 + 0 - 11/20*c**6 - 16*c**4 + 512*c**3. Factor w(i).
-3*(i - 2)*(i + 8)**3
Factor 14*k - 29/3*k**2 + 0 - 1/3*k**4 - 4*k**3.
-k*(k - 1)*(k + 6)*(k + 7)/3
Let m(x) be the first derivative of -2*x**3/3 + 3*x**2 + 540*x - 2612. Factor m(s).
-2*(s - 18)*(s + 15)
Determine b so that 82/9*b**2 + 74/9*b - 10/9*b**3 - 2 = 0.
-1, 1/5, 9
Suppose 2*x = -5*x + 28. Determine z so that -40*z**x - 12*z**3 - 8*z**3 - 68*z**5 + 53*z**5 = 0.
-2, -2/3, 0
Let b(u) be the first derivative of -8*u**3/3 + 6*u**2 - 2. Suppose 37*r = -2*r - 156. Let i(l) = -l**2 + l + 1. Let s(p) = r*i(p) + b(p). Solve s(v) = 0 for v.
1
Suppose -9*w = -3*j - 10*w - 94, 50 = -j - 5*w. Let o be j/(-36) + 90/(-108). What is s in 0 - 8/5*s**3 + o*s + 16/5*s**2 + 1/5*s**4 = 0?
0, 4
Let i(w) be the first derivative of -w**7/1680 + w**5/240 - 31*w**3 + 2*w + 249. Let d(m) be the third derivative of i(m). Solve d(v) = 0.
-1, 0, 1
Suppose -90*t + 741 = 145*t - 199. Let p(q) be the second derivative of -27*q - 3*q**5 + 0 - 175/12*q**t + 10*q**3 + 90*q**2 - 1/6*q**6. What is l in p(l) = 0?
-6, -1, 1
Let h(p) = 4*p**2 + 23*p + p**2 - 41 - 6*p**2. Let o be h(21). Factor 81*n**3 + 45*n**2 + o - 14*n - 18*n + 8 - 5.
(n + 1)*(9*n - 2)**2
Factor -45 - 25*f**4 - 203*f**2 + 57*f**2 - 104*f**2 - 24*f**5 + 175*f + 140*f**3 + 10*f**3 + 19*f**5.
-5*(f - 1)**4*(f + 9)
Suppose 23 = -4*d + 5*c, d - 65*c - 31 = -69*c. What is a in -2/7*a**4 + 40/7*a**d + 44/7*a + 86/7*a**2 + 0 = 0?
-1, 0, 22
Find z, given that -232*z + 19595*z**2 - 19592*z**2 - 660 + 79*z = 0.
-4, 55
Suppose 9*t - 4*t + 12 = -3*v, 3*t = 5*v + 20. Let p(g) be the third derivative of 0*g**4 + 0 - 1/90*g**5 - 9*g**2 + 0*g**3 + t*g + 1/180*g**6. Solve p(i) = 0.
0, 1
Let 896*r**2 - 176/3*r**3 + 21952/3 + 4/3*r**4 - 15680/3*r = 0. What is r?
2, 14
Solve -4 - 5*l - 10*l**3 + 35/2*l**2 + 3/2*l**4 = 0.
-1/3, 1, 2, 4
Let m be ((-8)/14)/(57/(-21) - -3). Let u(w) = -11*w**2 + 71*w - 89. Let a(i) = -3*i**2 + 18*i - 22. Let c(y) = m*u(y) + 9*a(y). Factor c(s).
-5*(s - 2)**2
Let z = 243/3898 + 24851/7796. Factor 15/4*w + 1/2 + z*w**2.
(w + 1)*(13*w + 2)/4
Let m(y) = -2*y + 7. Let t(g) = -g**2 - 60*g - 639. Let l(w) = -12*m(w) + 3*t(w). Factor l(z).
-3*(z + 23)*(z + 29)
Let u be (5 - (-42)/(-7) - (-4 - -3))/1. Let p(a) be the second derivative of 0 - 9*a + 1/30*a**4 - 1/5*a**2 + u*a**3. Factor p(l).
2*(l - 1)*(l + 1)/5
Let s(d) be the first derivative of 2*d**3/21 + 48*d**2 - 674*d/7 - 3561. Factor s(i).
2*(i - 1)*(i + 337)/7
Let q(d) be the second derivative of -d**4/36 + 9*d**3/2 - 40*d**2/3 - 9*d + 43. Solve q(c) = 0.
1, 80
Let -4264/3*o + 1420 - 1/3*o**3 + 1069/3*o**2 = 0. Calculate o.
2, 1065
Let t be 6/((-48)/(-43))*8. Factor t*l**2 + 0 + 17*l**2 + 8 + 111*l - 33*l**3 + 10.
