 4)
Suppose -9/5*r**3 + 0 - 1/5*r**5 + 0*r + 8/5*r**4 - 18/5*r**2 = 0. Calculate r.
-1, 0, 3, 6
Let g = -1 + 1. Suppose -3*j + 31 - 7 = g. Factor -2*m**4 - 4*m**5 + j*m**5 - 2*m**5.
2*m**4*(m - 1)
Let h = -2 + 4. Suppose -12 = -2*x - h*x. Determine q, given that -1 + 2*q**5 - q**5 - 2*q**x + 3*q**4 + q + 2*q**2 - 4*q**4 = 0.
-1, 1
Factor -77/4*z**2 - 25/4*z - 1/2.
-(7*z + 1)*(11*z + 2)/4
Suppose f + p + p = 0, 3*p = 5*f. Let a(h) be the third derivative of f*h**3 + 1/420*h**7 + 0*h**4 - 1/240*h**6 + 0*h**5 + 0*h + 0 - 2*h**2. Factor a(i).
i**3*(i - 1)/2
Let g(f) = -f**3 + 13*f**2 + 56*f + 33. Let o(v) = -v**2 - v + 3. Let c(y) = g(y) + 3*o(y). Factor c(s).
-(s - 14)*(s + 1)*(s + 3)
Let z = 135/7 + -2423/126. Let u(q) be the second derivative of -q + 1/9*q**3 + 0*q**2 - z*q**4 + 0. Solve u(m) = 0 for m.
0, 1
Let f = 835/7 + -119. Let m = -1373 - -9619/7. Find s, given that -m*s - 8/7 + f*s**3 + 2/7*s**2 = 0.
-2, -1, 2
Let y = -23 + 27. Factor -42*u**4 + y*u + 20*u**4 + 24*u**4 - 6*u**2.
2*u*(u - 1)**2*(u + 2)
Let p(z) be the third derivative of -z**5/100 - z**4/4 + 39*z**3/10 - 63*z**2. Factor p(c).
-3*(c - 3)*(c + 13)/5
Let i(x) be the first derivative of -x**9/13608 + x**8/1260 - x**7/315 + 2*x**6/405 + 11*x**3/3 + 10. Let s(y) be the third derivative of i(y). Factor s(a).
-2*a**2*(a - 2)**3/9
Let z(x) be the third derivative of x**5/90 + 23*x**4/18 + 88*x**3/9 - 3*x**2 - 2*x. Solve z(s) = 0 for s.
-44, -2
Find f such that 14/5*f - 14/5*f**3 - 44/15 - 2/15*f**4 + 46/15*f**2 = 0.
-22, -1, 1
Let j(k) be the third derivative of -k**6/40 + k**5/5 - k**4/8 - 3*k**3 - k**2 - 11*k. Determine c, given that j(c) = 0.
-1, 2, 3
Let f = -993/8 - -5061/40. Solve -8/5 + f*o - 4/5*o**2 = 0 for o.
1, 2
Let u(y) be the second derivative of -y**7/2520 - y**6/144 - 5*y**4/12 + 24*y. Let j(k) be the third derivative of u(k). Factor j(s).
-s*(s + 5)
Let l = -2/1579 - -6326/7895. Solve -l + 4/5*x**3 + 11/5*x + 19/5*x**2 = 0 for x.
-4, -1, 1/4
Let d(p) = p**3 + p + 1. Let t(i) = -30*i**3 - 480*i**2 - 1570*i + 495. Let a(r) = 5*d(r) - t(r). Determine f, given that a(f) = 0.
-7, 2/7
Let b(x) be the first derivative of 3*x**4/8 + x**3 - 15*x**2 + 36*x + 43. Determine t, given that b(t) = 0.
-6, 2
Let b = -271 + 4067/15. Let f(n) be the first derivative of -1/3*n**4 - 6 + 2/3*n**2 + 0*n**3 - 2/3*n + b*n**5. Let f(c) = 0. What is c?
-1, 1
Let h be 14/2*1 + (-2 - 1). Let q(u) be the second derivative of -1/21*u**h - 5*u + 0 + 3/140*u**5 - 2/21*u**3 + 0*u**2. Factor q(y).
y*(y - 2)*(3*y + 2)/7
Let t be 16/12*(-72)/(-32). Suppose 3*r - 12 = -3. Let -a**2 + t*a**2 + 1 - r*a**2 = 0. Calculate a.
-1, 1
Factor 2/17*b**2 - 54/17*b + 0.
2*b*(b - 27)/17
Suppose -2*h = -3 + 7, -h - 14 = -3*q. Suppose -k - q*k + 80 = 0. Determine f, given that -3*f**3 + 2 + 3*f**2 + 4*f**3 + 15*f**4 - k*f**4 - 5*f = 0.
