. Let o be p(6). Let f be o/115 + 6/(-10). Factor 2/5 + f*u**2 + 6/5*u.
2*(u + 1)*(2*u + 1)/5
Let u = -23 - -50. Determine d, given that u*d**4 + 0*d**5 + 6*d**3 - 3*d**5 - 24*d**4 = 0.
-1, 0, 2
Let m(g) be the third derivative of 0*g**5 + 0*g + g**2 + 1/8*g**4 + 0 + 1/3*g**3 - 1/120*g**6. Determine o, given that m(o) = 0.
-1, 2
Let t = -5212 + 5214. Solve 6/5*w + 0 + 2*w**3 - 14/5*w**t - 2/5*w**4 = 0.
0, 1, 3
Let v(d) = -d**3 + 4*d**2 - 2*d - 2. Let n = 14 + -12. Let u be v(n). Suppose -u*r**5 + 10*r**3 - 4*r**3 - 8*r**3 - 4*r**4 = 0. Calculate r.
-1, 0
Let b(x) = x**2 - 20*x - 1269. Let s be b(-27). Factor 0*d - 12/11*d**4 - 2/11*d**3 + s*d**2 + 0.
-2*d**3*(6*d + 1)/11
Let l(a) be the second derivative of 0 - 9/20*a**5 - 15*a + 1/10*a**6 + 1/2*a**4 + 0*a**2 + 0*a**3. Let l(m) = 0. What is m?
0, 1, 2
Let a = -60 + 67. Let l(i) be the third derivative of 0 - a*i**2 - 16/3*i**4 + 8/3*i**3 + 77/15*i**5 - 49/30*i**6 + 0*i. Factor l(r).
-4*(r - 1)*(7*r - 2)**2
Let f(s) = -s**3 + 45*s**2 - 3*s + 6. Let p(i) = -i**3 + 44*i**2 - 2*i + 4. Let a(c) = 2*f(c) - 3*p(c). Factor a(t).
t**2*(t - 42)
Let z = 5 + -2. Determine q, given that -3*q**2 - 1 - 5*q - z + 13 - q = 0.
-3, 1
Let v be (56 - 56)/((-12)/(-9)*-3). Factor -1/5*z**3 - 2/5*z**2 + v - 1/5*z.
-z*(z + 1)**2/5
Factor m**3 - 1/2 + 1/2*m**4 + 0*m**2 - m.
(m - 1)*(m + 1)**3/2
Determine s so that -2/7*s**3 + 4/7*s + 0 - 2/7*s**2 = 0.
-2, 0, 1
Let b(s) be the third derivative of s**5/140 + 3*s**4/28 + 122*s**2. Factor b(v).
3*v*(v + 6)/7
Let i(k) be the third derivative of -k**2 + 1/120*k**6 + 0*k + 1/2*k**3 + 1/60*k**5 + 0 - 5/24*k**4. What is h in i(h) = 0?
-3, 1
Let l(a) = -7*a**3 + 5*a**2 + 4*a - 2. Let z(g) = -8*g + 3*g + g + 6*g**3 + 1 - 4*g**2. Let c(i) = 5*l(i) + 6*z(i). Determine b, given that c(b) = 0.
-2, -1, 2
Let a(n) = -n - 109. Let l be a(-16). Let o be 28/21*(l/(-42) + -2). Factor 4/7 - 2/7*g**2 + o*g.
-2*(g - 2)*(g + 1)/7
Let f(j) = 2*j**2 - 2*j. Let v(m) = -2*m**2 - 6*m + 4. Let i be v(-4). Let l(p) = -1. Let d(x) = i*l(x) - f(x). Find s, given that d(s) = 0.
-1, 2
Let h(d) be the first derivative of -5*d**3/3 - 30*d**2 - 135*d - 46. Factor h(k).
-5*(k + 3)*(k + 9)
Let z = 69 + -66. Let j be (-20)/(-18)*z/5. Factor 8/3*r**3 + 0 + j*r**4 + 4/3*r + 10/3*r**2.
2*r*(r + 1)**2*(r + 2)/3
Let r(c) be the third derivative of 2*c**7/35 - c**6/15 - 3*c**5/5 + 2*c**4 - 8*c**3/3 + 2*c**2 - 3*c. Suppose r(z) = 0. Calculate z.
-2, 2/3, 1
Suppose -19*u + 16*u = -84. Let z be -2 + 5 - u/10. Suppose -z*k**3 + 4/5*k**2 - 3/5*k + 0 = 0. What is k?
0, 1, 3
Let f be (-1)/(-3 - 11/(-4)). Suppose 0 = -2*n - 9 + 1, 4*b = -3*n - f. Suppose k**2 - b*k + 10 - 28 + 15 = 0. Calculate k.
