Let -1/5*p - 2/5 + 2/5*p**l + 1/5*p**3 = 0. Calculate p.
-2, -1, 1
Suppose -w - 18 = -4*w. Let t(f) be the second derivative of -4/27*f**3 - 1/135*f**w + 4/9*f**2 + 2/45*f**5 + 0 - 2*f - 1/18*f**4. Let t(k) = 0. What is k?
-1, 1, 2
Let c(h) be the second derivative of h**6/660 + h**5/330 - 2*h**2 + h. Let j(n) be the first derivative of c(n). Factor j(r).
2*r**2*(r + 1)/11
Factor 0*s + 2/11*s**5 + 0*s**2 + 4/11*s**4 + 0 + 2/11*s**3.
2*s**3*(s + 1)**2/11
Suppose y - 3*n = -12, -2*y + 26 - 10 = 2*n. Suppose -2*p**2 - 11*p**y + 2*p - p**2 + 10*p**3 - 4*p**3 = 0. What is p?
-1, 0, 2/5
Let u(z) be the second derivative of z**7/42 + 2*z**6/15 + 3*z**5/20 - z**4/3 - 2*z**3/3 + 3*z. Determine b so that u(b) = 0.
-2, -1, 0, 1
Factor -13*z - 3*z**3 + 4*z + 0*z**2 - 12*z**2.
-3*z*(z + 1)*(z + 3)
Factor 363/2*a**5 - 66*a**4 + 0*a + 0 + 0*a**2 + 6*a**3.
3*a**3*(11*a - 2)**2/2
Let m = 8 + -9. Let v be (-8)/(-22) - (m + 1). Factor v*l + 2/11*l**2 + 2/11.
2*(l + 1)**2/11
Let k = 3/17 + 92/153. Let r = -5/18 + k. Suppose -1/2*d**2 - r + d = 0. Calculate d.
1
Let c(n) = n - 7. Let t be c(9). Let v be (-3)/(-2) - 22/20 - 0. Factor -v*r - 1/5 - 1/5*r**t.
-(r + 1)**2/5
Let q(h) be the first derivative of 3*h**5/140 - h**3/14 + 4*h + 3. Let v(y) be the first derivative of q(y). Factor v(u).
3*u*(u - 1)*(u + 1)/7
Let c(h) be the second derivative of 0 - 1/50*h**5 - 1/30*h**4 + 1/5*h**2 + 1/15*h**3 - 3*h. Factor c(w).
-2*(w - 1)*(w + 1)**2/5
Let d = 0 + 0. Factor -2 + d*p + p**4 + p**3 - 3*p**2 - p - 4*p.
(p - 2)*(p + 1)**3
Find o, given that 12/7*o**5 - 9/7*o**4 + 6/7 - 39/7*o**3 + 3/7*o**2 + 27/7*o = 0.
-1, -1/4, 1, 2
Let z(g) be the first derivative of -4*g**6/21 + 34*g**5/35 - 2*g**4 + 44*g**3/21 - 8*g**2/7 + 2*g/7 - 6. Factor z(u).
-2*(u - 1)**4*(4*u - 1)/7
Solve 2/11*z**2 + 8/11 + 10/11*z = 0 for z.
-4, -1
Let t(b) be the third derivative of 4/3*b**3 + 5/6*b**5 + 0*b + 0 + 5*b**2 + 5/3*b**4. Factor t(x).
2*(5*x + 2)**2
Let b be (-6)/(-4)*20/15. Suppose -p = -b*p + 5. Factor 5/2*n + 5*n**3 - 1/2 + 1/2*n**5 - 5/2*n**4 - p*n**2.
(n - 1)**5/2
Let k = -9 + 13. Let x be 3/(38/(-20) + k). Find c such that -x*c**3 - 6/7*c**4 + 0 + 6/7*c**2 + 2/7*c + 8/7*c**5 = 0.
-1, -1/4, 0, 1
Let v(n) = n**2 + 0 + 1 + 4*n - 2. Suppose -5*l - 40 = 5*g, -l - 5*g = -5*l + 4. Let d(a) = a**2 + 5*a - 2. Let y(h) = l*d(h) + 6*v(h). Factor y(t).
2*(t + 1)**2
Factor 1/2*b**3 - 3*b**2 + 0*b + 0.
b**2*(b - 6)/2
Suppose 2*o - o = -z - 14, -5*o = 4*z + 60. Let y be 4/6 + z/33. Suppose 2/11*q**2 + y*q + 2/11 = 0. What is q?
-1
Let m(l) be the first derivative of 3 + 0*l - 1/2*l**4 + 2/3*l**3 + 2/15*l**5 - 1/3*l**2. Factor m(j).
2*j*(j - 1)**3/3
Let h(w) be the first derivative of 4 - 4/3*w**2 - 1/18*w**4 - 4/9*w**3 - 16/9*w. Factor h(a).