-2, 1
Solve -119085 + 4*q**3 - 285*q**2 + 17328*q - 61183 - 39220 - 171*q**2 = 0.
38
Let r = -3365 - -3368. Determine u, given that 4/21*u**2 + 0 - 4/21*u**4 + 0*u**r - 2/21*u**5 + 2/21*u = 0.
-1, 0, 1
Let y(t) be the first derivative of -7*t + 10 - 1/21*t**4 + 4/21*t**3 - 2/7*t**2. Let a(b) be the first derivative of y(b). Determine m so that a(m) = 0.
1
Suppose 137157 = -24*l + 137157. What is d in 1/5*d**2 + l*d + 0 + 1/5*d**3 = 0?
-1, 0
Let v(d) be the second derivative of -d**7/280 - d**6/30 - d**5/10 - 4*d**3/3 + 10*d. Let o(h) be the second derivative of v(h). Factor o(k).
-3*k*(k + 2)**2
Factor -3/8*m**2 - 99/8 - 21/4*m.
-3*(m + 3)*(m + 11)/8
Factor 275*b + 12 - 11 + 62 - 133 - 190*b**2 - 15*b**3.
-5*(b - 1)*(b + 14)*(3*b - 1)
Factor -64*h - 95*h**2 - 4*h**4 - 72*h**3 - 42*h**2 + 5*h**2.
-4*h*(h + 1)**2*(h + 16)
Let y(f) = 4*f**3 - 2*f - 1 - 4*f**3 - 2*f**3 + 3*f**3 + 2*f**2. Let d be y(-2). Factor 3*o + 3*o - 7*o**3 + o - 4*o + 2 - d*o**2 - 3*o**4.
-(o + 1)**3*(3*o - 2)
Let w(y) = -y**4 - 2*y**3 - 45*y**2 + 2*y. Let o(j) = -15*j**4 - 25*j**3 - 540*j**2 + 25*j. Let l(g) = -2*o(g) + 25*w(g). Factor l(v).
5*v**2*(v - 3)*(v + 3)
Let c be (80/(-280))/(36/(-56)). Factor 10/9*b**4 + c*b**2 - 14/9*b**3 + 0*b + 0.
2*b**2*(b - 1)*(5*b - 2)/9
Let q(a) be the second derivative of -a**4/3 + 196*a**3/3 - 194*a**2 - 523*a. Factor q(h).
-4*(h - 97)*(h - 1)
Let l(r) be the first derivative of 0*r**2 + 15 + 0*r**4 + 5/3*r**3 + 0*r - r**5. Suppose l(d) = 0. What is d?
-1, 0, 1
Let o(p) be the third derivative of p**6/135 + 13*p**5/90 - 53*p**4/54 + 8*p**3/9 + 502*p**2. What is t in o(t) = 0?
-12, 1/4, 2
Let n(z) be the third derivative of -z**6/40 - 23*z**5/20 - 111*z**4/8 - 153*z**3/2 - 194*z**2. Factor n(x).
-3*(x + 3)**2*(x + 17)
Suppose 2*j - 6 - 2 = 0. Factor 7*p**2 + j + 5*p**2 - 20*p**2 + 7*p**2.
-(p - 2)*(p + 2)
Let 9 - 11/4*f**2 - 12*f + 3/4*f**3 = 0. Calculate f.
-3, 2/3, 6
Let d(i) = -i**4 + i**3 + 2*i**2 + i + 2. Let r(f) = 7*f**4 + f**3 - 4*f**2 - 28*f - 16. Let v(t) = -24*d(t) - 3*r(t). Suppose v(g) = 0. What is g?
-2, 0, 1, 10
Let v(y) be the second derivative of -5*y**4/6 + 16*y**3/3 - 12*y**2 + 99*y. Suppose v(b) = 0. What is b?
6/5, 2
Let 4/3*z + 1/12*z**2 + 5/4 = 0. What is z?
-15, -1
Let c = -45 - -47. Solve 20*m - 9*m**2 + 15*m**c - 11*m**2 = 0 for m.
0, 4
Let f(y) be the first derivative of -3*y**6/160 + 3*y**5/80 - y**4/32 - 16*y**3 + 47. Let s(u) be the third derivative of f(u). Factor s(l).
-3*(3*l - 1)**2/4
Let f = 40 + -41. Let j(s) = 7*s**2 - 8*s + 6. Let k(m) = -m**2 + m - 1. Let n(i) = f*j(i) - 6*k(i). Determine l, given that n(l) = 0.
0, 2
Let q be ((-12)/42)/((-5)/7). Let l(p) be the first derivative of p**2 + q*p**5 - 4/3*p**3 - p**4 + 1/3*p**6 + 2*p + 2. Factor l(s).
