15. Let a(t) = 2*n(t) - 25*u(t). Factor a(k).
5*(k - 6)*(k - 4)*(k + 1)
Let m be 2*1 + 3 + -3 + -2. Let f(t) be the third derivative of 0*t**3 + 0 + 1/5*t**5 + m*t + 2/5*t**6 + 0*t**4 + 1/10*t**7 + 10*t**2. Factor f(l).
3*l**2*(l + 2)*(7*l + 2)
Let x(w) be the first derivative of -5/2*w**2 + 0*w - 1/5*w**5 - 3/4*w**4 + 34 + 3*w**3. What is z in x(z) = 0?
-5, 0, 1
Let v(z) = 3*z**2 + 21*z. Let w(a) = -9*a**2 - 61*a. Let d(n) = 17*v(n) + 6*w(n). Solve d(q) = 0.
-3, 0
Suppose -8*f + 17*f = 0. Let h = -3812/9 + 424. Factor -h*u - 2/9*u**2 + f.
-2*u*(u + 2)/9
Let h(a) be the third derivative of a**6/120 - a**5/10 + 13*a**3/6 - 5*a**2. Let k(n) be the first derivative of h(n). Find x such that k(x) = 0.
0, 4
Let p(l) = -l**2 - l + 1. Let b(y) = -y**2 + 2. Let q = 0 - -3. Let k be q/7 + (-408)/119. Let w(o) = k*b(o) + 6*p(o). Factor w(r).
-3*r*(r + 2)
Let f(w) be the first derivative of 15*w**4/16 - 5*w**3/3 - 5*w**2/2 - 100. Determine g so that f(g) = 0.
-2/3, 0, 2
Determine v, given that 190*v + 57*v**3 - 395*v - 32 + 55*v**3 + 181*v + 444*v**2 = 0.
-4, -1/4, 2/7
Let l(q) be the third derivative of -q**5/60 + 3*q**3/2 + 133*q**2. Suppose l(b) = 0. What is b?
-3, 3
Let j(v) = -6*v**2 - 31*v - 2. Let f be j(-5). Let a(d) be the first derivative of 1/8*d**6 + 6 - 3/8*d**2 + 1/2*d**f - 3/10*d**5 + 0*d**4 + 0*d. Factor a(l).
3*l*(l - 1)**3*(l + 1)/4
Let d(v) = -v**2 - 31*v + 142. Let w be d(4). Let l(h) be the third derivative of 0 + 0*h + 1/33*h**3 - 1/66*h**4 - 8*h**w + 1/330*h**5. Factor l(z).
2*(z - 1)**2/11
Let h(l) be the first derivative of -5*l**4/16 + 5*l**3 + 75*l**2/8 - 65*l/2 + 480. Factor h(y).
-5*(y - 13)*(y - 1)*(y + 2)/4
Let d(p) be the first derivative of -30 - 24*p - 32/3*p**3 - p**4 - 26*p**2. Factor d(t).
-4*(t + 1)**2*(t + 6)
Factor 2/5*p**2 - 14/5 - 12/5*p.
2*(p - 7)*(p + 1)/5
Let q(t) = -t**3 - 6*t**2 - 6*t - 2. Let m be q(-5). Determine c, given that 11*c**4 + 10*c**m - 3*c**4 + 8*c - 10*c**4 - 16*c**2 = 0.
0, 1, 2
Let k = 1340 + -4148/3. Let q = k + 1414/33. Factor -6/11*x + q*x**2 + 4/11.
2*(x - 2)*(x - 1)/11
Suppose i + 2*z + 2 = 0, -3*z - 4 = -3*i - 1. Let b be ((-12)/14)/(15 - 9438/616). Factor b*r**4 + i + 0*r - 2/3*r**2 - 5/3*r**5 - 1/3*r**3.
-r**2*(r - 1)**2*(5*r + 2)/3
Suppose -5*y + 4*d + 30 = 0, 16 = 3*y - 2*d - 0*d. Factor -21*z**5 + 4*z**y - 5 + 5 - 3*z**4 + 22*z**5.
z**2*(z - 2)**2*(z + 1)
Let r(z) be the third derivative of z**6/660 + 2*z**5/165 + 732*z**2. Factor r(o).
2*o**2*(o + 4)/11
Determine b, given that 33 + 5*b**3 + 8 - 20*b**2 + 5*b - 11 = 0.
-1, 2, 3
Find k, given that 2/9*k**2 + 0 + 190/9*k = 0.
-95, 0
Let w(o) be the first derivative of -o**4/4 - o**3/2 + 18*o**2 + 6*o + 44. Let z(i) be the first derivative of w(i). Factor z(d).
-3*(d - 3)*(d + 4)
Let t(b) be the second derivative of 41/24*b**3 + 11/6*b**4 + 0 + 3/4*b**2 + 7/60*b**6 - 9*b + 67/80*b**5. Suppose t(x) = 0. Calculate x.
