19))/((-2)/1). Let t(k) be the third derivative of 0*k**4 - 1/10*k**3 + 0*k + 0 - k**l + 1/100*k**5. Determine a so that t(a) = 0.
-1, 1
Let d(t) = 15*t**4 - 60 - 21*t**3 + t**3 + 65. Let r(p) = -p**5 + p**3 + p**2 - 1. Let q(f) = d(f) + 5*r(f). Suppose q(k) = 0. What is k?
0, 1
Suppose -z - 4*c + 18 = 0, -3*z - 6*c + 19 = -c. Let d be (-4)/z*(-5 + 147/28). Suppose k**3 + 1/4 - 3/4*k**4 - k + d*k**2 = 0. What is k?
-1, 1/3, 1
Suppose 0 = -5*w + 2*n + 18, 4*w - 4*n - 7 = 5. Find b such that -b + 6*b - 3*b**2 - w*b + 8*b = 0.
0, 3
Factor -2/13*d**2 - 58/13 - 60/13*d.
-2*(d + 1)*(d + 29)/13
Suppose -4*r = -9*r - 45. Let c(a) = -a**2 - 8*a + 14. Let t be c(r). Determine n, given that 10/3*n + 20/3*n**3 + 10/3*n**4 + 2/3 + 2/3*n**t + 20/3*n**2 = 0.
-1
Let l(p) be the second derivative of -8/27*p**4 - 9*p + 0 - 4/27*p**3 + 0*p**2 + 7/45*p**6 - 1/90*p**5. Determine n, given that l(n) = 0.
-2/3, -2/7, 0, 1
Suppose 5*z = 2*c - 36, -3*c - 3*z + 72 = c. Let p be (3/c)/((-10)/(-320)). Find r such that 2/3*r**2 - p*r + 32/3 = 0.
4
Let f(z) be the second derivative of -1/90*z**5 + 0 - 12*z - 4/9*z**3 + 8/9*z**2 + 1/9*z**4. Find a such that f(a) = 0.
2
Let r(y) = y**2 + 9*y - 7. Let p(c) = -c**2 - 8*c + 8. Let z(k) = 3*p(k) + 2*r(k). Let v be z(-7). What is u in -3*u**v - u**2 + 8*u**2 + u**2 - 5*u**2 = 0?
0, 1
Let d(j) = j**2 + j + 1. Let c(k) = 8*k + 1. Let g(y) = -2*c(y) + 2*d(y). Factor g(m).
2*m*(m - 7)
Let m(x) = 2*x**4 + x**3 - x**2 + x + 2. Let k(a) = -3*a**4 - 2*a**3 + 4*a**2 - 4. Let o(q) = -5*k(q) - 5*m(q). Suppose o(w) = 0. Calculate w.
-2, -1, 1
Let c(g) be the third derivative of g**7/105 + 3*g**6/20 + 3*g**5/5 - g**4/3 - 8*g**3 - 14*g**2. Factor c(y).
2*(y - 1)*(y + 2)**2*(y + 6)
Let y = -75 - -79. Let 15*k + 20 - 10*k**5 + 45*k**y - 21*k**2 - 3*k**3 - 2*k**3 - 64*k**2 + 20*k**2 = 0. What is k?
-1, -1/2, 1, 4
Let u(f) = 2*f**3 + 12*f**2 + 2*f + 12. Let n be u(-6). What is w in -31*w + 4 + 2*w**3 + n + 25*w = 0?
-2, 1
Let j(z) be the first derivative of z**4/26 - 42*z**3/13 - 64*z**2/13 - 144. Factor j(v).
2*v*(v - 64)*(v + 1)/13
Let k(o) be the first derivative of -6*o**5/5 + 23*o**4/2 - 86*o**3/3 + 13*o**2 + 20*o + 102. Determine p so that k(p) = 0.
-1/3, 1, 2, 5
Let r be (-14)/4 + 4/8. Let a be (0 - 5)*r/(-15)*-3. Determine g, given that 0*g + 1/4*g**a + 0*g**2 - 1/4*g**4 + 0 = 0.
0, 1
Let h(x) = x**3 + 7*x**2 + 6*x + 2. Let s be h(-6). Factor 0 + 44*u - 24*u**s - 12 - 4 - 9*u**3.
-(u + 4)*(3*u - 2)**2
Let n = -157 - -160. Suppose 18 = -w + 7*w. Find r such that 0 - 12/5*r - 51/5*r**w + n*r**4 + 48/5*r**2 = 0.
0, 2/5, 1, 2
Let b(h) be the third derivative of -2*h**7/105 - 17*h**6/30 - 20*h**5/3 - 38*h**4 - 96*h**3 - 2*h**2 - 143. Find v such that b(v) = 0.
