25). Factor -4*d**4 + d**4 + 7*d**2 + 6*d + k*d**2.
-3*d*(d - 2)*(d + 1)**2
Let h = -2005 + 2007. Determine l, given that -4/3 - 10/3*l - 2/3*l**3 - 8/3*l**h = 0.
-2, -1
Determine c, given that -24*c + 23*c**2 + 88*c + c**2 - 1 - 8*c**3 - 2*c**4 - 127 = 0.
-4, 2
Let k(c) be the third derivative of -1/15*c**5 + 0*c - 24*c**3 + 24*c**2 - 2*c**4 + 0. Determine s so that k(s) = 0.
-6
Let w(d) be the third derivative of d**2 + 0*d**4 - 3/40*d**5 + 1/80*d**6 + 0*d**3 + 0 + 0*d. Determine x so that w(x) = 0.
0, 3
Let f(h) be the first derivative of 2/7*h**4 - 2/7*h**3 - 2/35*h**5 - 14 + 8/7*h - 4/7*h**2. What is c in f(c) = 0?
-1, 1, 2
Let t(n) be the first derivative of 5 - 1/15*n**3 + 1/50*n**5 - 1/5*n**2 + n + 1/30*n**4. Let c(v) be the first derivative of t(v). Factor c(h).
2*(h - 1)*(h + 1)**2/5
Let f(d) be the second derivative of -d**5/30 - 29*d**4/18 - 55*d**3/9 - 9*d**2 + d + 70. Factor f(v).
-2*(v + 1)**2*(v + 27)/3
Factor -2/7*t**2 + 48/7 + 46/7*t.
-2*(t - 24)*(t + 1)/7
Factor -4/5*j**3 - 144/5*j**2 + 144/5 + 4/5*j.
-4*(j - 1)*(j + 1)*(j + 36)/5
Let v = -3373/7 + 33829/70. Let k = 17/10 - v. Suppose -6/7 + 4/7*o + k*o**2 = 0. Calculate o.
-3, 1
Let g = 2/1597 - -4781/7985. Let v(o) be the second derivative of -1/20*o**4 - g*o**2 + 3/10*o**3 + 0 + 7*o. Factor v(n).
-3*(n - 2)*(n - 1)/5
Let b(q) = 5*q + 5. Let s be b(8). Factor 10*w + 35*w**3 + s*w**2 + 4805 - 4805.
5*w*(w + 1)*(7*w + 2)
Suppose -k + 39 = 4*k + 4*h, 4*h + 16 = 0. Suppose 8 = -v + k. Factor 0 + 1/7*a**v + 1/7*a**2 - 1/7*a - 1/7*a**4.
-a*(a - 1)**2*(a + 1)/7
Let k(b) = b - 6. Let n be k(13). Suppose n*q = 6*q. Solve q - 3/4*x**3 + 3/4*x**5 + 0*x + 3/4*x**2 - 3/4*x**4 = 0.
-1, 0, 1
Let m(n) be the third derivative of -1/616*n**8 - 3/220*n**6 + 0 - 1/77*n**7 + 0*n**3 - 23*n**2 + 0*n + 1/22*n**5 + 1/11*n**4. Determine o, given that m(o) = 0.
-4, -1, 0, 1
Let r be (-2 + 152)*2/6. Let z be r/(1*(-6)/(-9)). Solve -14*l**2 + 5*l**3 + z*l - 2 + 16*l**2 + 33*l**2 + 47 = 0.
-3, -1
Let n be 8/10 + 96/30. Let s(v) be the third derivative of 0*v**n + 1/6*v**3 + 0*v - 6*v**2 - 1/60*v**5 + 0. Factor s(j).
-(j - 1)*(j + 1)
Let q(x) be the first derivative of -16*x**3/45 + 23*x**2/15 - 28*x/15 + 243. Suppose q(b) = 0. What is b?
7/8, 2
Factor 7/3*t**3 - 1/3*t**4 - 7/3*t - 5/3*t**2 + 2.
-(t - 6)*(t - 1)**2*(t + 1)/3
Let s(f) = -30*f + 1. Let p be s(-1). Suppose 5*c = -q - 7 + p, 0 = q - 2*c + 4. Factor -10*n**q - 4*n**4 + 8*n**5 - 2*n**2 + 6*n**4 - 10*n**4 + 12*n**3.
2*n**2*(n - 1)**2*(4*n - 1)
Factor 12 - 2/3*f**3 - 6*f - 16/3*f**2.
-2*(f - 1)*(f + 3)*(f + 6)/3
Let u(w) = -25*w**2 + 311*w - 889. Let g(i) = 5*i**2 - 62*i + 178. Suppose 6*t + 65 = -1. Let m(c) = t*g(c) - 2*u(c). Factor m(v).
-5*(v - 6)**2
Let n = -943 - -943. Let q(r) be the third derivative of -1/15*r**5 + n*r + 1/6*r**4 + 0*r**3 + 0 - 7*r**2. Suppose q(l) = 0. Calculate l.
