uppose 0 = -17*w + 16*w + 5. Let i(l) be the first derivative of 0*l**2 + 9/5*l**w + 3 - 3/2*l**4 - l**3 + 0*l. Factor i(b).
3*b**2*(b - 1)*(3*b + 1)
Let d(a) be the third derivative of a**7/840 - 3*a**6/80 + 7*a**5/15 - 3*a**4 + 32*a**3/3 + 753*a**2 - 2. Determine b so that d(b) = 0.
2, 4, 8
Suppose -5*z + 4 = -2*z - 2*o, 0 = -2*z + 2*o + 2. Find n, given that 3 - 1 + n**z - 2 - 1 = 0.
-1, 1
Let a(o) be the first derivative of o**3/4 - 3*o**2/4 + 32. Solve a(u) = 0 for u.
0, 2
Suppose -b = -6*b + 10. Let a(z) = z**2 - 2*z. Let m be a(2). Solve -k**2 - 3 + m*k**b + 4 = 0 for k.
-1, 1
Let s be 8 - (-2 - 38*(-12)/48). What is y in -5/2*y - s*y**2 + 0 = 0?
-5, 0
Let l(u) be the second derivative of 0*u**3 + 0 - 1/20*u**5 - 6*u + 1/36*u**4 + 0*u**2. Factor l(t).
-t**2*(3*t - 1)/3
Let i be 7/(-21) + 669/9. Let t = -74 + i. Determine p, given that -2/9*p**2 + 2/3*p + t = 0.
0, 3
Let b(v) = v**2 + 1. Let r be b(-1). Let c be (-3)/(-7) + (-138)/(-21). Let -j**2 + j**r + j**3 - c*j + 6*j = 0. Calculate j.
-1, 0, 1
Suppose 4*o - u = 11, 3*u = 2*o + o - 6. Let -12 - p**o + 0*p + 3*p**3 - p - 13*p = 0. Calculate p.
-2, -1, 3
Let r(t) be the second derivative of 2*t**6/105 - 24*t**5/35 + 118*t**4/21 + 208*t**3/7 + 338*t**2/7 + 54*t - 3. Factor r(k).
4*(k - 13)**2*(k + 1)**2/7
Suppose 19*i - 3*i = 160. Factor 53 - 18*d + 50 - i*d + 2*d**2 - 5.
2*(d - 7)**2
Let a(o) be the first derivative of o**3/3 + 26*o**2 + 676*o + 369. Factor a(y).
(y + 26)**2
Let c(s) be the second derivative of -s**6/60 - 3*s**5/10 - 7*s**4/4 - 13*s**3/3 - 21*s**2/4 - 6*s + 7. Factor c(g).
-(g + 1)**2*(g + 3)*(g + 7)/2
Let c = -508 - -514. Let y(o) be the first derivative of 0*o + 11 + 0*o**3 + 2/13*o**5 - 4/39*o**c + 0*o**2 - 1/26*o**4. Factor y(d).
-2*d**3*(d - 1)*(4*d - 1)/13
Let p(s) be the third derivative of s**7/630 + s**6/60 - s**5/15 - 35*s**4/36 + 25*s**3/6 - 247*s**2. Factor p(x).
(x - 3)*(x - 1)*(x + 5)**2/3
Suppose -3*b + 4*t = 4, -39 = -2*b + 2*t - 41. Let h(x) be the second derivative of -1/36*x**4 + 1/60*x**5 + b + 6*x + 0*x**3 + 0*x**2. Factor h(k).
k**2*(k - 1)/3
Let p(x) be the first derivative of 2*x**5/15 + 7*x**4/3 + 26*x**3/3 - 18*x**2 + 171. Factor p(g).
2*g*(g - 1)*(g + 6)*(g + 9)/3
Let d(w) be the third derivative of 25/112*w**8 + 0*w + 0 - 1/3*w**5 - 5/6*w**6 + 0*w**3 - 19/42*w**7 - 3*w**2 + 0*w**4. Suppose d(h) = 0. What is h?
-2/5, -1/3, 0, 2
Let w(r) be the second derivative of 191*r**4/21 - 386*r**3/21 + 4*r**2/7 + 462*r. Factor w(a).
4*(a - 1)*(191*a - 2)/7
Let x(l) be the second derivative of -l**4/4 - 51*l**3/2 - 75*l**2 + 398*l. Find r such that x(r) = 0.
-50, -1
Let u be -6*((-56)/(-120))/(-7). Let x(a) be the first derivative of 2*a**3 + 3/2*a**4 + u*a**5 + 0*a + a**2 - 7. Let x(w) = 0. Calculate w.
-1, 0
Let r(h) be the second derivative of 1/66*h**4 + 0 + 11*h - 1/33*h**3 + 0*h**2. Find g such that r(g) = 0.