2*(s - 1)**2*(s + 1)**3
Let o(s) = 27*s**2 + 21*s + 18. Let u(t) = 8*t**2 + 6*t + 5. Let c(p) = 5*o(p) - 18*u(p). Suppose c(n) = 0. Calculate n.
-1/3, 0
Let n = 36/31 - 627/620. Let r(s) be the third derivative of 0*s**3 - n*s**5 + 1/70*s**7 + 0*s - 4*s**2 + 0 + 0*s**6 + 1/4*s**4. Solve r(t) = 0.
-2, 0, 1
Suppose 2*q = -98 + 350. Let s = -251/2 + q. Find d such that s*d**5 - d**3 - 2*d**2 + 1 + 1/2*d + d**4 = 0.
-2, -1, 1
Let x = -173 - -185. Suppose -64/3*l**3 + 8/3*l**2 - 8/3 + 0*l**4 + 28/3*l + x*l**5 = 0. What is l?
-1, 1/3, 2/3, 1
Let c(p) be the third derivative of 0*p + 0 + 1/3*p**3 + 0*p**5 - 1/24*p**4 - 5*p**2 + 1/360*p**6. Let m(u) be the first derivative of c(u). Factor m(j).
(j - 1)*(j + 1)
Let f(j) = -j**3 + 7*j**2 + 6*j + 4. Let b be f(6). Let z be -1*3 - b/(-20). Let -2/5*u**5 - 2/5 + z*u**3 - 2/5*u - 2/5*u**4 + 4/5*u**2 = 0. Calculate u.
-1, 1
Let q = 906 - 899. Let d(h) be the second derivative of -1/10*h**5 - 4/21*h**q + 0 - h**2 - 8/15*h**6 + 8*h + 1/3*h**3 + 5/6*h**4. Solve d(j) = 0.
-1, 1/2
Let d(z) = 18*z**3 - 11*z**2 - 8*z + 7. Let c(k) = -5*k**3 + 4*k**2 + 3*k - 2. Let g(q) = 7*c(q) + 2*d(q). Factor g(o).
o*(o + 1)*(o + 5)
Let q = 2807/3 + -935. Factor -2/9*o**2 + 0 - q*o.
-2*o*(o + 3)/9
Suppose 2*r = -3*w + 14, 5 = 4*w + r - 17. Let d be 4/8 - (-58)/4. Solve 12*f**2 + 5*f**4 + 3*f - d*f**3 + 5*f**4 - w*f**4 + f = 0.
-1/4, 0, 2
Let d(m) = 20*m**2 - 52*m - 16. Let r(l) = l**2 - l + 1. Let p(f) = d(f) - 24*r(f). Factor p(i).
-4*(i + 2)*(i + 5)
Suppose 2*b - 5*b - 36 = 0. Let g be (-3)/(0 + b/184). Factor -7*z**3 - 33*z**3 + 2 - 2*z + 2 - g*z**2.
-2*(z + 1)*(4*z - 1)*(5*z + 2)
Let v(k) be the first derivative of 9/4*k**4 + 3*k**2 - 10 + 0*k + 7*k**3. Factor v(l).
3*l*(l + 2)*(3*l + 1)
Let m be (0*-4*(-11)/220)/2. Determine y so that -4/11*y**2 + 0 + m*y + 2/11*y**3 = 0.
0, 2
Let a(m) be the first derivative of 2*m**7/21 - 11*m**6/30 + 9*m**5/20 - m**4/12 - m**3/6 + 37*m + 10. Let f(q) be the first derivative of a(q). Factor f(l).
l*(l - 1)**3*(4*l + 1)
Let h(r) = -4*r**4 - 6*r**3 + 32*r**2 + 6*r - 28. Let f(j) = 8*j**4 + 13*j**3 - 62*j**2 - 13*j + 54. Let p(w) = 6*f(w) + 11*h(w). Determine g so that p(g) = 0.
-4, -1, 1
Let o be 0*(-3 + 56/16). Let t(i) be the third derivative of 0*i**3 + 5*i**2 + 0 - 1/84*i**4 + o*i + 1/210*i**5. Factor t(z).
2*z*(z - 1)/7
Let x(y) be the third derivative of y**8/336 - y**7/30 + 3*y**6/20 - y**5/3 + y**4/3 - 82*y**2. Let x(s) = 0. Calculate s.
0, 1, 2
Solve -3*m - 260*m - 3*m**3 - 729 + 3 - 124*m - 108*m - 72*m**2 = 0 for m.
-11, -2
Suppose -21*a + 2573 = 2489. Determine o so that -a*o**3 + 4*o + 8/3 - 4/3*o**4 - 4/3*o**2 = 0.
-2, -1, 1
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