-q**8/1176 + q**6/210 - q**4/84 + 5*q**2/2 + 40*q. Let a(r) be the first derivative of h(r). Suppose a(m) = 0. What is m?
-1, 0, 1
Let c be (20/72)/(6*20/72). Let b(m) be the first derivative of 1/4*m**2 + 0*m + 6 - c*m**3. Suppose b(l) = 0. What is l?
0, 1
Let f(p) be the second derivative of 0 + 27/2*p**2 + 16*p + 25/4*p**4 - 15*p**3. Determine b, given that f(b) = 0.
3/5
Let h(j) be the third derivative of -j**7/315 + 17*j**6/90 - 433*j**5/90 + 68*j**4 - 576*j**3 - 133*j**2 + 1. Factor h(w).
-2*(w - 9)**2*(w - 8)**2/3
Suppose -7*b + 24*b = -51. Let v be (b + (-20)/(-7))*-4. Factor 0 + 4/7*g - v*g**3 + 0*g**2.
-4*g*(g - 1)*(g + 1)/7
Let l(b) be the second derivative of -b**7/21 - 5*b**6/6 - 3*b**5/5 + 12*b - 2. What is s in l(s) = 0?
-12, -1/2, 0
Let z be (-10 + 4 - -3) + (-11)/1. Let b be ((-6)/(-8) - 2)*z/35. Factor -15/2*g**2 + 0 - 7/2*g**3 - 9/2*g - b*g**4.
-g*(g + 1)*(g + 3)**2/2
Suppose -m + 0*n - 21 = -5*n, n = 3. Let o(u) = -u**3 - u. Let i(g) = -3*g**3 + 2*g**2 - 9*g - 2. Let t(c) = m*o(c) + i(c). Let t(d) = 0. What is d?
-1, -2/3, 1
Let k(f) be the second derivative of 1/5*f**5 + 0*f**3 + 0 - f**4 + 8*f**2 - 28*f. Determine t so that k(t) = 0.
-1, 2
Let r(x) = 185*x**2 + 145*x - 100. Let o(u) = 23*u**2 + 18*u - 12. Let g(i) = 25*o(i) - 3*r(i). Determine b, given that g(b) = 0.
-3/4, 0
Let s(o) be the first derivative of o**6/24 + 3*o**5/20 - 3*o**4/16 - 7*o**3/12 + 3*o**2/4 - 45. Determine d, given that s(d) = 0.
-3, -2, 0, 1
Let y be (4/12*-5)/((-9)/567). Let o be (-20)/y*-6*5. Factor -4/7*q**2 + o*q - 100/7.
-4*(q - 5)**2/7
Let k(q) = -34*q**2 + 4272*q - 453702. Let d(v) = -14*v**2 + 1709*v - 181481. Let p(w) = 12*d(w) - 5*k(w). Factor p(t).
2*(t - 213)**2
Let g be ((-20)/(-18)*33)/((-4)/(-6)). Let a be ((-9)/(-5))/(44/g). Determine x, given that a*x - 1/2*x**2 - 1 = 0.
1/2, 4
Let t(l) be the third derivative of l**7/70 + l**6/20 - 7*l**5/20 + l**4/2 - 25*l**2. Factor t(b).
3*b*(b - 1)**2*(b + 4)
Let l(b) = -10*b**2 - 55*b - 28. Let h(a) = -80*a**2 - 440*a - 225. Let n be ((-8)/12)/((-4)/18). Let f(x) = n*h(x) - 25*l(x). Factor f(o).
5*(o + 5)*(2*o + 1)
Let h(q) be the second derivative of q**5/10 - q**4/12 + q**3/2 - q**2 - 50*q. Let n be h(1). Factor 1/2*x**3 - 1/2*x + 0 + 0*x**n.
x*(x - 1)*(x + 1)/2
Let m = 3208 - 3203. Determine u, given that 10*u**m + 8*u**4 - 142/5*u**3 + 56/5*u + 16/5 - 4*u**2 = 0.
-2, -2/5, 1
Determine s, given that 0 + 0*s + 3/4*s**4 + 3*s**2 - 3*s**3 = 0.
0, 2
Let z(j) be the second derivative of 3/8*j**2 + 5/24*j**3 - 1/80*j**5 + 11*j + 0 + 1/48*j**4. Solve z(q) = 0 for q.
-1, 3
Solve -21/2*y - 15 - 3/2*y**2 = 0 for y.
-5, -2
Let o be (12/(12/(-3)))/(30/(-28)). Let q(w) be the first derivative of o*w**5 + 2 - 28*w**2 + 16*w - 4*w**3 + 19/2*w**4. Solve q(t) = 0 for t.