-6, -4, -1
Suppose -3*h - 3*m + 15 = 0, 0 = -6*h + 7*h + 5*m - 17. Factor 0 - 1/3*x**h + 0*x.
-x**2/3
Suppose 32 = -615*z + 623*z. Let s(m) be the second derivative of 0*m**2 - 1/60*m**z + 1/15*m**3 + 7*m + 0. Find i, given that s(i) = 0.
0, 2
Let o(d) be the first derivative of 0*d**2 + 6 + 0*d - 5/3*d**3. Let o(x) = 0. Calculate x.
0
Let o(q) be the third derivative of 2*q**2 + 0*q + 2/105*q**5 - 2/245*q**7 - 1/105*q**6 + 0 + 1/14*q**4 + 2/21*q**3 - 1/588*q**8. Find c such that o(c) = 0.
-1, 1
Let w be 30/20 + 15/36*-3. Find m, given that w - 3/2*m - 9/4*m**4 + 2*m**2 + m**5 + 1/2*m**3 = 0.
-1, 1/4, 1
Let f(a) be the second derivative of -1/114*a**4 - 1/19*a**2 - 11*a - 2/57*a**3 + 0. Factor f(n).
-2*(n + 1)**2/19
Let a = -23399 + 116997/5. Suppose 4/5*v + 0 - a*v**3 - 2/5*v**2 = 0. Calculate v.
-2, 0, 1
Find f such that -64*f**3 - 63*f**3 + 15*f**3 - 4*f**4 - 784*f**2 = 0.
-14, 0
Suppose 0 = 8*h - 2 - 6 - 8. Factor -2/9*f**h + 4/9*f + 16/9.
-2*(f - 4)*(f + 2)/9
Suppose 6*r - 5*r + 12*r = 0. Let o(w) be the third derivative of 0*w - 3*w**2 - 2/3*w**3 + r + 1/30*w**5 + 1/12*w**4. Suppose o(p) = 0. What is p?
-2, 1
Let h(k) be the third derivative of 5*k**5/48 - 9*k**4/32 + k**3/12 - 56*k**2. Let h(s) = 0. Calculate s.
2/25, 1
Let l = 7565/3 + -2521. Suppose p - 2*k = -0*p - 4, 5*k - 23 = -4*p. Factor -l + 1/2*v**p + 1/6*v**3 + 0*v.
(v - 1)*(v + 2)**2/6
Suppose 0 = -5*r - 25 + 45. Let d = 2 - 0. Factor 2*p**2 - 2 + 0 - d*p**2 + r*p - 2*p**2.
-2*(p - 1)**2
Factor 3*z**2 - 249*z - 11163 - 273*z - 8*z**2 + 156*z + 2*z**2.
-3*(z + 61)**2
Let d(s) be the second derivative of -s**7/280 - s**6/60 + 3*s**5/40 - 17*s**3/6 + s. Let i(u) be the second derivative of d(u). Suppose i(n) = 0. Calculate n.
-3, 0, 1
Let m(v) = v**5 + 8*v**4 + 12*v**3 + 10*v + 5. Let g(o) = -8*o**4 - 12*o**3 - 8*o - 4. Let x(h) = -5*g(h) - 4*m(h). Factor x(c).
-4*c**3*(c - 3)*(c + 1)
Let p(g) be the third derivative of 0*g + 0 - 1/40*g**4 - 40*g**2 + 0*g**3 + 1/50*g**5 - 1/200*g**6. Determine c so that p(c) = 0.
0, 1
Let v(p) = 57*p**5 + p**4 - 19*p**3 - 156*p**2 - 162*p - 37. Let i(b) = -10*b**5 + 3*b**3 + 26*b**2 + 27*b + 6. Let u(t) = -34*i(t) - 6*v(t). Factor u(h).
-2*(h - 3)*(h + 1)**3*(h + 3)
Suppose 2*d = -5*a + 19, -16*a = -17*a - d + 5. Let j(w) be the second derivative of 2*w**a - 5*w - 6*w**2 + 0 - 1/4*w**4. Let j(l) = 0. Calculate l.
2
Let j(h) be the second derivative of 2*h**6/15 + 3*h**5/5 - 37*h**4/3 + 22*h**3 + 144*h**2 - 12*h + 10. Factor j(p).
4*(p - 3)**2*(p + 1)*(p + 8)
Let g(c) be the first derivative of -15 + 4/3*c**3 - c**4 + 0*c**2 + 0*c. Factor g(w).
-4*w**2*(w - 1)
Let y(v) be the third derivative of v**8/3360 - v**6/120 + v**5/30 + v**4/8 + 3*v**2. Let w(j) be the second derivative of y(j). Solve w(g) = 0 for g.