-3, -1, -1/2, -2/7
Let p be 5/(-3) - (-2)/(-6). Let g be (65/(-10))/(p/8). Factor 60*x**4 - 28*x**2 + 24*x**5 + 44*x**2 + g*x**5 - 72*x**3.
2*x**2*(x + 2)*(5*x - 2)**2
Let -6*u - 8 + u + 13*u**2 - u - 11*u**2 = 0. What is u?
-1, 4
Suppose 0 = -7*t + 16 + 5. Let x(i) be the second derivative of -1/4*i**t - 1/8*i**4 + 0 - 5*i + 0*i**2 + 3/20*i**5. Factor x(l).
3*l*(l - 1)*(2*l + 1)/2
Let h(y) = -2*y + 3. Let x be h(8). Let t = -1 - x. Suppose -9*j**4 + 0 - 5 + 5 + 24*j**3 + t*j**2 - 27*j**5 = 0. What is j?
-2/3, 0, 1
Let m(g) = 3*g**5 + 74*g**4 - 8*g**3 - 152*g**2 + 7*g + 75. Let z(t) = -t**5 - 2*t**4 + 3*t - 1. Let v(s) = -m(s) + z(s). Find c such that v(c) = 0.
-19, -1, 1
Let u(s) = 5*s**2 + 10*s + 11. Suppose 0 = 5*c + 8 + 22. Let j(i) = 15*i**2 + 30*i + 32. Let d(f) = c*j(f) + 17*u(f). Find o such that d(o) = 0.
-1
Let a(z) be the third derivative of -z**6/200 + z**5/10 - 9*z**4/40 - 85*z**2. Factor a(r).
-3*r*(r - 9)*(r - 1)/5
Let -56/11*f**2 - 8/11*f**4 + 100/11 + 6*f**3 - 390/11*f = 0. What is f?
-2, 1/4, 5
Let c(g) be the third derivative of 9*g**5/20 - 3*g**4 + 7*g**3/2 + 12*g**2. Factor c(k).
3*(3*k - 7)*(3*k - 1)
Let p(r) be the first derivative of r**4/14 + 4*r**3/21 + r**2/7 + 74. Solve p(o) = 0.
-1, 0
Let t be ((-10)/(-4))/(2/4). Let g(a) = -a**3 - 20*a**2 - 19*a + 8. Let b be g(-19). Factor 20*d - 2*d - t*d**4 + 15*d**2 - b*d.
-5*d*(d - 2)*(d + 1)**2
Factor -5*j**3 - 27*j - 107387*j**2 + 312*j + 145 + 107522*j**2.
-5*(j - 29)*(j + 1)**2
Let y = -761 + 1525/2. Find r such that 9/4 - 3/4*r**4 + 3*r - 3*r**3 - y*r**2 = 0.
-3, -1, 1
Suppose -5*a - 114 + 124 = 0. Let r(t) = -t**3 - 4*t**2 - 3*t - 4. Let i be r(-4). Let 0*m - i*m + m**2 - 7*m**a + 11*m = 0. What is m?
0, 1/2
Let u = 14797 + -14785. Factor -11/4*l**2 - 1/4*l - u*l**4 - 10*l**3 + 0.
-l*(3*l + 1)*(4*l + 1)**2/4
Let r = -24 + 26. Let x = 5/11 - 3/55. Solve -x - 2/5*g + 4/5*g**r = 0 for g.
-1/2, 1
Let y(u) be the second derivative of -12*u + 1/30*u**6 + 0 - 1/12*u**4 + 0*u**3 + 1/5*u**5 - 2/21*u**7 + 0*u**2. What is x in y(x) = 0?
-1, 0, 1/4, 1
Factor 5/2*a**2 + 0 + 1/4*a**3 + 0*a.
a**2*(a + 10)/4
Suppose 0 = 3*f + 3 - 27. Let c be ((-6)/f)/((-2)/8). Suppose 2*l**2 + l**2 + 3*l**2 + 9*l - 3*l**c = 0. Calculate l.
-1, 0, 3
Let k(y) = 8*y**3 + 32*y**2 - 28*y. Let m(u) = -9*u**3 - 33*u**2 + 27*u. Let i = 54 + -59. Let f(w) = i*k(w) - 4*m(w). Suppose f(a) = 0. Calculate a.
-8, 0, 1
Let c(p) = p**3 - 10*p**2 - 12*p + 13. Let l be c(11). Let b be 56/(-30)*(-1 - 5/(-10)). Factor 0 - b*j**l - 4/15*j.
-2*j*(7*j + 2)/15
Suppose 2*w - 2*q = 20, -44 = -4*w + 2*q + 3*q. Suppose -3*c - 4 - 7*c - w*c**3 - c**2 - 5*c**2 + 8*c**3 + 2*c**4 = 0. Calculate c.