-2, 2/7, 1
Let p(q) be the second derivative of q**4/12 + 11*q**3/6 - 12*q**2 + 5*q. Let h be p(-13). Factor -4/3*r + 2/3*r**3 + 0 + 2/3*r**h.
2*r*(r - 1)*(r + 2)/3
Determine k, given that 46*k**2 + 23*k - 5*k**2 - 3 - 104*k + 43*k**2 = 0.
-1/28, 1
Let o = 33/757 - -723395/6813. Let j = o + -106. Factor 2/3*f + 4/9*f**2 + j.
2*(f + 1)*(2*f + 1)/9
Suppose 6*a = -3*a. Suppose 4*i = -2*x + 14, -2*i - x - 4*x + 11 = a. Suppose -p + i - 2*p**4 + 6*p**3 - p**4 - 5*p = 0. Calculate p.
-1, 1
Let f(g) be the first derivative of -4/15*g**2 + 0*g - 20 - 5/6*g**4 - 8/9*g**3. Factor f(i).
-2*i*(5*i + 2)**2/15
Factor 56/5 + 13/5*h**3 + 54/5*h**2 + 92/5*h + 1/5*h**4.
(h + 2)**3*(h + 7)/5
Let t(g) be the third derivative of g**7/1575 - g**6/900 - g**5/150 + g**4/180 + 2*g**3/45 - 385*g**2. What is y in t(y) = 0?
-1, 1, 2
Suppose 7*i + 25 = 12*i. Let n(a) be the third derivative of 3/40*a**6 + 0 + 1/112*a**8 + 0*a**4 + 1/20*a**i + 0*a + 2*a**2 + 3/70*a**7 + 0*a**3. Factor n(d).
3*d**2*(d + 1)**3
Solve 0*q**4 + 2*q + 1/2*q**5 + 0 - 5/2*q**3 + 0*q**2 = 0 for q.
-2, -1, 0, 1, 2
Let w(t) be the first derivative of 0*t**3 - 1/10*t**5 + 0*t**2 + 1/24*t**6 + 0*t - 29 + 1/16*t**4. Determine y so that w(y) = 0.
0, 1
Determine v so that -3/2 + 3*v**3 + 5/2*v**4 - v**2 + 1/2*v**5 - 7/2*v = 0.
-3, -1, 1
Let m(f) = -f**4 - f. Let q(h) be the second derivative of -h**6/5 - 2*h**5/5 - h**3/3 - 2*h**2 - 14*h. Let o(i) = 10*m(i) - q(i). Let o(r) = 0. Calculate r.
-1, 1
Let m(x) be the second derivative of -x**7/3780 + x**5/135 + 7*x**3/3 + 16*x. Let z(b) be the second derivative of m(b). Suppose z(f) = 0. Calculate f.
-2, 0, 2
Let n(s) be the first derivative of -2*s**5/85 - 5*s**4/17 - 26*s**3/51 + 60*s**2/17 - 72*s/17 + 199. What is r in n(r) = 0?
-6, 1
Let p(g) be the third derivative of -g**7/490 - 9*g**6/280 + 3*g**5/20 - 11*g**4/56 - g**2 - 9. Find u such that p(u) = 0.
-11, 0, 1
Factor -6 - 17/2*b - 1/2*b**4 + 5/2*b**3 + 1/2*b**2.
-(b - 4)*(b - 3)*(b + 1)**2/2
Let o(r) be the first derivative of r**6/30 - 2*r**5/25 - 3*r**4/20 + 4*r**3/15 + 2*r**2/5 - 77. Factor o(q).
q*(q - 2)**2*(q + 1)**2/5
Let r(i) be the second derivative of 841*i**4/48 - 29*i**3/2 + 9*i**2/2 - 12*i + 5. Factor r(d).
(29*d - 6)**2/4
Let c = 7009/2046 + -103/93. Let a = c + -20/11. Find v, given that -1/2*v**2 + 0 + a*v = 0.
0, 1
Let h(n) = -9*n**2 + 2*n - 3. Let t(q) = -5*q**2 + 2*q - 1. Let y(c) = 4*h(c) - 7*t(c). Factor y(w).
-(w + 1)*(w + 5)
Let x = -19737 + 215717/11. Let c = -126 - x. Let 10/11*k**4 - 2/11*k**5 - 18/11*k**3 - c*k + 0 + 14/11*k**2 = 0. What is k?
0, 1, 2
Factor l**2 + 0*l**2 - 70*l - 3 - 65*l + 5 + 138*l.
(l + 1)*(l + 2)
Let z(v) be the third derivative of -5*v**8/112 + 17*v**7/42 - 7*v**6/8 - 7*v**5/4 + 20*v**4/3 + 10*v**3 + 190*v**2. Suppose z(m) = 0. What is m?
