) = 3*q**4 + 9*q**3 + 9*q**2 + 10*q + 14. Let y(h) = 14*u(h) + 4*z(h). Determine p so that y(p) = 0.
-1, 0
Suppose 31*c - 28*c - 12 = 0. Let r(a) be the first derivative of 3 - 1/15*a**5 + 0*a**3 - 1/12*a**c + 0*a**2 + 0*a. What is j in r(j) = 0?
-1, 0
Factor -21*c**3 + 864 - 3456*c + 11*c**4 + 3*c**4 + 1584*c**2 - 235*c**3.
2*(c - 6)**3*(7*c - 2)
Let f = 375/7622 - -1/206. Let u = 96/407 - f. Find t, given that 0 - u*t**4 + 2/11*t**3 + 2/11*t**2 - 2/11*t = 0.
-1, 0, 1
Let n(w) = w**3 + 5*w**2 + 3*w. Let l be n(-2). Suppose -5*p - 18 = g, -5*g + 93*p = 90*p - 22. Solve -8*m**3 + 10/3*m**4 - 4/3*m + l*m**g + 0 = 0.
0, 2/5, 1
Let f(b) = b**2 - b + 5. Let a be f(0). Suppose a*o = o + 24. Factor -o*n**4 + 2*n**4 - 2*n**3 + 0*n**3 - 2*n**5.
-2*n**3*(n + 1)**2
What is a in -9 + 9 + 2*a - 2*a**2 = 0?
0, 1
Suppose -b + 2 = -4*d + b, -2*b + 18 = 4*d. Factor d*f + f**2 + 3*f**3 - f**3 - 5*f**2.
2*f*(f - 1)**2
Let s(b) be the third derivative of 0*b**5 + 0 + 0*b**7 - 1/1512*b**8 + 1/270*b**6 + 0*b + 0*b**3 + b**2 - 1/108*b**4. Determine x so that s(x) = 0.
-1, 0, 1
Let h(j) = 3 + j + 5 + 1 + 2. Let l be h(-9). Determine u, given that 4/3 + 1/3*u**l - 4/3*u = 0.
2
Let i(l) be the third derivative of l**7/630 + 7*l**6/360 + l**5/10 + 5*l**4/18 + 4*l**3/9 + 4*l**2. What is x in i(x) = 0?
-2, -1
Let n(c) = -c**2 + 4*c - 1. Let p be n(3). Let m(o) be the third derivative of 0*o + 1/15*o**5 + p*o**2 + 0 - 1/3*o**3 - 1/12*o**4. Factor m(f).
2*(f - 1)*(2*f + 1)
Let x(o) be the first derivative of 4*o**5/5 + 5*o**4/2 - 8*o**3 + o**2 + 8*o - 4. Suppose x(w) = 0. Calculate w.
-4, -1/2, 1
Let o(u) be the second derivative of u**4/20 + u**3/5 + 3*u**2/10 + 6*u. Factor o(a).
3*(a + 1)**2/5
Let a(n) be the second derivative of n**4/90 + 2*n**3/45 + n**2/15 - 11*n. Find p, given that a(p) = 0.
-1
Let v = 3/499 + 1981/2495. Solve v*q + 0 + 2/5*q**2 = 0.
-2, 0
Let m(j) = 8*j**3 + 5*j**2 - 8*j - 2. Let x(r) = 15*r**3 + 10*r**2 - 15*r - 5. Let l(n) = -5*m(n) + 3*x(n). Factor l(v).
5*(v - 1)*(v + 1)**2
Let g(x) be the first derivative of 3*x**7/14 - 4*x**6/5 + 21*x**5/20 - x**4/2 + x + 2. Let a(d) be the first derivative of g(d). Suppose a(h) = 0. What is h?
0, 2/3, 1
Factor 5 + 4*g - 2 - 5 + 10 - 4*g**2.
-4*(g - 2)*(g + 1)
Let o be (3/(-4))/((-1)/4). Suppose -4*d + o*v + 31 = 0, 5*d - 2*v - 26 = d. Factor 2*y**3 + 0*y**3 - d - y + 2*y**2 + 2 - y.
2*(y - 1)*(y + 1)**2
Suppose 10 = 3*l + 4. Solve 4*v**2 + 27 + v**3 + 4*v**l + 27*v + v**2 = 0.
-3
Let i(u) = 45*u - 55. Let m(q) = -q**2 - 44*q + 53. Let w(t) = 4*i(t) + 5*m(t). Find a such that w(a) = 0.
-9, 1
Let a be (-2)/6*(-3 + -6). Solve 0 - 3*k**2 + 6 - 3*k + 3*k**3 - a = 0.
-1, 1
Suppose 0*b = 3*b - 5*t - 7, 0 = 4*t - 4. Determine o, given that 4/5*o**3 + 0*o**2 + 2/5*o**b - 4/5*o - 2/5 = 0.
-1, 1
Let s = 7/6 - 5/6. Factor -x - 1/3 - s*x**3 - x**2.
-(x + 1)**3/3
Factor 3/8 + 0*z**2 - 3/4*z - 3/8*z**4 + 3/4*z**3.
-3*(z - 1)**3*(z + 1)/8
Let n(y) = 2*y**4 - 2*y**3 + y**2 - 4*y. Let m = 4 - 8. Let w(g) = -3*g**4 + 3*g**3 - g**2 + 5*g. Let f(a) = m*n(a) - 3*w(a). Let f(t) = 0. What is t?