0, 1
Let f be ((-27)/(-3) - 2) + 42/(-14). Let n(z) be the first derivative of -7 + 13/2*z**4 - z**2 + 2*z**5 - f*z + 6*z**3. Factor n(r).
2*(r + 1)**3*(5*r - 2)
Solve 1/4*t**4 + 3*t**3 + 25/4 + 15*t + 23/2*t**2 = 0.
-5, -1
Let c = 888631/21 - 42324. Let y = c - -29/3. What is r in -16/7*r + 8/7 + y*r**2 - 2/7*r**3 = 0?
1, 2
Let n(c) = c**2 - 6*c + 2. Suppose d - 3 = 3. Let w be n(d). Factor -8 - w*s**3 - 46 - 18*s**2 - 9*s + 14*s - 59*s.
-2*(s + 3)**3
Let f(g) be the third derivative of -g**8/1344 - g**7/840 + g**6/80 - g**5/120 - 5*g**4/96 + g**3/8 + 31*g**2 - 2. What is d in f(d) = 0?
-3, -1, 1
Let j be (-1)/(-2*(-1)/(-80)). Let o = -25 + j. Suppose 8 - 6*h**3 + 6*h**2 + 2*h**3 + 3*h + 3*h**3 - o*h = 0. What is h?
2
Let s(m) be the third derivative of -m**7/14 - 49*m**6/20 + 51*m**5/4 - 49*m**4/2 + 22*m**3 + 62*m**2. Determine y so that s(y) = 0.
-22, 2/5, 1
Factor -a**3 - 4/3*a**2 + 1/3*a**5 + 2/3*a**4 + 4/3*a + 0.
a*(a - 1)**2*(a + 2)**2/3
Let p = -18 + 29. Factor 25 - 40*f + 15*f**2 - p + 6.
5*(f - 2)*(3*f - 2)
Let w(b) be the second derivative of -b**7/105 + 7*b**6/75 - 9*b**5/25 + 2*b**4/3 - 8*b**3/15 - 10*b + 1. Factor w(y).
-2*y*(y - 2)**3*(y - 1)/5
Let f = -3548/3549 - -8/169. Let u = f - -32/21. Determine j so that 0 + u*j**2 + 0*j + 2/7*j**3 = 0.
-2, 0
Let f = -17160 + 17164. Factor 1/2*y**2 - 1/4*y + 1/4*y**5 - 1/2*y**f + 0*y**3 + 0.
y*(y - 1)**3*(y + 1)/4
Let x(p) = -65*p**3 + 195*p**2 - 55*p - 305. Let t(z) = -z**4 - 66*z**3 + 196*z**2 - 54*z - 303. Let m(l) = -5*t(l) + 6*x(l). Factor m(u).
5*(u - 7)*(u - 3)**2*(u + 1)
Let z(s) be the first derivative of 2*s**3/45 - 2*s**2/5 + 2*s/3 - 18. Suppose z(v) = 0. Calculate v.
1, 5
Let q(u) = -4*u**4 + u**2 - 5*u + u**3 + 15*u**4 - 20*u**2. Let h(v) = 10*v**4 - 20*v**2 - 5*v. Let r(b) = -4*h(b) + 5*q(b). Factor r(c).
5*c*(c - 1)*(c + 1)*(3*c + 1)
Let n(l) = -l**2 - 12*l + 39. Let i(z) = 2*z**2 - z + 1. Let w(c) = -i(c) - n(c). Let k be w(8). Factor k*u**2 - 4/7*u**4 - 2/7*u**5 + 0 - 2/7*u**3 + 0*u.
-2*u**3*(u + 1)**2/7
Let j(x) = -2*x**4 - x**2. Let p(c) = -9*c**4 + 35*c**3 - 130*c**2 + 145*c - 50. Let r(d) = 6*j(d) - 2*p(d). Find a such that r(a) = 0.
2/3, 1, 5
Let a(n) = 2*n**2 + 1. Let q(y) = -7*y**2 + 24*y - 26. Let l(f) = -6*a(f) - 2*q(f). Factor l(c).
2*(c - 23)*(c - 1)
Suppose -257*v**2 - 412*v - 408 + 507*v**2 - 254*v**2 = 0. Calculate v.
-102, -1
Suppose -6*j + 14*j + 24 = 0. Let z(t) = -2*t**2 + 2. Let f(n) = -3*n**2 - 2*n + 1. Let b(h) = j*f(h) + 4*z(h). Factor b(a).
(a + 1)*(a + 5)
Let b(j) = 3*j**2 + 1356*j + 149181. Let r(z) = 3*z**2 + 1353*z + 149182. Let f(a) = 5*b(a) - 6*r(a). Determine g, given that f(g) = 0.