-3*(l - 3)*(l + 1)*(11*l + 2)
Let y(h) be the third derivative of h**5/150 + 49*h**4/60 + 46*h**3/5 - 188*h**2. Determine l, given that y(l) = 0.
-46, -3
Let s(c) = -2*c**4 + 92*c**3 + 286*c**2 + 408*c + 162. Let b(l) = -7*l**3 + l + 3. Let w(t) = -6*b(t) - s(t). Factor w(d).
2*(d - 30)*(d + 1)**2*(d + 3)
Factor -9760*j**2 - 6*j**3 + 5*j**3 + 9874*j**2 + 468*j + 472.
-(j - 118)*(j + 2)**2
Let p(b) be the second derivative of b**4/18 - 38*b**3/9 + 24*b**2 + 1307*b. Factor p(t).
2*(t - 36)*(t - 2)/3
Let l(n) = -n**2 + 18*n - 29. Let y(t) = t**2 - 3*t + 28. Let c(p) = -2*l(p) - 3*y(p). Factor c(j).
-(j + 1)*(j + 26)
Factor -29282/3 - 2/3*p**2 + 484/3*p.
-2*(p - 121)**2/3
Let s(k) = k**4 - 500*k**3 - 20667*k**2 + 2*k + 2. Let p(h) = -7*h**4 + 2501*h**3 + 103335*h**2 - 11*h - 11. Let q(u) = 2*p(u) + 11*s(u). Factor q(o).
-3*o**2*(o + 83)**2
Let s(q) be the third derivative of q**6/200 + 7*q**5/20 + 49*q**4/20 + 32*q**3/5 + 675*q**2 - 1. Solve s(x) = 0 for x.
-32, -2, -1
Let l(m) be the second derivative of -1/12*m**6 + 89*m + 23/24*m**4 - 7/40*m**5 + 0 - 5/12*m**3 - 3/2*m**2. Find o, given that l(o) = 0.
-3, -2/5, 1
Let f(r) = r**2 - 5*r + 23. Let v be f(8). Suppose 16 = v*g - 43*g. Factor -60*t**g - 32*t + 117*t**4 + 8*t**3 - 61*t**4 + 16*t**2.
-4*t*(t - 2)**2*(t + 2)
Let l(w) = -8*w**2 - 119*w + 17. Let k be l(-15). Suppose 0*d**k + 0 + 2/7*d**3 - 2/7*d = 0. What is d?
-1, 0, 1
Let y(a) be the first derivative of -a**6/33 - 36*a**5/55 + a**4/11 + 24*a**3/11 - a**2/11 - 36*a/11 + 9940. Determine b so that y(b) = 0.
-18, -1, 1
Let l be -3 - (6 + -9)*1. Factor 2 + l + v**3 - v + 12*v**2 - 16*v**2 + 2*v**2.
(v - 2)*(v - 1)*(v + 1)
Suppose 324*n**2 + 288 - 1630*n**4 + 824*n**4 + 81*n**3 + 516*n + 812*n**4 = 0. Calculate n.
-8, -2, -3/2
Let z(w) be the second derivative of -1/200*w**5 + 0 + 0*w**3 + 0*w**2 + 1/420*w**7 - 1/300*w**6 - 107*w + 1/120*w**4. Factor z(y).
y**2*(y - 1)**2*(y + 1)/10
Suppose 603 + 159 + 621 = 676*a - 215*a. Let 26/3*s**a - 3*s**4 - 2/3*s + 0 - 5*s**2 = 0. Calculate s.
-1/9, 0, 1, 2
Factor 1702/9*b + 2/9*b**3 + 7406/9 + 106/9*b**2.
2*(b + 7)*(b + 23)**2/9
Solve -33484*k**2 - 6962*k**3 - 4*k**5 - 4324*k - 4*k**5 + 43244*k - k**5 - 424*k**4 + k**5 - 10192 = 0.
-26, -14, 1/2
Let b be 3472/(-558) + 7*4/126 + (-384)/(-20). Let -b*w**2 + 6/5*w**3 - 96/5 + 156/5*w = 0. What is w?
1, 2, 8
Let j be (-138)/69*(27/(-12) + 2). Factor -j*s - 7/10*s**3 + 11/10*s**2 + 1/10*s**4 + 0.
s*(s - 5)*(s - 1)**2/10
Suppose -3*n = 3 - 21. Let u be (-5)/(-20) + (-261)/4. Let w(d) = 5*d**3 + d**2 - 6. Let s(y) = 55*y**3 + 10*y**2 - 65. Let r(g) = n*s(g) + u*w(g). Factor r(x).
5*x**2*(x - 1)
Let z(q) = 4*q**3 + 604*q**2 + 618*q + 2703. Let a be z(-150). Factor -2/5*k**a + 64/5 - 8*k - 22/5*k**2.
