 j. Let x(q) = 32*q**2 + 2*q. Let o(k) = -k**3 - 2*k**2 + 4*k. Let z be o(-3). Let n(h) = z*x(h) - 10*v(h). Let n(s) = 0. Calculate s.
-2/7, 0
Determine w, given that 0*w**2 - 4*w**2 + 19*w - 11*w = 0.
0, 2
Let d = -6 + 9. Let h(g) be the second derivative of g - 1/18*g**d - 1/12*g**4 - 1/30*g**5 + 0*g**2 + 0. Factor h(x).
-x*(x + 1)*(2*x + 1)/3
Let d(n) = n**2 + n + 1. Let s(z) = 4*z**4 - 6*z**3 + 10*z**2 + 8*z + 8. Let i(g) = 8*d(g) - s(g). Factor i(w).
-2*w**2*(w - 1)*(2*w - 1)
Let k(h) be the third derivative of h**5/105 - 3*h**4/7 + 54*h**3/7 - 37*h**2. Factor k(a).
4*(a - 9)**2/7
Let m(x) be the third derivative of -x**8/2688 + x**7/1680 + x**6/960 - x**5/480 + 4*x**2. Solve m(q) = 0.
-1, 0, 1
Let t(k) = 35*k**2 - 15*k + 30. Let r(j) = j**2 - j + 1. Let i(x) = -30*r(x) + t(x). Suppose i(l) = 0. Calculate l.
-3, 0
Let k(i) be the second derivative of -i**4/42 + i**2/7 - 8*i. Factor k(a).
-2*(a - 1)*(a + 1)/7
Let x be 13/(-91) + 1/7. Let q(h) be the first derivative of 1 + 3/10*h**5 + 3/2*h + x*h**2 - h**3 + 0*h**4. Factor q(o).
3*(o - 1)**2*(o + 1)**2/2
Let x be 6/(-24) - 9/(-4). Factor -4 - 2*a**x + 1 - 2*a**3 + 2 + 3 + 2*a.
-2*(a - 1)*(a + 1)**2
Determine t so that -9*t**4 - 2*t**4 + 4*t**5 - 3*t**4 + 18*t**4 = 0.
-1, 0
Factor 5*j**2 - 5*j**2 - 3*j + 0*j - 6*j**2 - 3*j**3.
-3*j*(j + 1)**2
Let z be (2 + 26)/2*(-66)/(-693). Factor z*r**2 + 0 - 2/3*r.
2*r*(2*r - 1)/3
Let s(w) be the second derivative of w**4/6 + w**3/21 - 14*w. Suppose s(x) = 0. What is x?
-1/7, 0
Let p be 12/(-16) - (-154)/(-8). Let q = p + 22. Find n such that -2/5*n + 2/5*n**q - 2/5 + 2/5*n**3 = 0.
-1, 1
Suppose -4*q + 5*o = -3, 4*o - 12 - 1 = q. Suppose 11*d = q*d. Determine k, given that -2/5*k**4 - 6/5*k**2 - 6/5*k**3 + d - 2/5*k = 0.
-1, 0
Let v be ((-6)/10)/((-16)/80). Let z(c) be the second derivative of -1/80*c**5 + 0 + 4*c + 0*c**v + 0*c**2 - 1/60*c**6 + 1/48*c**4. Factor z(t).
-t**2*(t + 1)*(2*t - 1)/4
Let r(n) be the first derivative of n**3/12 + n**2/8 - 10. Suppose r(v) = 0. What is v?
-1, 0
Determine q, given that 5*q**2 - 2/3 + 13/3*q = 0.
-1, 2/15
Let w(a) = -14*a**2 + 16*a**2 - 26 + 24*a**2. Let q be 10/(-3) + (-2)/(-6). Let g(h) = -5*h**2 + 5. Let m(i) = q*w(i) - 16*g(i). Solve m(x) = 0.
-1, 1
Let z(l) be the second derivative of -l**6/180 + l**5/120 + l**4/36 + 5*l - 1. Determine b so that z(b) = 0.
-1, 0, 2
Let z(p) = 16*p**3 - 23*p**2 - 15*p + 11. Let q(o) = 8*o**3 - 12*o**2 - 8*o + 6. Let h(f) = 11*q(f) - 6*z(f). Solve h(s) = 0 for s.
-1/4, 0, 1
Let c be (-9 - 1)*(-9)/(-18). Let u(y) = -4*y**2 - 24*y - 31. Let k(p) = -20*p + 6*p - 6*p**2 - 22*p - 46. Let a(i) = c*k(i) + 8*u(i). Factor a(r).
-2*(r + 3)**2
Factor -2/5*d**3 - 4/5*d**2 + 0 + 0*d.
