) = 0?
-1, 2
Let v(r) be the third derivative of -r**5/30 + r**4/24 - r**3/6 - 12*r**2. Let c(y) = -14*y**2 + 30*y + 20. Let g(w) = c(w) - 6*v(w). Factor g(b).
-2*(b - 13)*(b + 1)
Let y(s) be the third derivative of 1/14*s**4 + 0 - 1/140*s**5 + 0*s - 2/7*s**3 - 22*s**2. Solve y(j) = 0 for j.
2
Let b(w) be the second derivative of w**4/18 - 2*w**3/3 + 3*w**2 - 144*w. Factor b(g).
2*(g - 3)**2/3
Let a = -54 + 56. Let 10*m**2 + 56*m + 7 + 15*m**2 + 5 - 25*m**3 + 30*m**a = 0. What is m?
-2/5, 3
Let u(x) = -x**2 - 1. Let n(i) = 7*i**2 - 42*i + 151. Suppose 10*o - 9*o - 4 = 0. Let y(z) = o*u(z) + n(z). Factor y(a).
3*(a - 7)**2
Let j(u) be the third derivative of u**6/24 - 7*u**5/12 - 25*u**4/24 + 125*u**3/2 + 189*u**2. Factor j(a).
5*(a - 5)**2*(a + 3)
Factor -16/5*d**2 - 3*d**3 + 0 + 0*d + 1/5*d**4.
d**2*(d - 16)*(d + 1)/5
Let s(r) = -12*r**4 - 102*r**3 - 408*r**2 - 414*r + 18. Let o(p) = -p**4 + p**3 - 2*p + 2. Let d(h) = 9*o(h) - s(h). Factor d(f).
3*f*(f + 2)**2*(f + 33)
Let u(d) be the first derivative of -1/4*d**4 + 1/2*d**2 + 1/2*d - 2/3*d**3 + 3/10*d**5 + 19. Solve u(i) = 0.
-1, -1/3, 1
Let k(l) be the third derivative of l**7/735 + 8*l**6/35 + 576*l**5/35 + 4608*l**4/7 + 110592*l**3/7 - 36*l**2. Factor k(s).
2*(s + 24)**4/7
Let k(q) = -20*q - 20*q - 8*q**2 + 28*q - 4*q. Let h(i) = 4*i**2 + 8*i. Let f(y) = 5*h(y) + 2*k(y). Let f(p) = 0. Calculate p.
-2, 0
Suppose 0 = -2*u + 6*u - 5*w - 145, 0 = -3*u - w + 104. Factor -u*h**2 + 34*h - 74*h + 35*h.
-5*h*(7*h + 1)
Let x(q) = q - 4. Let l be x(4). Suppose l = -t + 4*t - 6. Factor -t*p**3 + 7*p**3 - 3*p**5 - 3*p**2 + 0*p**3 - 2*p**3 + 3*p**4.
-3*p**2*(p - 1)**2*(p + 1)
Factor -512 - 62*z**2 + 177*z - 157*z**2 + 56*z**3 + 463*z - 69*z**2 - 4*z**4.
-4*(z - 4)**3*(z - 2)
Let t = 201041/280 + -718. Let h(d) be the third derivative of 0*d - 3/56*d**4 + 8*d**2 + t*d**6 + 0*d**3 + 0 + 1/70*d**5. Factor h(m).
3*m*(m - 1)*(m + 3)/7
Let w(h) be the second derivative of 0 + 1/35*h**5 + 18*h + 0*h**2 + 0*h**3 + 1/42*h**4 + 1/105*h**6. Let w(i) = 0. What is i?
-1, 0
Let w(l) = l**3 - 12*l**2 - 12*l + 149. Let u be w(12). Factor 0 - 5/3*o**2 + 0*o + u*o**3 + 5/3*o**5 - 5*o**4.
5*o**2*(o - 1)**3/3
Suppose 2/13*z**3 - 8/13*z**2 - 14/13*z + 20/13 = 0. What is z?
-2, 1, 5
Let v(c) be the second derivative of -8*c + 0*c**3 + 1/60*c**6 + 0 + 3/8*c**4 - 3/20*c**5 + 0*c**2. Let v(o) = 0. Calculate o.
0, 3
Let y(k) be the first derivative of -18*k**5/55 + 3*k**4/11 + 46*k**3/33 - 8*k**2/11 - 32*k/11 - 620. Factor y(j).
-2*(j + 1)**2*(3*j - 4)**2/11
Let a be -31 - -31 - (-6)/2. Let q(r) be the third derivative of 0*r + 0*r**a + 0*r**5 + 0 + 6*r**2 + 0*r**4 + 1/480*r**6. Solve q(n) = 0.
0
Suppose -4*l = -2*b + 12, -4*b + 9*b + 4*l + 12 = 0. Factor 0 + 0*u - 2/11*u**2 + b*u**3 + 2/11*u**4.
