*f - 5. Let h(d) = 57*d**3 + 2*d**2 - 3*d**2 + d - 2 - 58*d**3 + d**4. Let j(v) = -2*b(v) + 5*h(v). Factor j(q).
-q*(q - 1)*(q + 1)**2
Let m(b) be the third derivative of -b**6/135 + b**5/180 + 2*b**3 - 2*b**2. Let z(x) be the first derivative of m(x). Factor z(q).
-2*q*(4*q - 1)/3
Let c(n) be the second derivative of -4/3*n**3 + 2/5*n**5 + 0 + 1/6*n**4 + 4*n - n**2. Find f, given that c(f) = 0.
-1, -1/4, 1
Let x(f) be the second derivative of 0*f**3 + 0 + 0*f**4 + 3/40*f**5 + 0*f**2 - 25*f. What is q in x(q) = 0?
0
Let l(d) be the third derivative of 1/280*d**8 + 0*d**7 + 1/20*d**4 + 0*d**5 - 1/50*d**6 + 0*d + 21*d**2 + 0*d**3 + 0. Factor l(z).
6*z*(z - 1)**2*(z + 1)**2/5
Let q(o) = -o**2 - o**3 + 2*o**3 + 4*o**2. Let z(j) = -6*j**2 + 5*j**2 + 3*j**2. Let s(d) = 3*q(d) - 5*z(d). Factor s(p).
p**2*(3*p - 1)
Suppose -3*h = -0*r + 5*r - 8, -h = 3*r. Let x = h - 4. Factor -16*z**x - 13*z**2 - 9 + 32*z**2 - 6*z.
3*(z - 3)*(z + 1)
Factor 81/4*w - 3/2*w**4 + 45/4*w**3 - 27*w**2 + 0.
-3*w*(w - 3)**2*(2*w - 3)/4
Let x(w) be the second derivative of -5*w**7/56 + 17*w**6/40 - 9*w**5/40 - 5*w**4/4 + w**3 - 204*w. Find g, given that x(g) = 0.
-1, 0, 2/5, 2
Let p(k) be the second derivative of -1/5*k**5 + 13*k - 1/5*k**6 + 1/21*k**7 + 0*k**2 + 0 + 2*k**4 - 8/3*k**3. Determine l so that p(l) = 0.
-2, 0, 1, 2
Suppose -14*q + 10 = -9*q. Suppose 32 = 4*y + 4*j, -q*j + 2 = 4*y - 4*j. Solve -1/4*l**4 + 0 + 1/4*l**2 + 1/4*l**y - 1/4*l = 0 for l.
-1, 0, 1
Factor -1/2*k**3 + 0*k + 9/2*k**2 - 54.
-(k - 6)**2*(k + 3)/2
Let w = -6/35 - -46/7. Let o be 21*(7*18/(-1575))/((-6)/10). Determine i so that -64/5*i - 32*i**2 + o*i**5 - 8*i**3 + w + 38/5*i**4 = 0.
-2, -1, 2/7, 2
Let c = 438 + -433. Let z(h) be the first derivative of -1/22*h**4 + 0*h**2 + 0*h + 0*h**3 + 7 + 6/55*h**c. Factor z(w).
2*w**3*(3*w - 1)/11
Let u(k) be the first derivative of k**7/2940 - k**6/1260 + 8*k**3/3 - 10. Let g(w) be the third derivative of u(w). Factor g(t).
2*t**2*(t - 1)/7
Let r(y) = y**2 - y + 1. Let c(q) = -4*q + 12 + 8*q**2 + 2*q - 5*q - 2*q. Let b be 179/4 + (-42)/56. Let a(v) = b*r(v) - 4*c(v). Factor a(p).
4*(p - 1)*(3*p + 1)
Let f be 365/75 - (5 + -2)/1. Let l = f + -1/15. Factor -3/5*w**2 + l*w - 6/5.
-3*(w - 2)*(w - 1)/5
Suppose -7*m + 2*m = -20. Let x = 6 - m. Determine d so that d**3 - 3*d**2 + 2 + d**x + 6*d**2 + 5*d = 0.
-2, -1
Let h(y) = -84*y**2 + 468*y - 64. Let m(z) = 13*z**2 - 72*z + 10. Let d(p) = -5*h(p) - 32*m(p). Suppose d(o) = 0. Calculate o.