0, 1
Suppose -22 = 14*k - 106. Suppose k*p = -9*p. Let -6/7*l**3 + 4/7*l**4 + 6/7*l**5 + 0 + p*l - 4/7*l**2 = 0. What is l?
-1, -2/3, 0, 1
Factor 3/8*i**3 - 21/8*i**2 + 15/4*i + 0.
3*i*(i - 5)*(i - 2)/8
Let w(a) = 8*a**2 + 71*a + 34. Let b(t) = 3*t**2 + 24*t + 12. Let d(m) = -17*b(m) + 6*w(m). Factor d(g).
-3*g*(g - 6)
Let 400/7*c + 408/7*c**2 + 0 + 2/7*c**4 + 108/7*c**3 = 0. Calculate c.
-50, -2, 0
Let z = 316 + -314. Let g(k) be the first derivative of -4*k**z + 12*k - 3 - 4/3*k**3. Determine o so that g(o) = 0.
-3, 1
Let w(q) be the third derivative of -q**5/12 - 5*q**4/24 - 129*q**2. Factor w(k).
-5*k*(k + 1)
Let c = 122 + -118. Suppose -2*s + 4*s - 10 = 0, c*g + 3*s - 15 = 0. Find y such that -1/2 + 1/2*y**2 + g*y = 0.
-1, 1
Let k(t) = -t**3 + 7*t**2 - 15*t + 58. Let j be k(6). Determine a, given that -58*a**2 + 32/3*a**j - 8/3 - 70/3*a - 80/3*a**3 = 0.
-1, -1/4, 4
Let j(f) be the third derivative of -f**7/210 + f**6/90 - f**4/12 + 9*f**2. Let h(l) be the second derivative of j(l). Determine a, given that h(a) = 0.
0, 2/3
Let n(r) be the second derivative of 3*r**4/2 - 25*r**3/3 - 6*r**2 + 3*r + 3. Factor n(a).
2*(a - 3)*(9*a + 2)
Let m be ((-4)/14)/((-9)/126). Suppose -3*o**5 - 72 + 9*o**m + 3*o**2 + 72 - 9*o**3 = 0. What is o?
0, 1
Find s such that -2/3*s**5 - 10/3*s**4 - 2/3 - 20/3*s**2 - 10/3*s - 20/3*s**3 = 0.
-1
Let g = 3093 + -21645/7. Let k be 0/(-1 + 1 + -2). Factor -2/7*i**2 + g*i**4 + 4/7*i - 8/7*i**3 + k.
2*i*(i - 1)**2*(3*i + 2)/7
Let b(q) be the third derivative of q**6/40 - q**5/5 + 5*q**4/8 - q**3 + 4*q**2 + 10. Let b(k) = 0. What is k?
1, 2
Let z be (-5 - -11) + (1 - 3). Suppose -2*k + 0*k = -6. What is b in 2*b**2 - 3*b - 6*b**2 + 6*b + 1 - 2*b**3 - b + k*b**z = 0?
-1, -1/3, 1
Let j(o) = -47*o**2 + 6*o + 3. Let z(x) = 1. Let m(r) = -5*j(r) + 15*z(r). Find i, given that m(i) = 0.
0, 6/47
Let i(n) = 339*n**2 - 7 - 4*n + 9*n**3 - 6*n - 342*n**2. Let c(l) = -5*l**3 + 2*l**2 + 5*l + 4. Let o(r) = -11*c(r) - 6*i(r). Factor o(f).
(f - 2)*(f - 1)**2
Let a(i) be the first derivative of 1/9*i**3 - 2/3*i**2 + 0*i - 5. Factor a(l).
l*(l - 4)/3
Factor 15*s + 23*s + 5*s**2 - 3*s + 50.
5*(s + 2)*(s + 5)
Let w = -30 - -35. Let -8*u + w - 5*u**2 + 8*u = 0. What is u?
-1, 1
Let i(b) be the second derivative of b**6/315 - 4*b**5/105 + 11*b**4/63 - 8*b**3/21 + 3*b**2/7 + 185*b. Suppose i(g) = 0. What is g?
1, 3
Let p = 717/5 - 143. Let c = -22930 + 114651/5. Factor c*s**2 + p - 3/5*s.
(s - 2)*(s - 1)/5
Let o(n) be the first derivative of 8*n**5/5 - 25*n**4/2 + 100*n**3/3 - 35*n**2 + 12*n - 17. Let o(h) = 0. Calculate h.
1/4, 1, 2, 3
Let t = -43 + 5. Let b = t + 42. Determine q so that -7*q**3 + 0 - 4*q - 10*q**2 - 3/2*q**b = 0.