2*u**2*(u - 1)*(u + 1)/11
Let r(q) = q**2 - q + 2. Let l be r(1). Find k, given that 4 - 4*k**4 - 3*k**4 + 8*k + 2*k**2 + 3*k**5 - 11*k**3 - 5*k**l + 6*k**4 = 0.
-1, -2/3, 1, 2
Let a = -901327/78 + 11556. Let s = -5/26 + a. Let -1/3*q**2 + 0 + s*q = 0. Calculate q.
0, 1
Suppose 9*v = 10*v + 6. Let r be 1/3*5/((-40)/v). Factor 1/4*l + 1/4*l**2 - 1/4 - r*l**3.
-(l - 1)**2*(l + 1)/4
Let r(u) be the first derivative of 0*u + 2*u**2 + 1/20*u**5 + 4 + 1/4*u**4 - 3/2*u**3. Let s(m) be the second derivative of r(m). Factor s(h).
3*(h - 1)*(h + 3)
Let t be 520/39*(-1 + 17/5). Solve -t*v - 3*v**3 - 42 + 18*v**2 + 5*v + 54 = 0 for v.
1, 4
Let u(f) be the first derivative of f**4/5 + 8*f**3/5 - 18*f**2/5 - 56*f/5 - 54. Factor u(s).
4*(s - 2)*(s + 1)*(s + 7)/5
Let w be (-3 - 55) + 3/1. Let f be 22/w + 0 + 1. Suppose -27/5 - f*j**2 + 18/5*j = 0. What is j?
3
What is f in -69/2*f - 3 - 63/2*f**2 = 0?
-1, -2/21
Let w(q) = -6*q**3 + 20*q**2 + 8*q - 17. Let k(i) = -i**3 + i - 1. Let z(v) = -k(v) - w(v). Factor z(s).
(s - 3)*(s + 1)*(7*s - 6)
Suppose 11*g - 20*g = -18. Let f(u) be the first derivative of -2/9*u**3 + 6 + 0*u - u**g. Factor f(q).
-2*q*(q + 3)/3
Let p(o) be the first derivative of -2/55*o**5 - 15 + 0*o + 2/11*o**2 + 2/11*o**4 - 10/33*o**3. Let p(b) = 0. Calculate b.
0, 1, 2
Let a(i) be the second derivative of 1/10*i**6 + 0*i**2 + 0 - 20*i + 1/84*i**7 + 1/2*i**4 + 13/40*i**5 + 1/3*i**3. Factor a(r).
r*(r + 1)**2*(r + 2)**2/2
Let a(w) = 6*w**4 - 12*w**3 - 21*w**2 + 3. Let c(z) = -17*z**4 + 37*z**3 + 62*z**2 - 8. Let p(d) = -8*a(d) - 3*c(d). Factor p(o).
3*o**2*(o - 6)*(o + 1)
Suppose -6*c + 12 + 6 = 0. Find f such that 4*f**4 - 2*f**4 - c*f**4 - f**3 - 380*f**5 + f**2 + 381*f**5 = 0.
-1, 0, 1
Let v(t) = 174*t - 517. Let w be v(3). Find p such that 0*p + 1/4*p**4 + 0 + 0*p**2 + 1/8*p**w + 0*p**3 = 0.
-2, 0
Let x be (1/(-4))/(21 + -13 + -9). Solve o**2 - 5/4*o + 1/2 - x*o**3 = 0.
1, 2
Let w = -192 + 196. Let f(x) be the first derivative of 2/5*x**5 + 2/3*x**3 + 0*x**2 + 0*x - 2 + x**w. Factor f(i).
2*i**2*(i + 1)**2
Let w(t) = -t**2 - 12*t - 32. Let z be w(-8). Find h such that -9*h**2 - 72*h + 13*h**2 + z + 324 = 0.
9
Suppose 1/3*u + 4/3*u**2 - 2/3 - 2/3*u**3 - 2/3*u**4 + 1/3*u**5 = 0. Calculate u.
-1, 1, 2
Suppose 3*s - 5*v - 5 = 12, 5*s + 4*v = 16. Factor -4*x**4 + 17*x**3 - 19*x**3 + s*x**2 + 2*x**4.
-2*x**2*(x - 1)*(x + 2)
Let q be (0 - (10 - 5))/(2/(-20)). Find c, given that -56*c**2 + 26*c + 110*c**4 + 12*c**3 - q*c**5 - 23*c - 19*c = 0.
-2/5, 0, 1, 2
Let t be (-30)/(-9)*492/8. Find a, given that -5*a**4 - 185*a**3 + 20*a**2 + a**5 + t*a**3 - 6*a**5 = 0.
-2, -1, 0, 2
Solve 3/2*p**5 + 6*p**2 - 6*p**4 - 3/2*p**3 + 0 + 0*p = 0 for p.