-2, 1
Let u(t) be the second derivative of 1/9*t**2 + 0 + 1/30*t**5 + 1/27*t**3 - 5/54*t**4 - 11*t. Solve u(f) = 0 for f.
-1/3, 1
Let a(b) = -47*b - 111. Let v be a(-5). Let o = v + -122. Factor 2/7*r**o + 8/7 + 8/7*r.
2*(r + 2)**2/7
Let q = 372 + -370. Let j(n) be the first derivative of -1/2*n**q - 1/6*n**3 - 1/2*n - 10. Factor j(w).
-(w + 1)**2/2
Let c(j) be the second derivative of -1/36*j**3 + 1/72*j**4 + 33*j + 0 + 0*j**2. Factor c(y).
y*(y - 1)/6
Let c be (4/5)/(7/14). Suppose -2*o + a + 3 + 0 = 0, -o = -5*a + 3. Factor -2/5*x**2 - c*x**4 - o*x**3 + 0 + 0*x.
-2*x**2*(x + 1)*(4*x + 1)/5
Let v(j) = -j**3 - 28*j**2 - 95*j + 27. Let d be v(-24). Determine f, given that 0*f + 3/2*f**4 + 6*f**2 + 6*f**d + 0 = 0.
-2, 0
Let j be ((-2)/(-3) - (-13)/(-12)) + (-99)/(-132). Factor 5/6*g**3 + 0*g + 0 + j*g**2 - 1/2*g**4.
-g**2*(g - 2)*(3*g + 1)/6
Let b be ((-4)/(-12) - 0)*6. Let -5*x**2 - 5*x - 20 + 0*x**b - 20*x = 0. What is x?
-4, -1
Solve 5/2*k**2 + 0 + 9/4*k - 5/2*k**4 - 1/4*k**5 - 2*k**3 = 0 for k.
-9, -1, 0, 1
Suppose 2*b - t = 11, 108 = 5*b + 3*t + 97. Let u(l) be the second derivative of 0*l**2 - 12*l + 0 + 5/3*l**b - 4/3*l**3. Suppose u(o) = 0. Calculate o.
0, 2/5
Find j such that -8/15*j**2 - 4/5*j + 4/5*j**3 + 2/3*j**4 - 2/15 = 0.
-1, -1/5, 1
Let y(w) = 9*w**3 - 69*w**2 - 4. Let z(v) = 10*v**3 - 70*v**2 - 5. Let f(u) = -5*y(u) + 4*z(u). Determine s, given that f(s) = 0.
0, 13
Let q(o) be the first derivative of 14/15*o**2 + 2/45*o**3 + 9 + 98/15*o. Solve q(t) = 0 for t.
-7
Let p(x) = x + 5. Let v be p(-2). Factor -2*d - 10*d**2 + 0*d**3 - 4*d + 4*d**v.
2*d*(d - 3)*(2*d + 1)
Let h be (-2)/(-6) + (-175)/(-15) + 3. Suppose -3 + h = 4*d. What is y in -d + 3*y - 3/4*y**2 = 0?
2
Let w(h) = -56*h + 56. Let k be w(1). Let l(d) be the third derivative of 1/20*d**4 + 0*d - 3/10*d**3 + k + 1/100*d**5 - 13*d**2. Factor l(p).
3*(p - 1)*(p + 3)/5
Let v = -43 - -45. Factor 8*f + f**2 + 12*f**4 - 8*f**3 - 5*f**v - 10*f**2 + 2*f**2.
4*f*(f - 1)*(f + 1)*(3*f - 2)
Let a be ((-7)/1 - -5)/(14/(-1)). Let n(u) be the first derivative of -1/14*u**4 + a*u**2 + 4 + 4/7*u - 4/21*u**3. Factor n(l).
-2*(l - 1)*(l + 1)*(l + 2)/7
Suppose -3*m = 6*m - 2*m. Let g(f) be the first derivative of -1 + m*f + 2/21*f**3 - 1/7*f**2. Factor g(y).
2*y*(y - 1)/7
Let l(o) be the third derivative of o**8/1008 - o**7/105 - o**6/360 + o**5/30 + 227*o**2. Factor l(i).
i**2*(i - 6)*(i - 1)*(i + 1)/3
Suppose a + 10 - 12 = 0. Factor 4*y**2 - a*y**2 - 36 - 4*y**2 + 38.
-2*(y - 1)*(y + 1)
Factor -2/3*x**2 - 10/3*x - 8/3.
-2*(x + 1)*(x + 4)/3
Let o(q) be the third derivative of -q**5/20 - q**4/4 - q**3/2 - 4*q**2 + 18*q. Suppose o(d) = 0. Calculate d.
-1
Let p = 64 + -59. Solve 17*z - 4*z**2 - 4 + 0 - p*z - 4 = 0 for z.
1, 2
Suppose