0, 9
Let s(o) be the first derivative of 4/3*o**3 - 2/15*o**5 + 2*o + 8/3*o**2 + 26 + 0*o**4. Factor s(t).
-2*(t - 3)*(t + 1)**3/3
Let x(g) be the second derivative of g**6/105 + 2*g**5/35 - g**4/42 - 4*g**3/21 - g + 61. Factor x(u).
2*u*(u - 1)*(u + 1)*(u + 4)/7
Let f(k) be the first derivative of 0*k - 2/9*k**3 - 2/3*k**2 - 7. Factor f(n).
-2*n*(n + 2)/3
Let l(f) be the second derivative of -f**6/15 + f**5/2 + 3*f**4/2 - 27*f**3 + 108*f**2 + 318*f. Factor l(u).
-2*(u - 3)**3*(u + 4)
Let v(g) = g**2 - 1. Let f be v(-2). What is w in 1 - f*w**2 - 3*w + 2 - 3 = 0?
-1, 0
Let t(n) = n**4 + n**3 - 1. Let g(y) = 32*y**2 - 49*y**2 + 18*y - 22*y**2 - 12*y**4 - 45*y**2 + 4 + 46*y**3. Let q(a) = g(a) + 4*t(a). What is u in q(u) = 0?
0, 1/4, 3
Suppose -14*y - 754 + 26 = 0. Let z = y - -55. Solve -1/3*o**z - 1/3*o**4 + 1/3*o + 1/3*o**2 + 0 = 0.
-1, 0, 1
Let r(c) = -c + 14. Let h be r(8). Factor 7*l - 4*l**2 + 7*l - h*l - 3*l**3 - l**3.
-4*l*(l - 1)*(l + 2)
Suppose 471 - 455 = 4*h. Let p(c) be the second derivative of 0 - 2*c + 1/18*c**3 - 1/18*c**h - 1/60*c**5 + 1/3*c**2. Determine s so that p(s) = 0.
-2, -1, 1
Determine d, given that -10/7*d + 0 + 1/7*d**2 - 1/7*d**4 + 10/7*d**3 = 0.
-1, 0, 1, 10
Let h(p) = p**3 + p**2 + p + 1. Let z(j) be the first derivative of -j**5/5 + j**4 + 2*j**3 + 3*j**2 + 5*j - 5. Let u(w) = 10*h(w) - 2*z(w). Factor u(n).
2*n*(n - 1)*(n + 1)**2
Let m(p) = 26*p**2 + 30*p + 4. Let a(o) = 5*o**2 + 6*o + 1. Let z = -54 + 57. Let s(k) = z*m(k) - 16*a(k). Factor s(f).
-2*(f + 1)*(f + 2)
Let n(g) be the second derivative of 0*g**3 - 9*g + 0*g**2 + 1/105*g**6 - 3/70*g**5 + 1/21*g**4 + 0. Determine d so that n(d) = 0.
0, 1, 2
Let f(y) = 0*y**4 - 50*y**2 - 27*y**3 + 3*y**4 - 186 - 42*y + 158*y**2. Let x(j) = -j**3 - j - 1. Let a(m) = f(m) + 6*x(m). Factor a(s).
3*(s - 4)**3*(s + 1)
Let f be (-12)/(-11)*1837/154. Let n = f - 140/11. Solve 6/7*k**3 + 0 + 0*k**2 + 0*k - n*k**4 = 0.
0, 3
Determine n, given that -34/5*n**4 - 2/5*n**5 - 444/5*n**2 - 162/5 - 90*n - 188/5*n**3 = 0.
-9, -3, -1
Suppose 3*o - 7*v = -10*v + 24, 7 = -o + 2*v. Solve 0 + 24/5*u**2 - 36/5*u - 4/5*u**o = 0 for u.
0, 3
Let z(r) be the second derivative of -4/9*r**3 + 0 - 4*r + 0*r**2 - 1/9*r**4. Factor z(q).
-4*q*(q + 2)/3
Let n = 85 - 82. Factor 9*b**2 + 2*b**n - 2*b - 13*b**2 - 36 + 40.
2*(b - 2)*(b - 1)*(b + 1)
Let c(j) = -3*j**4 - 1