-1, 0, 1, 4
Let b(r) be the first derivative of 3/2*r**2 + 1/3*r**3 + 0*r + 7. Factor b(w).
w*(w + 3)
Suppose -16*v**2 - 132 + 3*v**3 - 1207*v - 110*v**2 + 946*v = 0. Calculate v.
-1, 44
Let j = -1055 - -1058. Factor -2/5*k**2 + 0 + 2/5*k**4 + 2/5*k**5 - 2/5*k**j + 0*k.
2*k**2*(k - 1)*(k + 1)**2/5
Let y = -35255 + 35258. Solve 27/4*u**y + 0*u + 3/2*u**2 + 0 = 0.
-2/9, 0
Let d(z) be the first derivative of -z**6/2 - 3*z**5/5 + 3*z**4 + 4*z**3 + 290. Suppose d(y) = 0. What is y?
-2, -1, 0, 2
Let o = -27391/36 - -761. Let u(m) be the second derivative of -1/15*m**5 - 1/18*m**3 - 5*m + 0*m**2 - o*m**4 + 0. Find n, given that u(n) = 0.
-1, -1/4, 0
Let w be 9/21*33/495. Let j(q) be the first derivative of -2/21*q**3 + 4 + 3/28*q**4 + 0*q + 0*q**2 - w*q**5. Factor j(h).
-h**2*(h - 2)*(h - 1)/7
Let o = -55 - -57. Factor -4*d**2 + 4*d + 6*d**o + 2*d + 12*d**2 + 8*d**3.
2*d*(d + 1)*(4*d + 3)
Suppose -26/5*g**2 - 2*g**3 - 8/5*g + 8/5 = 0. What is g?
-2, -1, 2/5
Factor 8/3*k**2 + 22*k + 70/3.
2*(k + 7)*(4*k + 5)/3
Let y(m) = -m**3 - 5*m**2 - 5*m - 1. Let v be y(-4). Let f(i) = i**2 + 6*i + 7. Let s be f(-5). Factor -s*k**v - 1 - 4*k**3 + 6*k**2 + 3*k + 3*k**3 - 5.
-3*(k - 2)*(k - 1)*(k + 1)
Let j(u) be the first derivative of -18 - 6*u**2 - 4/3*u**3 + 0*u. Factor j(w).
-4*w*(w + 3)
Suppose 0*h = h - 4*t - 2, -2*h = -5*t - 7. Find g such that g**2 - 7 + 1 + 4*g + 3 - h*g = 0.
-1, 3
Let p(g) be the first derivative of -2*g**3/15 - 136*g**2/5 - 9248*g/5 + 308. Solve p(r) = 0.
-68
Let f(p) be the third derivative of -4*p**7/945 + p**6/270 - p**5/720 + 11*p**4/24 + 12*p**2. Let i(h) be the second derivative of f(h). Factor i(v).
-(8*v - 1)**2/6
Let y(k) be the first derivative of k**4/2 - 4*k**3 + 5*k**2 - 135. Factor y(t).
2*t*(t - 5)*(t - 1)
Let n = -6307/2 + 3155. Let 0 + n*d**2 + 3/4*d**4 + 3/8*d + 15/8*d**3 = 0. What is d?
-1, -1/2, 0
Factor 1856/3*f + 1520*f**2 + 1750/3*f**4 + 256/3 + 4700/3*f**3.
2*(5*f + 4)**3*(7*f + 2)/3
Let w(g) be the second derivative of -2*g**7/105 - g**6/10 - g**5/15 + g**4/2 + 4*g**3/3 - 9*g**2 + 3*g. Let x(h) be the first derivative of w(h). Factor x(m).
-4*(m - 1)*(m + 1)**2*(m + 2)
Let x(m) be the first derivative of 2*m**3/51 - 2*m**2/17 - 6*m/17 + 131. Factor x(y).
2*(y - 3)*(y + 1)/17
Solve 371*m - 9*m**2 - 3*m**2 - 31*m**3 + 21*m + 116 - 77*m**3 + 12 = 0.
-16/9, -1/3, 2
Let a(c) be the first derivative of c**3 + 9*c**2/2 - 23. Factor a(i).
3*i*(i + 3)
Let j be 50/3*((-2)/16)/(170/(-272)). Suppose 4*x + j*x**4 - 14/3*x**3 + 2/3*x**5 + 0 - 10/3*x**2 = 0. What is x?
-6, -1, 0, 1
Let b(l) be the third derivative of l**8/448 + l**7/35 + 11*l**6/80 + 3*l**5/10 + 9*l**4/32 + 2*l**2 + 14. Suppose b(n) = 0. What is n?
-3, -1, 0
Suppose -k = 4*k + 110. Let c = 76 + k. Factor -6*j**3 + 27*j**2 