5*g**u - 2/5*g.
2*g*(g - 1)*(g + 1)**3/5
Let t(w) be the second derivative of -w**3/6 - w**2/2 - w. Let r(p) = 2*p**2 + 7*p + 1. Let o be 3 - 1/(1/(-2)). Let d(l) = o*t(l) + r(l). Factor d(q).
2*(q - 1)*(q + 2)
Let h(x) be the second derivative of 2*x**5/5 - x**4/3 - 2*x**3/3 + x - 10. Factor h(p).
4*p*(p - 1)*(2*p + 1)
Let h(g) be the second derivative of 2*g**7/21 - 4*g**6/5 + 8*g**5/5 + 2*g**4/3 - 6*g**3 + 8*g**2 + 39*g. Let h(r) = 0. What is r?
-1, 1, 4
Let f(y) be the third derivative of -y**7/210 - y**6/45 + y**5/10 + y**3/2 + 6*y**2. Let k(a) be the first derivative of f(a). Determine g, given that k(g) = 0.
-3, 0, 1
Let f(z) = -10*z**3 - 62*z**2 - 35*z - 17. Let r(w) = -3*w**3 - 21*w**2 - 12*w - 6. Let v(s) = 6*f(s) - 17*r(s). Factor v(m).
-3*m*(m + 1)*(3*m + 2)
Let p(f) be the third derivative of -f**5/45 - f**4/108 + 26*f**2. Let p(l) = 0. What is l?
-1/6, 0
Let z(k) be the second derivative of -k**5/5 + k**4/3 + 4*k**3/3 + 6*k. Find p, given that z(p) = 0.
-1, 0, 2
Let b(z) be the second derivative of z**6/120 - 7*z**5/80 + 17*z**4/48 - 17*z**3/24 + 3*z**2/4 + z + 1. Factor b(x).
(x - 3)*(x - 2)*(x - 1)**2/4
Let x(j) = 2*j**2 + 16*j + 12. Let s(y) = 4*y**2 + 31*y + 25. Let a(l) = -4*s(l) + 7*x(l). Factor a(z).
-2*(z + 2)*(z + 4)
Let u be ((-6)/(-20))/(((-63)/28)/(-3)). Factor -u*g + 2/5*g**2 + 0.
2*g*(g - 1)/5
Let z(r) be the first derivative of 8*r**5/25 + 7*r**4/10 + 4*r**3/15 - r**2/5 + 10. Factor z(q).
2*q*(q + 1)**2*(4*q - 1)/5
Let b(r) = -3*r - 1. Let j be b(-1). Let l(f) = 3*f**3 - f**2 + 2*f - 1. Let z be l(1). Suppose 0 - v**2 - j + z*v**2 = 0. Calculate v.
-1, 1
Let q = -202 + 1416/7. Factor 0*r**3 + 4/7*r**2 + 2/7*r + 0 - q*r**5 - 4/7*r**4.
-2*r*(r - 1)*(r + 1)**3/7
Suppose o - 4 = -p, 0 = 2*p - 6*p + 4*o + 24. Let j(h) be the second derivative of -32/45*h**p + 4/27*h**3 - 1/9*h**2 + 8/27*h**4 + h + 0. Factor j(k).
-2*(4*k - 1)**2*(4*k + 1)/9
Suppose -4*v = -v - 9. Suppose 0 = -v*u + c - 0*c + 11, c = -4*u + 17. Solve u - 2 - o**2 - 1 = 0.
-1, 1
Suppose -4*p + 7*p - 6 = 0. Factor 1/2*u**p - 1/2*u + 0.
u*(u - 1)/2
Let u be 3 + (2 + -2)/(-2). Let j(w) be the second derivative of -w + 0 - 1/36*w**4 - 1/9*w**u - 1/6*w**2. Determine q, given that j(q) = 0.
-1
Let t(r) = 21*r**3 + 24*r**2 + 12*r + 9. Let j(q) = -q**3 - q**2 - q - 1. Let s(u) = -9*j(u) - t(u). Factor s(p).
-3*p*(p + 1)*(4*p + 1)
Let m(d) be the third derivative of d**5/80 - 3*d**4/32 + d**3/4 + 4*d**2. Factor m(f).
3*(f - 2)*(f - 1)/4
Let m(j) be the second derivative of -j**4/48 + j**3/4 - 5*j**2/8 + 16*j. Let m(l) = 0. What is l?
1, 5
Let n(d) be the second derivative of -3*d**5/20 - 15*d**4/4 - 75*d**3/2 - 375*d**2/2 - 5*d. Factor n(m).
-3*(m + 5)**3
Let y = 5 + -7. Let l be 35/10 + y/(-4). What is w in -24*w**2 + 22*w**3 + 3*w - 6*w**4 + l*w + w = 0?