-2*(a + 2)**3/9
What is k in 0*k + 2/7*k**2 + 8/7*k**3 + 6/7*k**4 + 0 = 0?
-1, -1/3, 0
Let p(r) be the second derivative of 2/3*r**3 + r + r**2 - 1/15*r**6 + 0 + 0*r**4 - 1/5*r**5. Find a, given that p(a) = 0.
-1, 1
Let n(p) be the second derivative of 3/2*p**2 + 1/24*p**6 - 1/6*p**4 + 0 - 2*p + 0*p**3 + 2/15*p**5. Let y(d) be the first derivative of n(d). Factor y(k).
k*(k + 2)*(5*k - 2)
Let w(t) be the third derivative of -1/20*t**5 - 1/70*t**7 + 3/8*t**4 - 3/40*t**6 - 2*t**2 + 0 + t**3 + 0*t. Factor w(x).
-3*(x - 1)*(x + 1)**2*(x + 2)
Factor 2*i + 10*i**2 + i - 7*i**2.
3*i*(i + 1)
Let j(c) be the first derivative of c**6/13 - 14*c**5/65 + c**4/13 + 12. Solve j(t) = 0 for t.
0, 1/3, 2
Let y = -15 + 18. Factor o + 0*o**2 + 2/3 - 1/3*o**y.
-(o - 2)*(o + 1)**2/3
Let d(h) be the second derivative of -1/60*h**6 + 0*h**2 - 1/84*h**7 + 0*h**3 + 4*h + 0*h**4 + 0 + 0*h**5. Find j, given that d(j) = 0.
-1, 0
Let a(f) = f - 1. Let y(k) = -2*k**2 + 8*k - 7. Let p(w) = -3*a(w) + 3*y(w). Find v, given that p(v) = 0.
3/2, 2
Let m be ((-1)/1*-4)/(-1). Let a be m/2*4/(-2). Factor p**4 - 2*p**3 + 1 + p - a*p**5 - 2*p**2 + 6*p**5 - p**5.
(p - 1)**2*(p + 1)**3
Suppose f - 7 - 9 = 5*r, 5*r = -4*f + 14. Suppose u - f*u = -20. Factor 0 + 0*b**2 + 1/2*b**u + 0*b + 1/4*b**5 + 1/4*b**3.
b**3*(b + 1)**2/4
Let q = 23 + -23. Let m(o) be the second derivative of -2*o + 1/6*o**3 + q*o**2 + 0*o**5 - 1/6*o**4 + 1/15*o**6 - 1/42*o**7 + 0. Factor m(y).
-y*(y - 1)**3*(y + 1)
Let m(c) be the third derivative of -c**8/420 - c**7/140 + c**5/60 + c**3/2 - 3*c**2. Let y(k) be the first derivative of m(k). Factor y(i).
-2*i*(i + 1)**2*(2*i - 1)
Let k(b) be the first derivative of b**6/90 - b**5/15 + b**3/3 - 7. Let d(w) be the third derivative of k(w). Suppose d(a) = 0. What is a?
0, 2
Let w(u) = -2*u - 4. Let b be w(-4). Let 2/7*f**b + 0 + 2/7*f**3 - 2/7*f**2 - 2/7*f = 0. Calculate f.
-1, 0, 1
Let q(z) = -2*z**5 + 5*z**4 + 3*z**3 - 9*z**2 - 11*z - 1. Let i(p) = -p**4 + p**3 + p**2 + p + 1. Let c(m) = 5*i(m) + q(m). Find j such that c(j) = 0.
-2, -1, 1
Let k(w) be the third derivative of -w**7/630 - w**6/90 - w**5/60 + w**4/18 + 2*w**3/9 + 2*w**2. Factor k(i).
-(i - 1)*(i + 1)*(i + 2)**2/3
Let z(g) = 2*g**3 + 2. Let y be z(2). Suppose 5*m = 3*m + y. Factor 3*l**4 + l**2 + m*l**3 - 2*l**3 - 8*l**4 + l**5 - 8*l + 4.
(l - 2)**2*(l - 1)**2*(l + 1)
Let o(f) be the second derivative of f**5/300 - f**4/60 + f**2 + 3*f. Let p(d) be the first derivative of o(d). Factor p(s).
s*(s - 2)/5
Let a = 558 - 554. Determine v so that -2/3 - 1/3*v + 1/3*v**3 - v**a + 5/3*v**2 = 0.
-1, -2/3, 1
Let b(x) = -x**3 + 4*x**2 + 3*x - 10. Let o be b(4). Find s, given that -16/5*s**o + 4/5 + 2/5*s + 2*s**3 = 0.
-2/5, 1
Let z be 8 + (-2)/(-4)*-10. Find o such that 2/15*o + 2/15 - 2/15*o**z - 2/15*o**2 = 0.