-2*(k - 1)*(k + 4)*(k + 8)/5
Let u be 630/(-21) - (-6 - 6) - -18. Factor 56/9*d**2 + u - 2/9*d**4 + 0*d - 8/3*d**3.
-2*d**2*(d - 2)*(d + 14)/9
Let a(o) be the third derivative of 3*o**6/320 - 89*o**5/80 + 59*o**4/64 - 409*o**2. Factor a(f).
3*f*(f - 59)*(3*f - 1)/8
Let z(o) = -8*o**4 - 26*o**3 - 2*o**2 + 18*o + 2. Let b(f) = 33*f**4 + 107*f**3 + 8*f**2 - 75*f - 9. Let t(j) = -4*b(j) - 18*z(j). Find m such that t(m) = 0.
-3, -1, 0, 2/3
Let i(j) be the third derivative of -1/600*j**5 + 0 - 1/60*j**4 - 1/20*j**3 - 2*j**2 + 12*j. Suppose i(m) = 0. Calculate m.
-3, -1
Factor 2825761/2*k - 1681/2*k**2 - 4750104241/6 + 1/6*k**3.
(k - 1681)**3/6
Let g(n) be the third derivative of 1/140*n**6 - 1/70*n**5 - 1/735*n**7 + 1/84*n**4 + 57*n**2 + 0*n**3 + 0*n + 0. Determine h so that g(h) = 0.
0, 1
Let y(b) be the first derivative of b**4/4 + 229*b**3/3 - 461*b**2/2 + 231*b - 1694. Factor y(t).
(t - 1)**2*(t + 231)
Suppose -484/3*q + 304 + 10/3*q**2 + 2/3*q**3 = 0. What is q?
-19, 2, 12
Suppose 0 = 3*n + 5*j + 205, 310 = -4*n + 3*j + 27. Let g be 8*(483/n + 7). Factor -4/5*p**3 - 2/5*p**4 + 2/5 + 0*p**2 + g*p.
-2*(p - 1)*(p + 1)**3/5
Let d(s) be the third derivative of 5*s**8/168 - 9*s**7/14 - s**6/24 + 67*s**5/4 - 1265*s**4/24 + 65*s**3 + s**2 - 5634. Determine m, given that d(m) = 0.
-3, 1/2, 1, 2, 13
Let i = 761 + -759. Let j(d) = -3*d - 29. Let o be j(-11). Let -2/11*x**o + 0 - 4/11*x + 2/11*x**i + 4/11*x**3 = 0. What is x?
-1, 0, 1, 2
Let o(y) = 7*y**2 + 109*y. Suppose 15*g = 6*g - 36. Let m(t) = 8*t**2 + 108*t. Let l(r) = g*o(r) + 3*m(r). Factor l(b).
-4*b*(b + 28)
Suppose -11*k = -6*k - 3*a - 13, 0 = -2*k + 4*a + 8. What is q in -30 - 127 + 41 + 11 + 75*q - 3*q**k - 93 = 0?
3, 22
Let b(f) = 49*f**2 + 195*f + 6. Let r be b(-4). Find z, given that 2*z - 5*z**2 - r + 5*z + 141 + 8*z + 9 = 0.
-4, 7
Let y = -42771/32 + 1336. Let h = 31/32 + y. Factor 0 - h*r**2 - 1/8*r - 1/8*r**4 - 3/8*r**3.
-r*(r + 1)**3/8
Find u, given that 1197/2 + 3597/4*u + 3/4*u**3 + 603/2*u**2 = 0.
-399, -2, -1
Factor -3855*b + 3/2*b**2 + 4953675/2.
3*(b - 1285)**2/2
Let k be (3 + -5)/(-5 + 1). Let m = 288/13 + -563/26. Factor i - k*i**2 + 0 - m*i**3.
-i*(i - 1)*(i + 2)/2
Let o(r) = -8*r**2 - 3792*r - 868620. Let v(f) = 7*f**2 + 3776*f + 868621. Let p(c) = -3*o(c) - 4*v(c). Factor p(n).
-4*(n + 466)**2
Let i(u) = u**2 + 2*u. Let j(z) = -z - 1. Let m(t) = -i(t) - j(t). Let g(n) = -12*n**2 - 224*n - 60. Let x(f) = g(f) + 4*m(f). Factor x(p).
-4*(p + 14)*(4*p + 1)
Let l(v) be the first derivative of v**3/12 - 131*v**2/4 - 1385. Solve l(c) = 0 for c.
0, 262
What is m in -5*m**2 + 500*m**3 - 245*m**3 + 22*m**2 - 81 - 63*m - 256*m**3 = 0?
-1, 9
Let j(v) be the first derivative of -v**4/30 + 122*v**3/45 - 899*v**2/15 - 1922*v/15 - 921. Factor j(a)