*2 = 0.
2, 15
Suppose 9*k - 7*k = -20. Let j be k/15*-3 - -1. What is w in -27 + 23*w**3 - 3*w**4 + 6*w**2 + 22*w**j - 36*w - 33*w**3 = 0?
-1, 3
Let d = 33 - 34. Let h(x) = -5*x**3 + 30*x**2 - 64*x + 36. Let a(s) = -s - 1. Let b(m) = d*h(m) + 4*a(m). Solve b(j) = 0.
2
Let g(j) be the second derivative of j**5/4 - 5*j**4/6 - 10*j**3/3 + 20*j**2 + 20*j - 3. Suppose g(y) = 0. What is y?
-2, 2
Let w be 2 + 1 + -2 + 1. Let a be 17/(-238)*6 - 3/(-7). Let -2/7*y**w + 8/7 + a*y = 0. What is y?
-2, 2
Factor 138 - 75*o + 0*o**2 - 69 - 3*o**2 + 9*o.
-3*(o - 1)*(o + 23)
Let -28/3 - 10/3*k + 2/3*k**2 = 0. What is k?
-2, 7
Let r be (24/(-224)*-4)/(24/112). Factor 4/9*l - 2/3 + 2/9*l**r.
2*(l - 1)*(l + 3)/9
Let j(l) be the third derivative of -l**8/84 + l**6/30 - 132*l**2. What is n in j(n) = 0?
-1, 0, 1
Let i = 4849 + -33927/7. Find m, given that -i*m**4 - 2*m + 12/7*m**2 + 6/7*m**5 + 4/7 + 8/7*m**3 = 0.
-1, 2/3, 1
Solve -35*w**2 - 10 - 10*w**2 + w**4 - 6*w**4 - 35*w - 25*w**3 = 0 for w.
-2, -1
Determine k, given that 10/3*k**2 + 0*k + 0 + 26/3*k**4 + 4/3*k**5 + 32/3*k**3 = 0.
-5, -1, -1/2, 0
Let h be (18/4)/(-3)*(-24)/9. Suppose -20 = 7*f - 2*f, 0 = h*c - f - 12. Solve 5/7*k**c + 2/7 - k = 0.
2/5, 1
Let l(n) be the first derivative of -n**9/18144 + n**7/1680 - n**6/1080 - 11*n**3/3 + 9. Let z(h) be the third derivative of l(h). Determine v so that z(v) = 0.
-2, 0, 1
Suppose 4*v = 5*v - 3. Suppose -i - 23 = -5*g, v*g = 2*g + 2*i + 10. Factor g*r**2 - 3 + 2 + 3*r + 0*r**2.
(r + 1)*(4*r - 1)
Let t(x) be the first derivative of 32/51*x**3 + 0*x - 47 - 14/85*x**5 + 1/51*x**6 + 4/17*x**4 + 0*x**2. Solve t(f) = 0 for f.
-1, 0, 4
Let j(w) be the second derivative of -10*w + 1/4*w**4 + 3/2*w**2 + 0 + w**3. Factor j(a).
3*(a + 1)**2
Let z(y) be the second derivative of -y**2 - 7/36*y**4 + 23/18*y**3 + 0 + 12*y. Factor z(i).
-(i - 3)*(7*i - 2)/3
Let l be (-1976)/10374 + (-110)/(-357). Factor 2/17*m**2 + 0*m - l*m**3 + 0.
-2*m**2*(m - 1)/17
Let x(f) be the second derivative of -5*f**4/12 - 85*f**3 + 515*f**2/2 - 10*f + 7. Find k such that x(k) = 0.
-103, 1
Let p(c) be the third derivative of -c**8/8064 + c**7/672 + c**6/72 - 13*c**5/60 - 14*c**2. Let g(h) be the third derivative of p(h). Factor g(l).
-5*(l - 4)*(l + 1)/2
Let d(z) be the second derivative of 27/20*z**5 - 27*z**2 - 1/10*z**6 - 29/4*z**4 + 39/2*z**3 + 12*z - 3. Suppose d(j) = 0. What is j?
1, 2, 3
Let z(k) be the first derivative of k**4/84 - k**3/14 + k**2/7 - 9*k - 7. Let a(c) be the first derivative of z(c). Solve a(t) = 0 for t.
1, 2
Let z = -15934 - -207256/13. Let s = z + -258/65. Suppose -2/5*f**4 - 26/5*f**2 - s*f - 8/5 - 12/5*f**3 = 0. Calculate f.
-2, -1
Let a(h) = 7*h**4 + 31*h**3 + 199*h**2 + 293*h + 133. Let y(v) = -3*v**4 - 16*v**3 - 99*v**2 - 146*v - 66. Let w(b) = -2*a(b) - 5*y(b). Factor w(n).