-1, -1/3, 2, 3
Factor 8*m**3 + 256*m**2 + 294*m - 11*m**3 + 162*m + 4*m**4 + 252 + 23*m**3 + 36*m**3.
4*(m + 1)*(m + 3)**2*(m + 7)
Suppose -10*l + 39 = 3*l. Factor -330 + 330 + x**3 + 18*x - 15*x**2 + 2*x**l.
3*x*(x - 3)*(x - 2)
Suppose -187 = -y - 28. Let d = y + -157. Find m such that 4/7*m**3 + 4/7*m**d + 0*m + 0 = 0.
-1, 0
Let v(r) be the third derivative of r**7/1050 + 23*r**6/600 + r**5/5 - r**4/30 - 8*r**3/3 + 3*r**2 - r. Determine z so that v(z) = 0.
-20, -2, 1
Suppose 5*t = 9 + 1. What is a in -a**t + a**2 + a - 5*a + 4*a**2 - 8 = 0?
-1, 2
Let f(p) be the first derivative of -p**5/25 - 2*p**4/5 - 7*p**3/15 - 128. Factor f(v).
-v**2*(v + 1)*(v + 7)/5
Let q = 58/7 - 211/28. Factor 9/4*v**2 - 3/2*v**3 - q*v**4 + 0*v + 0.
-3*v**2*(v - 1)*(v + 3)/4
Let u = 34 - 26. Find y such that 23*y - 9*y - 28*y**3 - u*y**2 + 14*y + 6 + 2 = 0.
-1, -2/7, 1
Let x(u) be the second derivative of -1/24*u**4 + 1/2*u**2 + 0 + 1/12*u**3 - 10*u. Factor x(l).
-(l - 2)*(l + 1)/2
Let z be 2 - (12/(-33) + (-50)/(-440)). Factor -27/4 - 27/4*t - 1/4*t**3 - z*t**2.
-(t + 3)**3/4
Suppose 0 = 4*d - 54 + 42. Let o(x) be the second derivative of 0 - 7*x + 2*x**d - 1/4*x**4 - 6*x**2. Determine u, given that o(u) = 0.
2
Find i, given that -3/5*i**2 + 0*i + 1/5*i**3 + 4/5 = 0.
-1, 2
Determine b so that -153*b - 247*b**2 + 120*b**2 + 124*b**2 = 0.
-51, 0
Let d(p) = -p**2 - 45*p - 10. Let b(j) = j**2 + 23*j + 6. Let n(f) = 11*b(f) + 6*d(f). Factor n(y).
(y - 3)*(5*y - 2)
Factor -18*w**3 - 2*w**3 - 53*w**2 - 2*w**5 - 83*w**2 - 80*w - 58*w**3 - 6*w**3 - 22*w**4.
-2*w*(w + 2)**3*(w + 5)
Suppose 0 = 7*i - 12*i - q + 5, 0 = -2*i - 4*q + 20. Factor i*x**3 + 4/5*x**4 + 0*x + 4/5*x**5 + 0 + 0*x**2.
4*x**4*(x + 1)/5
Let v(m) = -2*m**4 + 43*m**3 - 133*m**2 + 69*m + 25. Let k(i) = i**4 - 2*i**2 + 2*i. Let p(l) = -2*k(l) + v(l). Factor p(w).
-(w - 5)**2*(w - 1)*(4*w + 1)
Factor 0 - 10*k + 2/5*k**4 + 2/5*k**3 - 10*k**2.
2*k*(k - 5)*(k + 1)*(k + 5)/5
Factor -1/6*x**5 + 4/3*x**4 + 3*x**2 - 7/2*x**3 + 0 + 0*x.
-x**2*(x - 3)**2*(x - 2)/6
Let v(l) be the third derivative of 7/24*l**4 - 9 + 5/72*l**6 + 1/9*l**3 + 2*l**2 + 0*l + 1/3*l**5. Factor v(r).
(r + 2)*(5*r + 1)**2/3
Let s be -7 + 12 - (-2 + 5). Suppose -7*a + s*a = w + 2, 4 = -4*a. Let -5*d**2 - 2*d**3 + w*d - 5*d**3 - d**4 - 5*d + 3*d**3 = 0. What is d?
-2, -1, 0
Let r be (-2)/11 - 1/(22/(-48)). Let w be (-5 + 4 - -2)*r. Factor 0 + 2/7*q + 2/7*q**w.
2*q*(q + 1)/7
Let y(s) be the first derivative of -s**6/6 + 3*s**5/5 + s**4/2 - 4*s**3 + 4*s**2 + 33. Factor y(r).
-r*(r - 2)**2*(r - 1)*(r + 2)
Suppose -f = -4*j + 14, 4*j + 8 = 8*j + 2*f. Let y(k) = k**2 - k - 1. Let l(d) = -5*d**2 - 9*d - 1. Let u(q) = j*