ive of 3*f**8/112 - 67*f**7/140 + 15*f**6/8 + 247*f**5/40 - 39*f**4/4 - 45*f**3 + 1072*f**2. Find r such that v(r) = 0.
-1, -5/6, 1, 6
Let i(b) = -b**3 + b**2 - 2*b + 2. Let a(x) = -25*x**2 - 15*x - 20. Let y be 3*10*(-5)/30. Let l(o) = y*i(o) - a(o). Factor l(k).
5*(k + 1)**2*(k + 2)
Let u be (-100)/(-40)*(-112)/(-3150). Let q(k) be the first derivative of -1/3*k**2 - u*k**5 - 1 + 8/27*k**3 - 4/9*k + 1/6*k**4. Let q(w) = 0. Calculate w.
-1, -1/2, 1, 2
Suppose -4*s + 32 = 2*g, -5*g + 5*s = -0*s - 110. Let x = -18 + g. Factor -2*j + 0*j**2 + 2*j**2 + 0*j**x.
2*j*(j - 1)
Let v(j) be the third derivative of -2*j**5/15 - 133*j**4/132 - j**3/11 - 71*j**2 - 1. Solve v(o) = 0.
-3, -1/44
Let m(z) = 9*z**4 + 29*z**3 + 423*z**2 + 1835*z + 2900. Let s(n) = -7*n**4 - 30*n**3 - 414*n**2 - 1841*n - 2901. Let j(p) = -3*m(p) - 4*s(p). Factor j(w).
(w + 3)*(w + 8)*(w + 11)**2
Let v(w) = 140*w**2 - 125*w + 55. Let k(r) = 10*r**2 - 9*r + 4. Suppose 12*u - 400 = 260. Let s be -4*(1 - 0) + 0. Let g(h) = s*v(h) + u*k(h). Factor g(x).
-5*x*(2*x - 1)
Let p(t) = -2*t**3 + 4*t**2 + 2*t. Let x(z) = 16*z**3 + 70*z**2 - 106*z - 28. Let w(m) = 12*p(m) + x(m). What is a in w(a) = 0?
-1/4, 1, 14
Let t(h) be the first derivative of 6*h**2 + 0*h + 12*h**3 + 39/4*h**4 + 18/5*h**5 - 10 + 1/2*h**6. Factor t(g).
3*g*(g + 1)**2*(g + 2)**2
Let g(a) = a**3 + 7*a**2 + 6*a + 3. Let x be (-152)/26 + 2/(-13). Let y be g(x). Factor 6 - 10*z**3 - 2*z**y + 10 - 28*z**2.
-4*(z + 1)*(z + 2)*(3*z - 2)
Let w(n) = -26*n**2 + 20461*n + 3699. Let t(p) = -17*p**2 + 13641*p + 2465. Let i(k) = 7*t(k) - 5*w(k). Suppose i(v) = 0. Calculate v.
-2/11, 620
Let g(t) be the second derivative of -2*t**6/15 - 3*t**5 + 16*t**4/3 + 191*t. Factor g(u).
-4*u**2*(u - 1)*(u + 16)
Let u be (6/(-8))/(1736/(-26784)). Let c = 80 + -542/7. Find m such that u + 1/7*m**2 - c*m = 0.
9
Let p be (4/(-2))/(-18) + 1251/(-11259). Let i(r) be the first derivative of -42 - 2/9*r**3 + 0*r + p*r**2 + 5/12*r**4 + 7/15*r**5. Let i(d) = 0. What is d?
-1, 0, 2/7
Let c(m) be the first derivative of m**4/4 + 128*m**3/5 + 303*m**2/10 - 76*m/5 + 28. Factor c(j).
(j + 1)*(j + 76)*(5*j - 1)/5
Let d be (20/16)/(404/32 - (-33 - -45)). Factor 5/3*g**d - 40/3 - 10/3*g.
5*(g - 4)*(g + 2)/3
Let i(g) be the first derivative of -24*g**5/5 + 31*g**4 + 292*g**3/3 + 58*g**2 - 28*g - 1147. What is r in i(r) = 0?
-1, 1/6, 7
Let a(g) be the third derivative of 31 - 1/30*g**5 - 1/12*g**4 + 2/3*g**3 + 2*g**2 + 0*g. Factor a(b).
-2*(b - 1)*(b + 2)
Let f(a) = -a**4 - a**2 + a - 5. Let j(c) = 6*c**4 - 35*c**3 + 293*c**2 + 319*c + 25. Let b(k) = 5*f(k) + j(k). Factor b(o).
o*(o - 18)**2*(o + 1)
Let a = 1067413/3735921 + -1/533703. Determine h, given that a*h + 1/7*h**2 - 1/7*h**4 + 3/7*h**5 - 5/7*h**3 + 0 = 0.