-2*d**2*(d + 2)/5
Let a(b) = -2*b**4 + 8*b**3 - 2*b**2 - 2*b. Let p(y) = -y**3 - y**2 + y. Let q(n) = a(n) + 2*p(n). Factor q(t).
-2*t**2*(t - 2)*(t - 1)
Let r(c) be the second derivative of 0 - 6/5*c**6 - 2*c**3 + 7*c + 3*c**4 + 0*c**2 + 9/14*c**7 - 3/4*c**5. Solve r(q) = 0.
-1, 0, 2/3, 1
Factor 15/4*n**2 + 5/2*n + 5/4*n**3 + 0.
5*n*(n + 1)*(n + 2)/4
Let m = -200 + 202. Factor -2/7 + 2/7*a**m - 2/7*a**3 + 2/7*a.
-2*(a - 1)**2*(a + 1)/7
Let t = 193 - 769/4. Factor -1/2*g + 0 + 5/4*g**3 - t*g**2.
g*(g - 1)*(5*g + 2)/4
Let b(v) = 3*v**3 - 4*v**2 + 7. Let z(f) = -f**3 + f**2 - 2. Let y(s) = 2*b(s) + 7*z(s). Factor y(m).
-m**2*(m + 1)
Let q(r) be the third derivative of -r**6/660 + 7*r**4/132 + 2*r**3/11 - 15*r**2. Find u, given that q(u) = 0.
-2, -1, 3
Let q(f) = f**2 - 1. Let g(w) = 5*w**2 + 4*w - 3. Let z be 3*(13/(-3) + 1). Let m = -7 - z. Let v(y) = m*q(y) - g(y). Solve v(s) = 0.
-2, 0
Suppose -20*c + 55*c**3 + 28*c**2 - 8*c**2 - 60*c**3 = 0. Calculate c.
0, 2
Let u(n) = -n**2 - n + 1. Let b(a) = 1. Let j(o) = -2*b(o) + u(o). Let f(w) = -3*w**2 - 15. Let z(k) = f(k) - 18*j(k). Factor z(q).
3*(q + 1)*(5*q + 1)
Factor 3*k + 1/8*k**3 + 2 + 9/8*k**2.
(k + 1)*(k + 4)**2/8
Suppose 8 = -7*r - 13. Let i be -36*-3*r/(-18). Factor -1 - 53/2*m**2 + i*m**3 + 19/2*m.
(m - 1)*(4*m - 1)*(9*m - 2)/2
Let r(v) = -v**2 - 13*v + 18. Let n be r(-13). Suppose 5*o - n = 3*j, -j - 13 = -0*o - 4*o. Factor 0 - 1/3*i**o - 1/3*i - 2/3*i**2.
-i*(i + 1)**2/3
Find u, given that -3/2*u**2 + 3*u - 3/2 = 0.
1
Let f(x) = -x**4 + x**3 + 2*x**2 - 2. Let n(b) = -11*b**2 - b. Let d be n(-1). Let w(l) = 3*l**4 - 2*l**3 - 5*l**2 + 5. Let m(r) = d*f(r) - 4*w(r). Factor m(t).
-2*t**3*(t + 1)
Let k(o) be the third derivative of -o**8/112 + 16*o**2. Suppose k(x) = 0. Calculate x.
0
Let p(k) be the first derivative of -3*k**5 - 10*k**4 - 35*k**3/3 - 5*k**2 - 16. Solve p(o) = 0.
-1, -2/3, 0
Let a(o) be the third derivative of -o**7/1260 + o**6/180 - o**4/12 - 2*o**2. Let d(k) be the second derivative of a(k). Factor d(y).
-2*y*(y - 2)
Suppose -s + 2*o = -11, -s = -4*o - 3 - 18. Let a(q) be the first derivative of -13*q**2 + 16*q**3 - 9/2*q**4 + s + 4*q. Factor a(u).
-2*(u - 2)*(3*u - 1)**2
Determine r, given that 2/7*r**2 + 0 - 6/7*r = 0.
0, 3
Let h(p) be the second derivative of -p**7/14 - p**6/10 + 3*p**5/20 + p**4/4 - 8*p. Factor h(c).
-3*c**2*(c - 1)*(c + 1)**2
Let p = -38/11 - -332/77. Find z such that p*z + 2/7*z**2 + 4/7 = 0.
-2, -1
Factor -j**2 - 6 + j**4 - 11*j - 3*j**3 - 3*j**2 + 6*j**3 + j**2.
(j - 2)*(j + 1)**2*(j + 3)
Let d(o) be the second derivative of -o**6/21 - o**5/5 - 2*o**4/7 - 2*o**3/21 + o**2/7 + 3*o. Factor d(x).
