 - 19*g - 68. Let o(r) be the first derivative of q(r). Determine s, given that o(s) = 0.
2
Let v(n) be the second derivative of n**4/36 + 7*n**3/3 + 99*n**2/2 - n - 11. Factor v(j).
(j + 9)*(j + 33)/3
Let g(l) be the second derivative of l**4/54 + 101*l**3/9 - 610*l**2/9 + 605*l + 1. Determine w, given that g(w) = 0.
-305, 2
Let i(g) be the second derivative of 13/15*g**3 + 26*g - 8/5*g**2 - 1 - 1/6*g**4. Find q such that i(q) = 0.
1, 8/5
Let q(t) be the third derivative of -t**7/1050 + t**6/450 + 17*t**3/3 - 9*t**2 + 3*t. Let r(w) be the first derivative of q(w). Factor r(c).
-4*c**2*(c - 1)/5
Let c(z) be the third derivative of z**5/30 - 179*z**4/12 - 60*z**3 - 534*z**2. Factor c(f).
2*(f - 180)*(f + 1)
Let w(o) be the second derivative of -o**6/270 + 29*o**5/20 - 5633*o**4/36 - 17161*o**3/54 - 74*o - 43. Solve w(x) = 0.
-1, 0, 131
Suppose 29483*u + 108 = 29501*u. Let j(m) be the second derivative of 0 - 12*m - u*m**2 + 1/6*m**4 + 5/3*m**3. Factor j(l).
2*(l - 1)*(l + 6)
Determine x, given that 0*x**3 + 125 + 1/5*x**4 + 0*x - 10*x**2 = 0.
-5, 5
Let w(g) be the second derivative of -280*g + 3/25*g**6 - 1/315*g**7 - 169/15*g**2 + 13/3*g**3 + 71/45*g**4 - 97/75*g**5 + 0. What is m in w(m) = 0?
-1, 1, 13
Let p be 7/2 + ((-3)/6)/1. Solve -3*t**4 + 7*t**3 + 0*t**p - 10*t**3 + 6*t**3 = 0.
0, 1
Let l(x) = 18*x - 28. Let z be l(4). Suppose -2*q - 22 = -z. Factor 2*w**3 + 50*w**2 + 8*w**3 - 4*w - 70*w**2 - q*w + 20*w**4 + 5*w**5.
5*w*(w - 1)*(w + 1)**2*(w + 3)
Let b(x) be the second derivative of x**6/20 + 33*x**5/40 + 19*x**4/8 + 9*x**3/4 + 929*x. Suppose b(h) = 0. What is h?
-9, -1, 0
Suppose -i - 9 - 15 = 4*d, -3*d - 3*i = 27. Let b be (2/(-26))/(d - (-190)/40). Factor -2/13*y**5 + 0*y**2 - b*y**4 + 0 - 2/13*y**3 + 0*y.
-2*y**3*(y + 1)**2/13
Factor -15/7*k - 6/7*k**2 + 9/7*k**3 + 0.
3*k*(k + 1)*(3*k - 5)/7
Let d(i) = -i**3 - i**2. Let o(p) = -4*p**3 + 20*p**3 - 12*p + 5*p + 10*p**2 + 9*p. Let g(l) = 28*d(l) + 2*o(l). Solve g(r) = 0 for r.
0, 1
Let i be ((-23)/(-3))/((-11)/99). Let l = i - -74. Factor -7 - 8*w**2 - 10*w**3 + 2 + 15*w**4 + 15*w - 2*w**2 - 5*w**l.
-5*(w - 1)**4*(w + 1)
Let l be -4 + (-174)/(-18) + 4/(-6). Suppose -4*k**2 + 4*k**4 + 4*k**3 + 1 - 16*k**5 - 50*k**5 - 1 + 62*k**l = 0. Calculate k.
-1, 0, 1
Determine p so that 183108*p - 182828*p - 3*p**2 + 7*p**2 = 0.
-70, 0
Let l be ((-3887)/(-78))/23 - (0 - 15/18). Let y(k) be the second derivative of -1/28*k**4 + 0*k**2 + 1/14*k**l - 38*k + 0. Find v, given that y(v) = 0.
0, 1
Determine h so that 48*h - 1570*h**2 - 1567*h**2 - 52 + 3141*h**2 = 0.
-13, 1
Let s = -21 + 24. Factor -20*x**3 - 2187*x + 2223*x + 12*x**2 + s*x**4 + x**4.
4*x*(x - 3)**2*(x + 1)
Let c(i) be the third derivative of 1/90*i**5 + 0*i + 1 - 1/360*i**6 - i**2 - 1/3*i**3 + 5/72*i**4. Factor c(h).