-1, 1
Let y(j) be the first derivative of -2/5*j**5 + j**4 - 2*j**2 + 1 + 0*j**3 + 2*j. Determine u, given that y(u) = 0.
-1, 1
Let s be (-4)/6 + (-343)/(-504). Let u(t) be the third derivative of 0*t + 0*t**3 + s*t**4 - 1/180*t**5 + 0 - t**2. Determine i so that u(i) = 0.
0, 1
Let h(j) be the third derivative of j**9/151200 - j**8/25200 + j**7/12600 + j**5/20 - 3*j**2. Let q(l) be the third derivative of h(l). Factor q(y).
2*y*(y - 1)**2/5
Factor 16*c**2 - 5*c + 3*c - 4*c**2 + 16*c**3 - 2*c.
4*c*(c + 1)*(4*c - 1)
Let m(r) be the third derivative of 0*r**4 + 0*r + 0 - 5*r**2 + 0*r**3 - 1/210*r**7 + 0*r**6 + 1/60*r**5. Factor m(y).
-y**2*(y - 1)*(y + 1)
Solve -5*g + 2*g**2 + 329 - g**2 - 325 = 0.
1, 4
Let h(c) be the third derivative of -1/20*c**5 - c**2 - 1/70*c**7 + 0*c - 1/20*c**6 + 0*c**4 + 0 + 0*c**3. Suppose h(t) = 0. Calculate t.
-1, 0
Let i(g) = -g**3 + 17*g**2 - 14*g - 29. Let y be i(16). Factor 0*q + 1/4*q**2 + 3/4*q**4 - 3/4*q**y - 1/4*q**5 + 0.
-q**2*(q - 1)**3/4
Let i(w) = w**2 - 15*w + 2. Let a be i(15). Let h(n) be the first derivative of -2*n**a - 2*n - 2 - 2/3*n**3. Suppose h(k) = 0. What is k?
-1
Let i(l) = -l**2 + 21*l - 20. Let s be i(20). Factor 0*j**4 - 1/5*j + s - 1/5*j**5 + 0*j**2 + 2/5*j**3.
-j*(j - 1)**2*(j + 1)**2/5
Let f(l) = l**4 + 6*l**3 + 21*l**2 - 10*l - 6. Let o(x) = 5*x**4 + 35*x**3 + 125*x**2 - 60*x - 35. Let b(s) = -35*f(s) + 6*o(s). Factor b(d).
-5*d*(d - 1)**2*(d + 2)
Let l(a) be the second derivative of -1/9*a**4 - 1/3*a**2 - 1/60*a**5 - 5/18*a**3 + 0 + 3*a. Factor l(y).
-(y + 1)**2*(y + 2)/3
Let j be (1*(3 + -3))/(-4). Let q(g) be the third derivative of 1/12*g**4 + 1/3*g**3 + j*g + 0 - 1/30*g**5 - 1/60*g**6 - 3*g**2. Determine t so that q(t) = 0.
-1, 1
Let c(r) = 2*r**2 - 8*r + 6. Let d = -10 - -8. Let l(f) = -2*f + 3. Let q be l(5). Let z(w) = -6*w**2 + 24*w - 17. Let k(h) = d*z(h) + q*c(h). Factor k(p).
-2*(p - 2)**2
Suppose 4 = -5*d + 19. Factor -2/5*c**4 + 0*c**d + 0 - 1/5*c + 2/5*c**2 + 1/5*c**5.
c*(c - 1)**3*(c + 1)/5
Let z(a) = -a**2 + 3*a - 1. Let h be z(1). Factor -h - 2*v + 0*v + v**4 + 2*v**3 + 0*v.
(v - 1)*(v + 1)**3
Let h be (3 - 168/60)*(-40)/(-6). Find u such that 8/3*u - 16/9 - h*u**2 + 2/9*u**3 = 0.
2
Let z be (-18)/(-15)*(-50)/(-15). Let m be z*(20/8 + -2). Factor 6/5*h**m - 4/5 + 2/5*h.
2*(h + 1)*(3*h - 2)/5
Factor 6 + 1 + 4*u + 2 - 3*u**2 + 2*u.
-3*(u - 3)*(u + 1)
Let s(i) = i**3 - 2*i + 1. Let k be s(2). Suppose 0*y - k*y = -20. Find w, given that -2/3*w**3 - 2/9*w - 2/3*w**2 + 0 - 2/9*w**y = 0.
-1, 0
Let z(f) = -f**4 + 4*f**3 - 6*f**2 - 8*f + 5. Let j(l) = -l**4 + 8*l**3 - 12*l**2 - 16*l + 11. Let u(v) = 3*j(v) - 5*z(v). Find b such that u(b) = 0.
-2, 1
Let y = 6 