0, 2/3, 1, 2
Let j(y) = 8*y**2 - 6*y - 3. Let k(m) = 2*m**2 + 4*m**2 - 4*m**2 - 1 + m**2 - 2*m. Let r(z) = -4*j(z) + 11*k(z). Factor r(v).
(v + 1)**2
Factor -12*f - 5*f**3 + 8 + 10*f**3 - f**3.
4*(f - 1)**2*(f + 2)
Let z be (0 + 2/(-2))*-2. Let y be -2*1 + 13 + -10. Factor -y + 5/2*h + 7/2*h**z.
(h + 1)*(7*h - 2)/2
Suppose 0 = 4*x + 5 + 15, -2*p = -3*x - 19. Let d be p - (0/(-2) - -2). Let d + 0*y**3 + 2/5*y**5 - 2/5*y + 4/5*y**2 - 4/5*y**4 = 0. What is y?
-1, 0, 1
Let j(l) be the first derivative of l**6/36 + l**5/30 - 5*l**4/24 + l**3/6 + 21. Factor j(i).
i**2*(i - 1)**2*(i + 3)/6
Let z(o) be the second derivative of -o**8/5880 - o**7/1470 - o**6/1260 + o**3/6 - o. Let p(f) be the second derivative of z(f). Find q such that p(q) = 0.
-1, 0
Factor -2/11*j**2 + 0 - 10/11*j.
-2*j*(j + 5)/11
What is s in 0*s + 3*s**2 + 0 - 3/2*s**3 = 0?
0, 2
Let l = -18/13 - -67/39. Factor 0*c**2 + l*c + 0 - 1/3*c**3.
-c*(c - 1)*(c + 1)/3
Suppose 5*d - 3 = 7. Factor -2*n**3 - 2*n - 3*n**3 + 2*n**4 + 6*n**d - n**3.
2*n*(n - 1)**3
Let o(n) be the first derivative of -1/120*n**5 + 0*n**3 + 0*n + 1 + 0*n**4 + 1/2*n**2. Let s(v) be the second derivative of o(v). Factor s(t).
-t**2/2
Let u(q) be the second derivative of -2*q**6/75 + q**5/25 - 4*q. Factor u(p).
-4*p**3*(p - 1)/5
Let p be 9/12 + (-1)/(-4). Factor -2*n**2 - 3 + p + 1 + 3.
-2*(n - 1)*(n + 1)
Let b(r) = r**2 + 6*r + 7. Let u be b(-5). What is g in 2 - g**u + 0 - 8 - 4*g + 2 = 0?
-2
Suppose -4*x - 3*b + 18 - 7 = 0, 5*b = -4*x + 13. Factor 0*k**2 - 4*k - 2*k**x + 2*k.
-2*k*(k + 1)
Let n = 21008 - 693152/33. Let r = n + -30/11. Find w, given that 0*w + r*w**3 - 2*w**2 + 8/3 = 0.
-1, 2
Let i(q) be the second derivative of -q**7/420 - q**6/120 + q**2/2 + 6*q. Let r(p) be the first derivative of i(p). Factor r(m).
-m**3*(m + 2)/2
Let l be 3/(-2) + 378/180. Let w be (-52)/(-80) - (-1)/(-4). Factor -1/5*i**3 + 0*i**2 + l*i + w.
-(i - 2)*(i + 1)**2/5
Let i(g) be the first derivative of -3*g**6/4 + 6*g**5 - 41*g**4/4 + 6*g**3 - 5*g**2/4 + 1. Determine d so that i(d) = 0.
0, 1/3, 1, 5
Let b(d) be the third derivative of -27*d**6/260 + 93*d**5/130 - 28*d**4/39 + 4*d**3/13 - 25*d**2. Factor b(j).
-2*(j - 3)*(9*j - 2)**2/13
Suppose 17*k - 13*k - 20 = 0. Find x, given that 1/3*x**k + 2/3*x**4 + 0 - 1/3*x + 0*x**3 - 2/3*x**2 = 0.
-1, 0, 1
Suppose 0 - 4/7*y**5 + 8/7*y**2 - 20/7*y**3 + 16/7*y**4 + 0*y = 0. Calculate y.
0, 1, 2
Let a(g) be the third derivative of -g**7/210 + g**5/30 - g**3/6 + 27*g**2 + g. Suppose a(x) = 0. Calculate x.
-1, 1
Let u(x) be the first derivative of -x**7/189 + 2*x**6/135 - x**5/90 + 3*x + 1. Let h(c) be the first derivative of u(c). Factor h(i).