(n + 1)**2*(n + 8)**2
Let t(l) = 3*l**2 + 139*l - 334. Let h(p) = p**2 + 46*p - 112. Let n(c) = -11*h(c) + 4*t(c). Factor n(a).
(a - 2)*(a + 52)
Let t(j) = -j**2 - 90*j - 1239. Let n be t(-17). Find a such that -n*a + 4/11 + 14/11*a**5 - 32/11*a**4 + 28/11*a**2 + 8/11*a**3 = 0.
-1, 2/7, 1
Let j(p) = -3*p - 9. Let c be j(-4). Let c + 5*h - 5*h**2 - 10*h + 7 = 0. What is h?
-2, 1
Let m(c) be the first derivative of 2*c**4/17 - 10*c**3/3 + 173*c**2/17 - 76*c/17 + 138. Determine f so that m(f) = 0.
1/4, 2, 19
Let q(n) be the second derivative of -26*n + 0*n**3 - 1/25*n**6 + 0*n**2 + 0 - 1/105*n**7 - 1/30*n**4 - 3/50*n**5. Solve q(d) = 0 for d.
-1, 0
Let o be (4/(-72))/((-46)/69). Let t(v) be the second derivative of 0 - 2*v + 2*v**2 + 2/3*v**3 + o*v**4. Let t(d) = 0. Calculate d.
-2
Let s(v) = -8*v**4 + 20*v**3 - 16*v**2 + 4*v - 4. Let x(b) = -15*b**4 + 39*b**3 - 32*b**2 + 7*b - 7. Let h(c) = 7*s(c) - 4*x(c). Factor h(g).
4*g**2*(g - 2)**2
Let f be ((-4)/12)/(3/(-171)). Suppose -6*g - f = -i - g, -5*i + 3*g = -29. Suppose -2*k**i - 2 + k**2 + 3*k**2 + 0*k**4 = 0. What is k?
-1, 1
Let t(z) be the first derivative of z**6/10 - 3*z**5/10 + z**4/4 - 4*z - 6. Let i(d) be the first derivative of t(d). Factor i(h).
3*h**2*(h - 1)**2
Let p = -58 - -71. Factor -p*z**2 - 6*z**2 + 50*z - 24 - 9*z**2 + 2*z**3.
2*(z - 12)*(z - 1)**2
Let j(g) be the first derivative of -4*g**5/45 - g**4/3 + 4*g**3/3 - 10*g**2/9 + 76. Factor j(y).
-4*y*(y - 1)**2*(y + 5)/9
Let w(c) be the first derivative of 17*c**3/7 + 54*c**2/7 + 12*c/7 - 35. Factor w(z).
3*(z + 2)*(17*z + 2)/7
Suppose 1/5*p**3 - 72/5 + 72/5*p**2 - 1/5*p = 0. What is p?
-72, -1, 1
Let o = 2191/264 - -3/88. Determine d, given that -55/3*d**2 + 5 + 5*d**3 + o*d = 0.
-1/3, 1, 3
Let h(f) = -68*f - 3927. Let o be h(-58). Suppose o*d - 289/2 - 1/2*d**2 = 0. Calculate d.
17
Factor 0*r + 2/7*r**4 - 12/7*r**3 + 0 + 16/7*r**2.
2*r**2*(r - 4)*(r - 2)/7
Let t be (9 - 184/21)*(-1)/(-5). Let s(o) be the second derivative of -1/147*o**7 + 0*o**3 + 0 + 0*o**2 + 0*o**6 + 3/70*o**5 - t*o**4 - 4*o. Factor s(a).
-2*a**2*(a - 1)**2*(a + 2)/7
Let c be (-38)/(-21) + (-1532)/(-8043). Let v be 10/(-4)*(-21)/15. Factor -h**c + 0*h + 0 - v*h**4 - 9/2*h**3.
-h**2*(h + 1)*(7*h + 2)/2
Let j(n) = 76*n**3 + 14*n**2 - 12*n - 6. Let i(v) = -v**2 + 2*v + 1. Let a(o) = 6*i(o) + j(o). Factor a(s).
4*s**2*(19*s + 2)
Let c(t) be the second derivative of -t**6/80 + 153*t**5/80 - 2701*t**4/32 + 1275*t**3/4 - 1875*t**2/4 + 167*t. Factor c(k).
-3*(k - 50)**2*(k - 1)**2/8
Factor 2/9*j**2 + 98 - 28/3*j.
2*(j - 21)**2/9
Let t(m) be the first derivative of -3*m**5/20 - 7*m**4/12 - 8*m**3/9 - 2*m**2/3 + 14*m + 14. Let d(r) be the first derivative of t(r). Factor d(q).