-1, -2/3, 0, 1
Let t = 39 + -11. Suppose -10*j + t - 8 = 0. Determine k, given that -2*k + k + k**2 - 2*k**j = 0.
-1, 0
Let n(i) be the first derivative of 3*i**5/50 - 31*i**4/20 + 7*i**3/5 + 9*i**2/2 - 165*i - 93. Let l(c) be the first derivative of n(c). Factor l(q).
3*(q - 15)*(q - 1)*(2*q + 1)/5
Determine z so that -242/3*z**2 + 7688 - 6944/3*z - 2/3*z**3 = 0.
-62, 3
Let j be 150/18 - (190/26 - (-60)/(-195)). Factor -2/9*n - j - 2/9*n**3 + 8/9*n**2.
-2*(n - 3)*(n - 2)*(n + 1)/9
Let q = -264 + 327. Solve -26*w + q - 1917*w**2 + 1920*w**2 - 40*w = 0.
1, 21
Suppose -24 = -2*j + 4*z, -3*j + 57 = 4*z + 61. Factor -5*f - f + 33 + f**2 - 38 - 3*f + f**3 - j*f**2.
(f - 5)*(f + 1)**2
Let l(j) be the second derivative of 1/16*j**3 + 1/112*j**7 + 0 + 177*j - 15/16*j**4 + 3/16*j**6 - 3/80*j**5 + 45/16*j**2. Solve l(f) = 0.
-15, -1, 1
Let t(f) be the second derivative of f**5/30 - 19*f**4/9 - 13*f**3/3 + 1440*f. Factor t(h).
2*h*(h - 39)*(h + 1)/3
Let h(g) = -171*g + 2055. Let v be h(12). Let n(d) be the first derivative of 12 + 21*d + 15/2*d**2 - 2*d**v. What is j in n(j) = 0?
-1, 7/2
Let z be 300/(740/37) - (-45)/(-3). Let 2/3*o**4 + 0*o + 1/3*o**5 + z - 1/3*o**3 - 2/3*o**2 = 0. Calculate o.
-2, -1, 0, 1
Let o(z) be the third derivative of z**6/160 + 37*z**5/80 + 191*z**4/32 + 155*z**3/8 - 279*z**2 + 2*z + 5. Solve o(u) = 0 for u.
-31, -5, -1
Let o(q) = -2 + 7*q - 1 + 0 + q**2. Let x be o(-8). Find c, given that -c**4 + x*c**4 - 2*c**5 - 12*c**2 + 6*c**2 + 2*c**2 + 2*c = 0.
-1, 0, 1
Factor 32420*n + n**2 - 17521*n + 3*n**2 + 283024 - 17027*n.
4*(n - 266)**2
Factor 833*m**2 - 7*m - 1672*m**2 - m**3 - 117 + 832*m**2 + 76*m.
-(m - 3)**2*(m + 13)
Let c(h) be the second derivative of h**6/120 - 7*h**5/40 + 35*h**4/48 + 25*h**3/12 + 3279*h. Factor c(f).
f*(f - 10)*(f - 5)*(f + 1)/4
Let h = 60 - 34. Suppose 21*t - 88 = 10*t. Factor -2*a**4 - h*a - 23*a + t*a**3 + 53*a - 10*a**2.
-2*a*(a - 2)*(a - 1)**2
Determine h so that 408*h**2 + 8*h**3 + 624*h - 273*h**2 - 420 + 315*h**2 + 7*h**3 + 609*h**2 = 0.
-70, -1, 2/5
Let s(d) be the first derivative of d**6/24 - 857*d**5/20 + 855*d**4/8 + d**3/6 - 1711*d**2/8 + 855*d/4 + 7298. Factor s(q).
(q - 855)*(q - 1)**3*(q + 1)/4
Let l(b) be the first derivative of b**4/3 + 16*b**3/3 + 80*b + 25. Let r(m) be the first derivative of l(m). What is y in r(y) = 0?
-8, 0
Let z(x) = -92*x - 642. Let n be z(-7). Suppose 4*g = 4*t - 4, -3*t + 3*g = -2*t + 1. Solve 28*h**t - 15*h - 16*h**2 + 5*h**3 - 13*h**2 - 9*h**n = 0 for h.
-1, 0, 3
Let c = 28 + -16. Suppose c*l - 22 = l. Find z such that -6*z**2 + 3*z**l - 12*z - 2 - 10 = 0.
-2
Factor 128/9*i + 58/9*i**2 + 32/9 + 7/9*i**3.
(i + 4)**2*(7*i + 2)/9
Let i(r) be the second derivative of 0 + 0*r**2 + 1/3*r**3 - 5/4*r**4 + 50*r. Find d, given that i(d) = 0.