-2*(x + 1)**3*(5*x - 1)/7
Let k(w) be the second derivative of -w**4/3 - 4*w**3/3 + 6*w**2 + 63*w. Factor k(o).
-4*(o - 1)*(o + 3)
Let d(x) be the third derivative of 0 - 1/42*x**4 - 1/30*x**5 - 3*x**2 + 1/21*x**3 + 0*x - 1/105*x**6. Factor d(v).
-2*(v + 1)**2*(4*v - 1)/7
Factor 4*f**3 - 695*f**2 + 695*f**2.
4*f**3
Suppose -3*g - 5*t - 10 = 0, 3*g = -t - 0*t - 2. Let a = 31/132 + 1/66. Factor a*m + g + 1/4*m**2.
m*(m + 1)/4
Let k(g) be the third derivative of g**5/30 + g**4/4 + 2*g**3/3 - 16*g**2. What is x in k(x) = 0?
-2, -1
Suppose -2*d = 5*l - 6, -3 = -2*l + 2*d + 5. Let o(w) = -w**3 - 7*w**2 - 5*w + 8. Let m be o(-6). Suppose 4*y**l + 6*y - 3*y + m*y**3 - y = 0. Calculate y.
-1, 0
Let s(v) be the third derivative of -2*v**7/105 + v**6/120 - 6*v**2. Factor s(n).
-n**3*(4*n - 1)
Let h(s) be the second derivative of -13/3*s**4 + 6/5*s**5 + 8*s**3 - 2/15*s**6 - s + 0 - 8*s**2. Factor h(l).
-4*(l - 2)**2*(l - 1)**2
Let i(p) be the third derivative of p**7/280 + p**3/3 - p**2. Let x(o) be the first derivative of i(o). Factor x(d).
3*d**3
Let s(j) be the second derivative of j**4/15 - 4*j**3/15 - 6*j**2/5 + 11*j. Determine h, given that s(h) = 0.
-1, 3
Suppose -j + 29 = -4*p - p, 4*p + 32 = 3*j. Let k(o) be the first derivative of -1 + 1/16*o**j - 1/4*o**2 + 1/12*o**3 + 0*o. Factor k(m).
m*(m - 1)*(m + 2)/4
Let a(t) be the first derivative of 9/2*t**2 + t**3 - 2 + 6*t. What is d in a(d) = 0?
-2, -1
Let a = 295/3 - 95. Suppose 2/3 + 8/3*l**2 + a*l = 0. Calculate l.
-1, -1/4
Suppose 0 - 8 = -4*p. Determine m so that 6*m**3 - 3*m**4 - p*m + 6*m**2 - 6 - 3*m**5 - m + 3 = 0.
-1, 1
Let x = 20 + -17. Find v, given that -2/5*v + 0 + 2/5*v**x - 2/5*v**2 + 2/5*v**4 = 0.
-1, 0, 1
Let n(u) be the second derivative of u**5/40 - u**3/12 - 2*u. Let n(f) = 0. What is f?
-1, 0, 1
Let s(m) = 57*m**5 + 103*m**4 + 45*m**3 - 53*m**2 - 23*m + 8. Let h(r) = r**5 - r**4 + r**3 - r**2 - r. Let a(p) = -14*h(p) + 2*s(p). What is u in a(u) = 0?
-1, 2/5
Let r(o) be the second derivative of o**5/5 - 2*o**4/3 - o. Suppose r(l) = 0. Calculate l.
0, 2
Let h(j) be the second derivative of -j**6/2700 + j**5/450 - j**4/180 + j**3/6 + 4*j. Let a(r) be the second derivative of h(r). Factor a(m).
-2*(m - 1)**2/15
Let u(b) be the third derivative of -b**6/540 - b**5/90 + b**4/108 + b**3/9 - 11*b**2. Solve u(i) = 0.
-3, -1, 1
Let c(j) be the first derivative of -7*j**4/12 - 5*j**3/6 + j**2 + j + 1. Let k(x) be the first derivative of c(x). Factor k(v).
-(v + 1)*(7*v - 2)
Let p(h) be the second derivative of -h**7/399 - 2*h**6/285 - h**5/190 - 49*h. Factor p(y).
-2*y**3*(y + 1)**2/19
Suppose -4*a - 6 = -18. Factor -2*y**3 + 2 + a*y - 1 + 1 - y - 2*y**2.
-2*(y - 1)*(y + 1)**2
Let t be (-8 - -9 - (0 + -2))*1. Let l(d) be the second derivative of 0 - 1/6*d**4 - 2/3*d**3 + 4*d + t*d**2. Factor l(r).
-2*(r - 1)*(r + 3)
Factor -1/2*v**2 + 0 + 1/6*v**3 - 2/3*v.
v*(v - 4