-(h - 3)*(h - 1)*(h + 2)/3
Let c(k) = 64*k + 4738. Let a be c(-74). Let o(v) be the first derivative of -1/9*v**a - 1/27*v**3 - 1 + 1/3*v. Factor o(g).
-(g - 1)*(g + 3)/9
Let m(x) be the first derivative of 5*x**6/6 - 3*x**5 - 65*x**4/4 + 85*x**3 - 90*x**2 + 88. Factor m(d).
5*d*(d - 3)**2*(d - 1)*(d + 4)
Solve 1/7*m**5 + 0 + 85/7*m**2 - 150/7*m - 9/7*m**4 + 9/7*m**3 = 0.
-3, 0, 2, 5
Let x(m) = 5*m**5 - 86*m**4 - 56*m**3 + 93*m**2 + 23*m - 7. Let g(w) = -w**5 - w**4 - w**3 - 2*w + 1. Let s(p) = 14*g(p) - 2*x(p). Let s(f) = 0. Calculate f.
-1, -2/3, 1/4, 1, 7
Suppose -2*s - 3140 = 5*q, q + 314 + 314 = -2*s. Let a be (-2)/(-8) + 157/q. Let a + 1/3*f**2 - 1/3*f**3 - 1/3*f**4 + 1/3*f**5 + 0*f = 0. Calculate f.
-1, 0, 1
Let -78/5*d**2 - 63/5*d + 1/5*d**5 - 2/5*d**3 + 7/5*d**4 + 27 = 0. What is d?
-5, -3, 1, 3
Let i(x) = -2*x**5 + x**4 + x**3 - 2*x**2 - x - 1. Let m(p) = -3*p**5 + 2*p**4 - 158*p**3 - 1284*p**2 - 3842*p - 4098. Let y(q) = 6*i(q) - 3*m(q). Factor y(f).
-3*(f - 16)*(f + 4)**4
Let j = 7873/4 + -39361/20. Let m(o) be the third derivative of 2*o**3 + 1/30*o**6 - j*o**5 - 1/6*o**4 + 0*o - 35*o**2 + 0. Find l such that m(l) = 0.
-1, 1, 3
Let r = 110 - 6. Factor -89*u**4 + r*u**4 + 17*u**2 + 4*u**2 + 6*u + 3*u**5 + 27*u**3.
3*u*(u + 1)**3*(u + 2)
Suppose 59*d - 649 = -0*d + 708. Let z(n) be the third derivative of -1/945*n**7 + 0*n**3 + 0 - d*n**2 + 2/135*n**5 + 0*n - 2/27*n**4 + 1/270*n**6. Factor z(g).
-2*g*(g - 2)**2*(g + 2)/9
Let v = 324 + -321. Let y = 2592 + -2588. Find a such that 18/5*a**v - 8/5*a**y + 4/5*a**2 - 18/5*a + 4/5 = 0.
-1, 1/4, 1, 2
Let c = 4725 - 4721. Let z(d) be the third derivative of 0*d - 5/8*d**c + 0*d**3 - 19*d**2 - 1/12*d**5 + 0. Factor z(f).
-5*f*(f + 3)
Suppose 175*l - 875*l + 50400 = 0. Let a(g) be the second derivative of -2*g - 1/15*g**6 - 18*g**4 + l*g**3 + 0*g**2 + 0 + 9/5*g**5. What is h in a(h) = 0?
0, 6
Factor -18460/7*q - 60492/7 - 4/7*q**3 + 556/7*q**2.
-4*(q - 71)**2*(q + 3)/7
Let o(v) be the second derivative of -2*v**5/5 - 9*v**4/2 - 18*v**3 - 27*v**2 + 1235*v. Factor o(d).
-2*(d + 3)**2*(4*d + 3)
Let m = -135806 + 1493870/11. Factor -4/11*h**4 + 2/11*h**5 - 2/11*h + 0*h**3 + 0 + m*h**2.
2*h*(h - 1)**3*(h + 1)/11
Let t be 62/(-22) + 7 + (-4)/22. Let p be (21 + -25)*(t + (-27)/6). Factor 11/3*d**2 - 4/3*d**3 + 0 - 1/3*d**4 - p*d.
-d*(d - 1)**2*(d + 6)/3
Let z = -102 - -147. Suppose 46*v = z*v. Suppose 1/2 - 1/2*n**2 + v*n = 0. Calculate n.
-1, 1
Let a be (44 - 22)/(4/2). Let k(j) be the first derivative of -2*j**2 - 8*j - a - 1/6*j**3. Factor k(v).
-(v + 4)**2/2
Factor 5*c**2 + 160*c - 1006*c + 122*c + 5036 - 5658 - 829*c.
(c - 311)*(5*c + 2)
Suppose 47*u = 159*u - 931 + 147. Suppose 1/2*p**2 + u - 9/2*p = 0. What is p?