0, 2/15
Let d(r) be the second derivative of -1/6*r**6 + 0*r**3 + 5/4*r**5 - 5/4*r**4 - 5/42*r**7 + 0*r**2 + 0 + 67*r. Find w such that d(w) = 0.
-3, 0, 1
Let p(s) be the third derivative of -s**6/120 + s**5/15 - 5*s**4/24 + s**3/3 - 15*s**2 - 5*s. Factor p(f).
-(f - 2)*(f - 1)**2
Let a be ((-40)/(-50))/(6/4 - (-33)/(-30)). Let s(g) be the second derivative of -1/30*g**4 - g**a - 2*g - 28 + 2/5*g**3. Factor s(z).
-2*(z - 5)*(z - 1)/5
Let z(k) be the first derivative of 12*k**3 + 177*k**2 - 122*k - 305. Factor z(h).
2*(3*h - 1)*(6*h + 61)
Let p be (-5026)/(-1077)*(-1)/(-28). Factor 98/3 - 14/3*v + p*v**2.
(v - 14)**2/6
Let y be 2/(-12) - (-6 + 61/(-6)). Suppose s - 19 + y = 0. Factor 217*a**2 + 198*a**2 - 625*a**s - 40*a**2 - 75*a + 5.
-5*(5*a - 1)**3
Suppose -4*c - 22*m + 24*m + 26 = 0, -4*c + 16 = -4*m. Let g be (-10)/(c/27*-27). Solve 14/9*l**2 - 2/3*l - g*l**3 + 0 + 2/9*l**4 = 0.
0, 1, 3
Suppose n + 18*v + 68 = 6*v, 3*n + 5*v = -18. Let f(l) be the first derivative of -4/15*l**2 + 2/45*l**3 + 1/30*l**n - 47 - 8/15*l. Solve f(j) = 0 for j.
-2, -1, 2
Factor -24*k + k**3 + 52*k**2 + 36*k**2 - 18*k**4 + 24*k**2 - 15*k**3.
-2*k*(k - 2)*(k + 3)*(9*k - 2)
Suppose -y = 0, 51 = 5*n + y + 1. Suppose -4*q + 2*f + n = 0, -5*q + 2 = 2*f + 12. Factor 2/3*h**3 + 0*h**2 - 2/3*h + q.
2*h*(h - 1)*(h + 1)/3
Suppose 0 = -2*h + 5*t - 11, 5*t + 6 = 7*t. Suppose y + 19 = 4*x, 0 = -h*x + 7*x + 2*y - 27. Solve 0*o**2 - 4/7*o**3 + 2/7*o + 0*o**4 + 2/7*o**x + 0 = 0.
-1, 0, 1
Let t(n) be the third derivative of 11/72*n**4 + 0 + n**2 + 1/3*n**3 + n + 1/36*n**5. Determine p, given that t(p) = 0.
-6/5, -1
Let v be (-2)/234 - 18/10*20/(-156). Let -4/3*u**3 + 0 - v*u**4 - 8/3*u**2 - 16/9*u = 0. What is u?
-2, 0
Let i(g) = -4*g**2 + 2*g - 1. Let h(y) = -14*y**2 - 186*y - 4611. Let q(d) = -h(d) + 3*i(d). Solve q(a) = 0.
-48
Solve 2/7*j**2 + 7928162/7 - 7964/7*j = 0.
1991
Let -33/2 - 3/4*t**2 - 33/4*t**3 + 101/4*t + 1/4*t**4 = 0. What is t?
-2, 1, 33
Let i(s) be the first derivative of -3*s**5/10 + 111*s**4/4 - 145*s**3/2 + 54*s**2 + 3425. Let i(n) = 0. Calculate n.
0, 1, 72
Let d(r) = -60*r**2 + 5535*r - 10935. Let w(p) = -5*p**2 + 461*p - 911. Let n(v) = -3*d(v) + 35*w(v). Determine u, given that n(u) = 0.
2, 92
Let s(g) = -2*g**4 + 2*g**3 - 15*g**2 - 3*g + 3. Let o(v) = 3*v**4 - 3*v**3 + 29*v**2 + 5*v - 5. Let f(k) = 3*o(k) + 5*s(k). Factor f(j).
-j**2*(j - 4)*(j + 3)
Let z(j) be the first derivative of -j**5 - 845*j**4/2 - 1680*j**3 - 2515*j**2 - 1675*j - 3230. Factor z(r).
-5*(r + 1)**3*(r + 335)
Let v be 42/30 - 2 - (-7)/35*(37 + -34). Let v - x**3 + 1/3*x**2 - 1/3*x**4 + 1/3*x**5 + 2/3*x = 0. Calculate x.
-1, 0, 1, 2
Let h(a) be the second derivative of 0 + 8/27