-1, 3
Let x(p) be the first derivative of -p**4/4 + 7*p**3/3 - 7*p**2 + 8*p + 4. Suppose x(m) = 0. Calculate m.
1, 2, 4
Let u(v) be the third derivative of -v**7/490 + 71*v**6/280 - 37*v**5/4 + 175*v**4/8 + 31*v**2. What is m in u(m) = 0?
0, 1, 35
Factor 74 + 164*q - 539 - 64 + 185 + 4*q**2.
4*(q - 2)*(q + 43)
Let d(t) be the third derivative of -t**5/30 + 23*t**4/3 - 2116*t**3/3 + t**2 + 134. Factor d(l).
-2*(l - 46)**2
Let i(b) = 34*b**2 - 33*b + 6. Let m(r) = -33*r**2 + 33*r - 6. Let v be (4 - 3)/((-3)/21). Let j(p) = v*m(p) - 6*i(p). Factor j(c).
3*(c - 1)*(9*c - 2)
Let o(r) = -1 - 4 - r**3 + 4*r**2 + 7*r + 0*r**3 - 1. Let u be o(5). Factor 43*s**2 - 12*s + u*s + 12*s**4 - 15*s**2 - 32*s**3.
4*s*(s - 1)**2*(3*s - 2)
Let g(m) be the third derivative of m**6/480 + 23*m**5/40 + 529*m**4/8 + 12167*m**3/3 - 281*m**2. Solve g(a) = 0 for a.
-46
Let y be (-17 - -12)/(1/(-10)). Find k, given that 4*k**2 - 5*k**2 - 307 - 14*k**2 + 292 + y*k = 0.
1/3, 3
Let b(k) be the second derivative of k**4/4 - 19*k**3/2 + 411*k. Find h such that b(h) = 0.
0, 19
Let y(v) be the first derivative of -v**7/700 + v**6/900 + v**5/75 - v**3 + 13. Let f(n) be the third derivative of y(n). Suppose f(k) = 0. Calculate k.
-1, 0, 4/3
Let -12*w + 9/2 - 9/8*w**2 + 15/8*w**4 + 27/4*w**3 = 0. Calculate w.
-3, -2, 2/5, 1
Let b(k) = -5*k**4 + 120*k**3 + 215*k**2 + 135*k. Let g(r) = -r**4 + 30*r**3 + 54*r**2 + 34*r. Let u(w) = 6*b(w) - 25*g(w). Let u(p) = 0. Calculate p.
-2, 0
Let v(k) = 10*k + 9 - 14*k**3 + 15*k**3 - 6*k**2 - 3*k. Let g be v(4). Find t such that -2*t + g*t + 5*t - 4*t**2 = 0.
0, 2
Suppose 0 = -4*l - 2*y - 8, 0 = l + 8*y - 6*y + 17. Factor -3/2*s**4 + 0*s + 0 + 2*s**2 + 0*s**l + 1/2*s**5.
s**2*(s - 2)**2*(s + 1)/2
Let z be 1 + -2 + 11 + -8. Let -3*a - 3*a**3 + 4*a - 3*a**2 + z*a + 3*a = 0. Calculate a.
-2, 0, 1
Let n(g) be the second derivative of 7*g + 7/2*g**2 - 1/120*g**5 + 0 - 1/12*g**3 + 1/24*g**4. Let j(u) be the first derivative of n(u). Factor j(m).
-(m - 1)**2/2
Let v(a) be the third derivative of a**8/672 - 3*a**7/280 + 13*a**6/480 - a**5/48 - a**4/32 + a**3/12 - 3*a**2 + 1. Factor v(s).
(s - 2)*(s - 1)**3*(2*s + 1)/4
Let u(t) = 6*t**5 - 6*t**4 - 22*t**3 - 22*t**2 - 12*t + 4. Let l(y) = -y**5 + y**4 + y**3 + y - 1. Let s(p) = -4*l(p) - u(p). Let s(o) = 0. What is o?
-1, 0, 4
Let o(f) = -f + 14. Let j be o(12). Find w such that 3*w**3 - 231*w**5 - 3*w**4 - 2*w + 3*w**2 - j*w**3 + 232*w**5 = 0.
-1, 0, 1, 2
Suppose 22668*k - 22668*k + 9*k**2 - 2*k**4 - k**4 + 6*k**3 = 0. What is k?
-1, 0, 3
Let l(q) be the second derivative of -q**9/5292 - q**8/1470 + q**6/315 + q**5/210 - 8*q**3/3 + 6*q. Let k(u) be the second derivative of l(u). Factor k(z).
-4*z*(z - 1)*(z + 1)**3/7
Suppose 33*t = -5*b + 38*t + 30, 5*t + 28 = 4*b. Factor -9/2*p**b + 0 + 3*p + 3/2*p**3.