-(q + 1)*(3*q + 2)**2/3
Let m(q) be the second derivative of -2*q**6/45 + 2*q**4/3 + 16*q**3/9 + 2*q**2 + 135*q - 2. Solve m(w) = 0 for w.
-1, 3
Factor -n - 3 - 3*n**2 - 5*n + 12 + 0*n.
-3*(n - 1)*(n + 3)
Find x such that 16/5 - 12/5*x - 4/5*x**2 = 0.
-4, 1
Suppose -2*r - 4*j = -6, r - 3*r + 6 = 2*j. Let -2*b - 3*b + 5*b**4 - 5*b**5 - 10*b**2 + 5 - 956*b**3 + 966*b**r = 0. Calculate b.
-1, 1
Let c be (-12)/8 + 0 - (-8)/4. Let j(l) be the second derivative of 0 + 2*l - c*l**3 + 1/20*l**5 + l**2 + 0*l**4. Find f such that j(f) = 0.
-2, 1
Let h = -12133/3 + 120757/30. Let m = 39/2 + h. Factor 2/5*v + m*v**2 - 2/5*v**3 + 0 - 2/5*v**4.
-2*v*(v - 1)*(v + 1)**2/5
Solve 1/4*q + q**5 - 3/4*q**2 - 5/4*q**3 + 3/4*q**4 + 0 = 0.
-1, 0, 1/4, 1
Factor 9/5*l + 18/5 + 1/5*l**2.
(l + 3)*(l + 6)/5
Suppose 45*g = 47*g - 10. Let b(s) be the second derivative of -1/110*s**g + 0 + 2/33*s**4 + 5*s + 0*s**2 - 4/33*s**3. Determine d so that b(d) = 0.
0, 2
Factor -1/3*z**2 + 0*z - 2/3*z**4 + 0 - 5/6*z**3 - 1/6*z**5.
-z**2*(z + 1)**2*(z + 2)/6
Let y(p) be the first derivative of -p**4/40 - 59*p**3/30 - 899*p**2/20 - 841*p/10 - 33. Factor y(v).
-(v + 1)*(v + 29)**2/10
Let s be (3/2)/(9/12). Factor -s*q + 54*q**2 - 28*q**2 - 28*q**2.
-2*q*(q + 1)
Let c be 4/3*(-21)/2. Let j be (5/(-2))/(7/c). What is u in 0*u**j + 3*u + u**5 - 6*u**3 - 2*u**5 + 4*u**5 = 0?
-1, 0, 1
Let r(b) be the first derivative of b**9/5292 + b**8/980 + b**7/735 + 7*b**3/3 - 35. Let f(o) be the third derivative of r(o). Determine m so that f(m) = 0.
-2, -1, 0
Let q(a) be the first derivative of -4*a**5/5 - 8*a**4 - 8*a**3/3 + 64*a**2 - 84*a - 119. Suppose q(b) = 0. Calculate b.
-7, -3, 1
Let p(q) be the second derivative of q**7/630 - q**5/90 + q**3/6 - 5*q. Let y(l) be the second derivative of p(l). Factor y(v).
4*v*(v - 1)*(v + 1)/3
Factor 3/2*a**4 + 0 + 0*a + 0*a**2 + 0*a**3.
3*a**4/2
Let m(z) be the second derivative of z**6/30 + 11*z**5/20 + 11*z**4/4 + 5*z**3/6 - 25*z**2 - 490*z. Factor m(n).
(n - 1)*(n + 2)*(n + 5)**2
Factor 3698 - 86*q + 1/2*q**2.
(q - 86)**2/2
Factor 3219 - 340*n - 147*n**2 + 339 + 2222 + 152*n**2.
5*(n - 34)**2
Let c(f) be the third derivative of f**10/680400 - f**8/90720 - 13*f**5/60 + 9*f**2. Let h(i) be the third derivative of c(i). Factor h(j).
2*j**2*(j - 1)*(j + 1)/9
Suppose 4*w - 8 = -2*n, -4 - 9 = -3*w + 2*n. Let j be -5*w/(-28 + (1 - -2)). Find o such that j*o**2 + 3/5*o + 0 = 0.
-1, 0
Let b(l) be the second derivative of 0*l**5 - 1/75*l**6 + 0*l**3 + 0*l**2 + 1/315*l**7 - 6*l + 0 + 2/45*l**4. Factor b(j).
2*j**2*(j - 2)**2*(j + 1)/15
Let t = -251 + 251. Let c(w) be the second derivative of -2/15*w**4 + 0*w**2 + 0*w**3 + 27/35*w**7 + 3*w - 39/25*w**6 + 4/5*w**5 + t. S