-223
Let p(b) = -210*b - 1. Let u be p(5). Let v = 7369/7 + u. Let 8/7*l + v*l**2 - 16/7 - 10/7*l**3 + 2/7*l**4 = 0. Calculate l.
-1, 2
Let 17/8*x - 5/8*x**3 + 3/8*x**2 - 1/8*x**4 + 5/4 = 0. What is x?
-5, -1, 2
Let s be ((-276)/(-60))/((-24)/10). Let v = -5/4 - s. What is r in 2/9*r**2 + v*r + 4/9 = 0?
-2, -1
Let i be 13/4 + 12/(-48). Factor -16*l**5 + 5*l**2 + l**5 + 36*l**4 - 15*l**i + l**2 - 12*l**3.
-3*l**2*(l - 1)**2*(5*l - 2)
Suppose -3*n + 0 = -4*z - 10, 2*n + 3*z - 1 = 0. Determine i so that -9*i**3 + 0*i**2 - 4*i**n - 2*i**2 - 3*i**4 = 0.
-2, -1, 0
What is c in 3/11*c**3 - 3/11*c - 10/11 + c**2 - 1/11*c**4 = 0?
-2, -1, 1, 5
Suppose -2*c + 1 = -5*x + 21, 0 = 3*c. Find p, given that 3 - 83*p**x + 9*p**3 + 86*p**4 - 3 = 0.
-3, 0
Let y = -80 - -83. Factor 7*z**2 + z**2 - 4*z**5 - 4*z**4 + 4*z**y - 4*z**2.
-4*z**2*(z - 1)*(z + 1)**2
Let t(s) be the first derivative of -7*s**3/12 + 89*s**2/8 - 15*s + 21. Factor t(w).
-(w - 12)*(7*w - 5)/4
Suppose -2*n + 4 = -q, -9 = -n - 2*n. Suppose -2*h + 57 - 18 = 3*b, 5*h + 3*b = 84. Solve i**3 + 6*i**4 - h*i**3 - 5*i**q + 15*i**2 - 2*i = 0 for i.
0, 1/3, 1
Let b(w) = -5*w**4 - 11*w**3 - 11*w**2 - 3*w - 3. Let j(s) = 0*s**4 - 5*s**3 - 4*s**4 - 2*s - 10*s**2 - 5*s**3 - 2. Let y(f) = 2*b(f) - 3*j(f). Factor y(x).
2*x**2*(x + 2)**2
Suppose -5*w = -5*o + 30, -28*w + 29*w = 4*o - 18. Factor 0 + 0*k + 1/3*k**2 + 0*k**3 - 1/3*k**o.
-k**2*(k - 1)*(k + 1)/3
Factor 6*p - 4/3 + 4*p**2 - 10/3*p**3.
-2*(p - 2)*(p + 1)*(5*p - 1)/3
Let d(a) = 47*a + 802. Let x be d(-17). Let j(s) be the first derivative of 1/2*s**2 + 1/9*s**x - 7 + 0*s. Let j(c) = 0. What is c?
-3, 0
Suppose 4*b + 2 = 10. Suppose -10*k + 17 = -3. Factor -g**2 + 3*g**2 - 6*g**k + g**b + g.
-g*(3*g - 1)
Let c(u) = -u**3 - 12*u**2 - 33*u - 21. Let f be c(-2). Determine w so that -2/3*w**f + 0*w + 0 - 2*w**3 + 2/3*w**2 + 2*w**4 = 0.
0, 1
Suppose -h - 57*j = -55*j - 8, 2 = 2*j. Factor 3/8*t**5 - 15/8*t**3 + 15/8*t**4 - 75/8*t**2 - h + 15*t.
3*(t - 1)**3*(t + 4)**2/8
Let q(n) be the first derivative of n**6/300 + 7*n**5/50 + 49*n**4/20 + 343*n**3/15 + 21*n**2/2 - 28. Let r(u) be the second derivative of q(u). Factor r(a).
2*(a + 7)**3/5
Factor 14/3*b + 1/3*b**4 + 0 + 4/3*b**3 - 19/3*b**2.
b*(b - 2)*(b - 1)*(b + 7)/3
Let u be (-90)/(-6) - (-3 + 3). Factor 12*i**4 - 43*i**4 + 55*i**2 + 20*i**3 + 11*i**4 + 30*i + u*i**4.
-5*i*(i - 6)*(i + 1)**2
Let d(x) = -9*x - 2*x**2 - x + 12 + 11*x**2 + 4 - x**3. Let p be d(8). Find z, given that 0*z + 1/4*z**3 + 1/4*z**2 + p = 0.
-1, 0
Let l(c) = c**3 - 9*c**2 - 9*c - 2. Let k be l(10). Suppose 5*w = k*w - 6. Factor 12*i**w - 25 + 25 - 20*i**3 + 8*i.
-4*i*(i - 1)*(5*i + 2)
Let x be (3 + 63/(-18))*-4. Let q(g) be the third derivative of -1/300*g**6 + 0