-2*i**3*(i - 1)**2/9
Let t(b) = b**2 - 8*b + 14. Let n be t(6). What is c in 0 + 1/3*c**n - 1/3*c**4 + 0*c**3 + 0*c = 0?
-1, 0, 1
Let z(y) be the third derivative of y**5/10 + 3*y**4/8 - y**3 - 51*y**2. Factor z(q).
3*(q + 2)*(2*q - 1)
Let v = -238 + 28561/120. Let g(f) be the second derivative of f - 1/48*f**4 + 0*f**2 + 1/80*f**5 + v*f**6 + 0 - 1/24*f**3. Let g(z) = 0. Calculate z.
-1, 0, 1
Factor 3*u - 6*u**3 + 2*u + u**3 + 0*u**3.
-5*u*(u - 1)*(u + 1)
Let z(d) be the third derivative of 0 - 1/210*d**7 + 0*d**4 - 8*d**2 + 0*d + 0*d**5 + 0*d**6 + 0*d**3. Factor z(q).
-q**4
Let f = -7 + 9. Suppose -f*a + 36 = 5*p - 46, -44 = -3*p + 4*a. Factor -210*q**3 + 9*q - 140*q**3 + 15*q + 76*q**2 + p - 256*q**2.
-2*(5*q + 2)**2*(7*q - 2)
Suppose -2*m = -4*t + 12, 15 = t + 4*t + m. Let h(a) be the first derivative of -a**2 - 2/3*a**t + 1 + 1/2*a**4 + 2*a. Factor h(v).
2*(v - 1)**2*(v + 1)
Let -4/15*g**4 - 2/5*g**5 - 4/15 + 8/15*g**2 - 2/5*g + 4/5*g**3 = 0. Calculate g.
-1, -2/3, 1
Let k(q) be the second derivative of 1/20*q**5 + 1/120*q**6 + 0 + 1/8*q**4 + 1/6*q**3 + 1/8*q**2 + 2*q. Find u such that k(u) = 0.
-1
Let u(z) be the third derivative of 1/840*z**8 - 2/15*z**3 + 0 - 3*z**2 - 1/75*z**5 - 1/12*z**4 + 0*z + 4/525*z**7 + 1/75*z**6. Factor u(w).
2*(w - 1)*(w + 1)**3*(w + 2)/5
Let h(z) be the first derivative of -z**6/18 + z**5/15 + z**4/12 - z**3/9 - 7. Factor h(a).
-a**2*(a - 1)**2*(a + 1)/3
Factor 4*z**4 - 154*z**2 + 152*z**2 - 3*z**4 - z**3.
z**2*(z - 2)*(z + 1)
Let s(v) be the first derivative of 0*v - 1/4*v**3 + 6 + 1/16*v**4 + 1/4*v**2. Factor s(b).
b*(b - 2)*(b - 1)/4
What is v in 8/3*v**4 - 2/3*v**5 - 4*v**3 + 8/3*v**2 + 0 - 2/3*v = 0?
0, 1
Let j = -35/4 - -9. Factor 0 - 1/4*r**4 + j*r**5 + 1/4*r**2 + 0*r - 1/4*r**3.
r**2*(r - 1)**2*(r + 1)/4
Let i(g) be the third derivative of -g**6/1260 + g**4/84 + 5*g**3/6 + 3*g**2. Let z(k) be the first derivative of i(k). Factor z(p).
-2*(p - 1)*(p + 1)/7
Let o(g) be the first derivative of g**5/20 - g**4/2 + g**3/2 + 5*g**2 + 25*g/4 + 19. Find i, given that o(i) = 0.
-1, 5
Let l(p) be the second derivative of -p**4/6 + p**2 - 12*p. Factor l(s).
-2*(s - 1)*(s + 1)
Let k(a) = a**2 - a + 1. Let z(b) = 3*b**3 + b - 9. Let f(s) = 5*k(s) + z(s). Factor f(l).
(l - 1)*(l + 2)*(3*l + 2)
Let u be -11 - 3/((-6)/2). Let t be ((-3)/(-6))/((-15)/u). Factor 0*n + t*n**2 + 0.
n**2/3
Let t(r) be the second derivative of 2*r**7/105 - r**5/15 + 3*r**2 + 7*r. Let u(q) be the first derivative of t(q). Determine k, given that u(k) = 0.
-1, 0, 1
Factor 0 - 1/2*p - 1/2*p**2.
-p*(p + 1)/2
Let g = 142 + -1559/11. Let b(t) be the third derivative of 0*t - 1/330*t**5 + 0 - g*t**3 + t**2 + 1/22*t**4. Find d, given that b(d) = 0.
3
Let i = 13 - 9. Suppose -5*u = -16 - i. Factor 2*r**2 + u*r**4 + 3*r**2 + 