3*p*(p - 2)*(p - 1)/2
Let z(v) = v**2 + 7*v - 28. Let f be z(-10). Let t(o) = -1. Let p(s) = 4*s**3 - 16*s**2 + 12*s + 2. Let y(h) = f*t(h) + p(h). Find k, given that y(k) = 0.
0, 1, 3
Factor 5/2 - 1/6*c**2 - 7/3*c.
-(c - 1)*(c + 15)/6
Let u(v) be the second derivative of v**5/150 - v**4/15 + 4*v**3/15 - 8*v**2/15 + 3*v - 68. Let u(b) = 0. Calculate b.
2
Let t(u) be the third derivative of u**6/180 - u**5/12 + u**4/2 + u**3/6 + 13*u**2. Let p(i) be the first derivative of t(i). Solve p(n) = 0.
2, 3
Determine s so that 2/7*s**4 + 4 - 30/7*s**2 + 26/7*s**3 - 26/7*s = 0.
-14, -1, 1
Let y(p) = 7*p - 20. Let h be y(5). Factor -35*z**2 - 5*z - h*z + 5*z.
-5*z*(7*z + 3)
Let g(s) be the first derivative of -7*s**4/6 - 22*s**3/3 - 32*s**2/3 + 8*s + 126. Suppose g(z) = 0. What is z?
-3, -2, 2/7
Let 27*o**3 + 1883*o**4 - o - 1880*o**4 + 24*o**2 - 3*o + 4*o = 0. What is o?
-8, -1, 0
Let b(m) be the first derivative of 1/16*m**2 - 1/8*m**4 + 1/8*m**3 + 0*m - 35. Suppose b(w) = 0. Calculate w.
-1/4, 0, 1
Factor 158/5 - 32*b + 2/5*b**2.
2*(b - 79)*(b - 1)/5
Suppose -3*c - 173 = 3*i - 8, 0 = 2*i + 2. Let x be (c/(-252))/((-6)/(-7)). Factor -3/4 - x*o**2 + o.
-(o - 3)*(o - 1)/4
Let l(i) = -9*i**4 - 3*i**3 + 6*i**2 - 6*i - 6. Let r(w) = 8*w**4 + 3*w**3 - 6*w**2 + 5*w + 5. Let t(k) = 5*l(k) + 6*r(k). Factor t(o).
3*o**2*(o - 1)*(o + 2)
Let n(q) be the third derivative of -q**7/280 + q**6/30 + 3*q**5/40 - 9*q**4/4 - 2*q**3 - 20*q**2. Let t(k) be the first derivative of n(k). Factor t(p).
-3*(p - 3)**2*(p + 2)
Let d(n) be the third derivative of 1/48*n**4 + 0*n + 1/80*n**5 + 0 + 15*n**2 + 0*n**3 + 1/480*n**6. Factor d(o).
o*(o + 1)*(o + 2)/4
Let m be (-3)/14*232/(-87). Suppose -14*v = -21*v. Factor m*b + 4/7*b**2 + 1/7*b**3 + v.
b*(b + 2)**2/7
Let i = -6720 + 47064/7. Solve -6/7 + 9/7*h**3 + 3*h - i*h**2 = 0.
2/3, 1
Let r(v) be the first derivative of -v**3 + 18*v**2 - 96*v + 261. Factor r(y).
-3*(y - 8)*(y - 4)
Let i(k) = 13*k**2 + 43*k. Let x(g) = g**2. Let n(q) = 168*q**2 + 140*q. Let y(b) = -2*n(b) + 252*x(b). Let o(d) = -32*i(d) - 5*y(d). Factor o(h).
4*h*(h + 6)
Let a(i) be the third derivative of i**9/60480 + i**8/20160 + i**5/60 + 5*i**2. Let n(z) be the third derivative of a(z). Factor n(x).
x**2*(x + 1)
Let j(u) be the first derivative of -1/3*u**3 + 0*u**2 - 4/15*u**6 - 5 - 5/6*u**4 + 3*u - 4/5*u**5. Let q(f) be the first derivative of j(f). Factor q(y).
-2*y*(y + 1)*(2*y + 1)**2
Let b(g) = 3*g**4 - g**3 + 6*g**2 + 6*g - 2. Let q(t) = 5*t**4 - t**3 + 7*t**2 + 7*t - 3. Let h(i) = 6*b(i) - 4*q(i). Suppose h(u) = 0. What is u?
-2, -1, 0, 2
Let s(y) be the first derivative of y**3/18 - 7*y**2/2 + 147*y/2 + 69. What is a in s(a) = 0?
21
Let y(j) be the third derivative of -j**7/231 + 2*j**6/55 - j**5/22