-2, -2/3, 0
Let q be 2/(-14) + 195*23/3220. Let 5/2*t - 5/4 - q*t**2 = 0. What is t?
1
Let v(p) = 13*p**3 + 4*p**2 - 9*p - 8. Let a(l) = 15*l**3 + 5*l**2 - 10*l - 10. Let j(m) = 4*a(m) - 5*v(m). Let j(g) = 0. What is g?
-1, 0, 1
Let f be (-40)/6*(-9)/6. Let k be ((-18)/(-15))/(20/50). Suppose 6*g - f + 2*g**3 - 14*g + 3*g + 10*g**2 + k*g**3 = 0. What is g?
-2, -1, 1
Let i(c) be the first derivative of 2/27*c**3 - 2/9*c + 1/9*c**2 + 23 - 1/18*c**4. Determine a so that i(a) = 0.
-1, 1
Suppose -134*f = 39*f. Find r such that 0 - 2/13*r**2 + f*r = 0.
0
Let y(r) = r**3 - r**2 + 94*r + 96. Let v be y(-1). Solve 1/4*m**4 + 0*m - 3/4*m**3 + v - m**2 = 0 for m.
-1, 0, 4
Let x(t) be the third derivative of -t**5/4 - 85*t**4/12 - 55*t**3/6 + 2*t**2 + 11. What is d in x(d) = 0?
-11, -1/3
Let i = -47361/5 - -9477. What is w in -6/5 + i*w**5 - 33/5*w - 51/5*w**2 + 6/5*w**3 + 12*w**4 = 0?
-2, -1/2, 1
Let y(g) be the third derivative of 1/75*g**7 - 3*g**2 - 1/75*g**5 + 0 + 0*g**3 - 1/60*g**6 + 0*g**4 + 0*g. Factor y(b).
2*b**2*(b - 1)*(7*b + 2)/5
Let j(a) be the first derivative of -a**6/8 + 12*a**5/5 - 117*a**4/8 + 28*a**3 - 147*a**2/8 - 62. Solve j(k) = 0 for k.
0, 1, 7
Factor -t**5 - 4*t**3 + 6698 - 13398 + 5*t**4 + 6700.
-t**3*(t - 4)*(t - 1)
Factor -8*q**3 - 30*q**4 + 4*q**2 + 34*q**4 - 9 + 9.
4*q**2*(q - 1)**2
Suppose -303 = 5*a - 318. Let o(l) be the second derivative of 0 - 4/15*l**a - 1/30*l**4 - 4/5*l**2 + 4*l. Find n such that o(n) = 0.
-2
Suppose l**5 - 8 + 10*l**4 + 10*l**3 + 12*l**3 - 5*l - 8*l**3 - 11*l - 2*l**2 + l**5 = 0. Calculate l.
-2, -1, 1
Let s(p) = p**4 - 7*p**3 - p**2 + 2*p. Suppose 0 = -4*w - 0*w - 24. Let d(m) = -m**4 + 8*m**3 + m**2 - 2*m. Let j(f) = w*s(f) - 5*d(f). Factor j(q).
-q*(q - 2)*(q - 1)*(q + 1)
Factor -2/3*a**2 - 2/3 + 4/3*a.
-2*(a - 1)**2/3
Let c be (-297)/(-6) + (-1)/2*-1. Let y = c + -45. Solve 0 + 12/5*i**4 + 3/5*i**y + 3*i**3 + 0*i + 6/5*i**2 = 0.
-2, -1, 0
Factor -5 + i**3 - 18*i - 6*i**3 + 48*i + 15*i**2 - 35.
-5*(i - 4)*(i - 1)*(i + 2)
Let j(h) be the second derivative of -5*h + 0*h**2 + 1/1980*h**6 + 0*h**5 - 1/132*h**4 + 0 + 1/3*h**3. Let z(r) be the second derivative of j(r). Factor z(o).
2*(o - 1)*(o + 1)/11
Let c be (((-9)/(-2))/9)/((-55)/(-33)). Let k(s) be the first derivative of -3/2*s**3 + 0*s - c*s**5 + 9/8*s**4 - 6 + 3/4*s**2. Suppose k(q) = 0. What is q?
0, 1
Let y(l) = -2*l + 1. Let c be y(-1). Let r be 6 - c - 0 - 1. Factor 3*h - 2*h - 8 + 13*h**2 - h**r + 3*h.
4*(h + 1)*(3*h - 2)
Let i be (3 - 1324/(-14)) + 21/49. Let y be (-21)/i*(-8)/6. Factor 0 + 2/7*d**2 + y*d**3 + 0*d.
2*d**2*(d + 1)/7
Let k = 12/59 + -85/708. Let s(a) be the third derivative of -1/60*a**6 + k