-1, 2
Let p(x) be the first derivative of -x**3/18 + 4*x**2/3 - 71. What is b in p(b) = 0?
0, 16
Let x(a) = 6*a**2 + 5*a + 2. Let n be x(-1). Let h(d) be the first derivative of n + 2/5*d + 1/15*d**3 - 3/10*d**2. Factor h(g).
(g - 2)*(g - 1)/5
Let a(f) be the third derivative of 3*f**7/70 - 2*f**6/5 + f**5/6 + f**4 + 5*f**3/6 + 112*f**2 - f. Factor a(s).
(s - 5)*(s - 1)*(3*s + 1)**2
Let i(b) = -b**4 - b**3 - b**2 + 2*b. Let d(c) = 20*c**4 + 56*c**3 - 36*c**2 - 80*c + 64. Let n(k) = -d(k) - 24*i(k). Suppose n(j) = 0. What is j?
-1, 1, 4
Let t be -7 + 0 - (-11 + (-4 - -10)). Let n be (0*t/(-14))/3. Find d, given that -1/5*d**3 + n + 0*d**2 + 1/5*d = 0.
-1, 0, 1
Let y(q) be the third derivative of -q**6/600 + q**5/100 - q**4/60 - 2*q**2 + 62*q. Factor y(r).
-r*(r - 2)*(r - 1)/5
Factor 17 + 65*o - 12 - 30*o**3 - 20*o**2 - 26 + 5*o**5 - 9 + 10*o**4.
5*(o - 1)**3*(o + 2)*(o + 3)
Let p(f) be the first derivative of 0*f + 3*f**4 - 8/5*f**5 - 4/3*f**3 + 0*f**2 + 13. Factor p(i).
-4*i**2*(i - 1)*(2*i - 1)
Let d = 8526 - 76730/9. Factor -8/9*u - d - 1/9*u**3 - 5/9*u**2.
-(u + 1)*(u + 2)**2/9
Let f(w) be the second derivative of -1/8*w**2 + 1/96*w**4 + 0 - 1/48*w**3 + 2*w. Factor f(n).
(n - 2)*(n + 1)/8
Let k(u) = 47*u**3 - 54*u**2 + 7*u - 5. Let g(o) = -24*o**3 + 27*o**2 - 3*o + 3. Let q(c) = 5*g(c) + 3*k(c). Let q(i) = 0. Calculate i.
0, 2/7, 1
Let k be -2 + 9 + (-3 - 4). Let g(w) be the first derivative of k*w - 8 + 1/2*w**2 - 1/3*w**3. Factor g(q).
-q*(q - 1)
Factor 3*w + 1/4*w**2 + 8.
(w + 4)*(w + 8)/4
Let l(u) be the first derivative of u**6/21 - 2*u**5/7 - 3*u**4/2 - 46*u**3/21 - 8*u**2/7 - 396. Factor l(z).
2*z*(z - 8)*(z + 1)**3/7
Let k(g) be the first derivative of 2*g**6/5 - 13*g**5/40 - g**4/8 - g**3/3 - 15*g - 56. Let f(i) be the third derivative of k(i). Solve f(o) = 0 for o.
-1/16, 1/3
Let k(l) = -l**2 + l. Let t(q) = 18*q - 20. Let v(o) = k(o) - t(o). Let b be v(-18). Suppose 0 + 0*c**b + 2/9*c - 2/9*c**3 = 0. Calculate c.
-1, 0, 1
Solve -1/7*g**2 + 62/7*g - 961/7 = 0.
31
Suppose -32 - 48 = 5*j. Let b be (j/(-6))/(2/3). Factor -2*w**4 + 0*w**4 + 2*w**4 + 3*w**b.
3*w**4
Suppose 146 = 27*s + 11. Let q(c) be the second derivative of 6*c - 1/45*c**6 + 1/15*c**s + 0*c**2 - 1/18*c**4 + 0 + 0*c**3. Factor q(w).
-2*w**2*(w - 1)**2/3
Let y(x) = -8*x**3 + 11*x**2 - x - 11. Let c(a) = -38*a**3 + 56*a**2 - 4*a - 56. Let o(i) = -3*c(i) + 14*y(i). Factor o(d).
2*(d - 7)*(d - 1)*(d + 1)
Factor 4/19*i**2 + 0*i + 690/19*i**3 + 0.
2*i**2*(345*i + 2)/19
Suppose -j + 7 = -2. Let i = -6 - -6. Find d, given that -12*d**2 + 4*d**4 + i*d**2 - d**4 - j*d + 15*d**3 + 3*d**4 = 0.
-3, -1/2, 0, 1
Suppose 0 = -11*h + 725 + 199. Solve l**2 +