2, 7
Find t, given that 88*t**2 - 28*t**2 - 5041 - 29*t**2 - 142*t - 32*t**2 = 0.
-71
Suppose 184*q - 160*q - 77*q = -159. Factor -4/7*j**2 - 4/7 - 22/21*j - 2/21*j**q.
-2*(j + 1)*(j + 2)*(j + 3)/21
Suppose o + 87*s - 4 = 86*s, 1 = o - 2*s. Let l(p) be the second derivative of -32*p**2 + 20*p + 8*p**o + 1/20*p**5 - p**4 + 0. Factor l(k).
(k - 4)**3
Let q(g) = 45*g - 186. Let y be q(4). Let x(b) = b**3 - 15*b**2 - 129*b - 16. Let t be x(y). Factor 486/5*d + 54/5*d**t + 1458/5 + 2/5*d**3.
2*(d + 9)**3/5
Let n be ((-8)/(-6) - (-14446)/(-16077))*8/10. Find a, given that 0 + 2/23*a**2 - n*a = 0.
0, 4
Let k(l) be the third derivative of 1/88*l**4 + 0 + 0*l + 1/33*l**3 + 1/660*l**5 + 40*l**2. Suppose k(c) = 0. Calculate c.
-2, -1
Let 546/5 + 614/5*d + 2/5*d**3 + 14*d**2 = 0. What is d?
-21, -13, -1
Let y(l) be the third derivative of 0*l - 255*l**2 - 3/35*l**5 + 2/735*l**7 + 8/7*l**3 + 0 + 2/21*l**4 + 0*l**6. Suppose y(z) = 0. Calculate z.
-3, -1, 2
Let t(x) = -8*x - 7*x + 387 + 32 + 2*x. Let v be t(32). Factor 2/3*r**4 - 8/3*r**v + 8/3*r + 0 - 2/3*r**2.
2*r*(r - 4)*(r - 1)*(r + 1)/3
Factor 6*i**3 - 2*i**3 - 5*i**4 - 8*i**3 - 11*i**3 + 10*i**3.
-5*i**3*(i + 1)
Let y(h) be the second derivative of h**4/12 - h**3/2 - 104*h**2 + 9699*h. Factor y(b).
(b - 16)*(b + 13)
Suppose -2 = 2*a + 3*t, -5 = -5*a + 26*t - 31*t. Factor 2*b**2 - 6 + 159 - 30*b - a*b**2 - 12*b.
-3*(b - 3)*(b + 17)
Suppose -2*h = 2*u - 6*h - 28, 5*u - 122 = -3*h. Factor -198*q**3 + u*q - 25*q**4 - 336*q**2 - 144*q - 4*q**5 - 31*q**4 - 46*q**3 - 22*q.
-4*q*(q + 1)**2*(q + 6)**2
Let l(a) be the third derivative of a**6/120 + 38*a**5/5 + 17175*a**4/8 - 52441*a**3/3 + 1896*a**2. Let l(g) = 0. What is g?
-229, 2
Let u(j) be the first derivative of j**6/255 - 4*j**5/85 + j**4/6 - 10*j**3/51 + 64*j - 16. Let m(r) be the first derivative of u(r). Find y such that m(y) = 0.
0, 1, 2, 5
Let z be ((10 - 20) + 8)/((-856)/10). Let c = z - -515/856. Factor -9/8*i + 0 + c*i**3 - 3/8*i**2 - 1/8*i**4.
-i*(i - 3)**2*(i + 1)/8
Let n(t) be the third derivative of t**6/420 + 8*t**5/105 + 85*t**4/84 + 50*t**3/7 - 17*t**2 - 64. Factor n(i).
2*(i + 5)**2*(i + 6)/7
Let w(y) be the third derivative of y**8/1008 + y**7/63 - 23*y**6/360 + y**5/15 - 1704*y**2. Find q such that w(q) = 0.
-12, 0, 1
Let x(v) = -2*v**2 - 2*v + 1. Let f(m) = -50*m**2 - 131*m + 2. Let y(r) = -3*f(r) + 15*x(r). Factor y(q).
3*(q + 3)*(40*q + 1)
Let w(j) be the first derivative of -j**4/8 - 70*j**3/3 + 867*j**2/4 - 657*j + 233. Determine f so that w(f) = 0.
-146, 3
Suppose -5*w + 745 = 5*j, -w + 2*j + 41 = -111. Factor 400*r - w*r**3 + 240 - 115*r**2 + 193 + 45*r**4 - 113.
5*(r + 1)**2*(3*r - 8)**2
Let f(q) = -q**3 - 21*q**2 + 20*q - 30. Let s be f(-22). Su