-1, 0, 1
Let d(t) = -4*t + 1. Let z be d(-1). Suppose b + z = 5*y, 5*b - 12 - 11 = y. Determine k, given that 0 + 2/7*k + 2/7*k**y = 0.
-1, 0
Suppose -4*u = l - 5, 2*u - l + 4 + 1 = 0. Factor -w**2 + 1/2*w**3 + u + 1/2*w.
w*(w - 1)**2/2
Let g be (0/(-1))/(15/5). Let c be (g - -2) + 2/(-4). Factor -c*a**2 - 1/2*a + 0 - 3/2*a**3 - 1/2*a**4.
-a*(a + 1)**3/2
Let l(a) be the third derivative of a**7/2520 - a**5/120 - a**4/8 - 2*a**2. Let i(q) be the second derivative of l(q). Factor i(m).
(m - 1)*(m + 1)
Let j(c) = -c**4 - c**3 - c**2 + c + 1. Let s(d) = 11*d**4 - 29*d**3 + 51*d**2 + 129*d - 276. Let h(v) = 6*j(v) + s(v). Factor h(a).
5*(a - 3)**3*(a + 2)
Let g be 1/(-3*(-1 - (-2)/3)). Let h(s) be the first derivative of g - 1/2*s**2 - 1/2*s - 1/6*s**3. What is l in h(l) = 0?
-1
Let i = 59 - 36. Factor 2*o**5 - 2*o**2 - 34*o**5 - 32*o**4 + 5*o**3 - 16*o**4 - i*o**3.
-2*o**2*(o + 1)*(4*o + 1)**2
Let u = 120 - 117. Suppose -y**2 - 1/2*y - 1/2*y**u + 0 = 0. What is y?
-1, 0
Let o(c) be the third derivative of 2*c**7/105 + c**6/6 + 3*c**5/5 + 7*c**4/6 + 4*c**3/3 - 28*c**2. Solve o(l) = 0.
-2, -1
Let n(l) be the first derivative of -2/5*l**3 + 0*l**5 + 9/20*l**4 - 1/10*l**6 + 0*l**2 + 1 + 0*l. Solve n(x) = 0.
-2, 0, 1
Let j = 1897/2540 + 2/635. Factor -3/4*v**2 + 3/2*v - j.
-3*(v - 1)**2/4
Let p(u) = 3*u**5 - 5*u**4 - 2*u**2 - 2*u - 2. Let s(x) = 25*x**5 - 41*x**4 - x**3 - 17*x**2 - 17*x - 17. Let d(w) = -51*p(w) + 6*s(w). Factor d(f).
-3*f**3*(f - 2)*(f - 1)
Let h(f) be the second derivative of 9*f**5/80 + f**4/4 - f**3/2 - 8*f. Factor h(r).
3*r*(r + 2)*(3*r - 2)/4
Let u(r) = 4*r**3 - r**2 + 1. Let a = 4 + -3. Let k be u(a). Factor k + v**2 + 3*v + 3*v - 2*v.
(v + 2)**2
What is f in 3/4*f**2 - 9*f + 27 = 0?
6
Let m(z) = 3*z - 3. Let t be m(-3). Let y be -1 - -1 - 3/t. Factor -y*h + 0 - 1/2*h**2 - 1/4*h**3.
-h*(h + 1)**2/4
Let u(v) be the first derivative of -6*v**5/5 - v**4/2 + 2*v**3 + v**2 - 3. Find o, given that u(o) = 0.
-1, -1/3, 0, 1
Factor 4*t**2 + 14 + 16*t + 13 - 15.
4*(t + 1)*(t + 3)
Let w = 1 - -1. Suppose w*u + 0*u - 1 = -z, 5*z - 4*u - 19 = 0. Factor 3*f**2 + 4*f**2 - 8*f + 8*f**z - 8 + 2*f**4 - f**2.
2*(f - 1)*(f + 1)*(f + 2)**2
Let c be ((-76)/152)/(1/3 + -1). Factor 9/4*i**2 + 9/4*i + 3/4 + c*i**3.
3*(i + 1)**3/4
Let w(i) = -5*i**2 - 10*i + 6. Let z(n) = -1. Let k(u) = w(u) + 6*z(u). What is b in k(b) = 0?
-2, 0
Let a(h) be the second derivative of -3*h**7/14 + h**6/10 + 3*h**5/10 - 6*h. Suppose a(c) = 0. Calculate c.
-2/3, 0, 1
Let d(n) = -4*n**3 + 14*n**2 + 2. Suppose 2*a = -a + 3. Suppose -14 = 3*g + a. Let l(x) = 3*x**3 - 14*x**2 - x - 3. Let j(m) = g*d(m) - 4*l(m). Factor j(i).
2*(i - 1)**2*(4*i + 1)
Let s be (2 - (-2 + 3))*8. Determine m, given that -s*m**3 - 3*m**5 + m**5 + 10*m**3 = 0.
-1, 0, 1
Find l such that 0 + 1/5*l**2 + 6/5*l = 0.
-6, 0
Let c(f) be the first derivative of f**4 - 4*f**3 - 18*f**2 - 20*f - 2. Factor c(t).
4*(t - 5)*(t + 1)**2
Let x be 0 + -1 - 1/(-1) - 0. Factor 2/5 - 2/5*z**2 + x*z.
-2*(z - 1)*(z + 1)/5
Let v be 9/5*(-24)/(-108). Find h, given that -8/5 + 8/5*h - v*h**2 = 0.
2
Let o(n) be the third derivative of 0 + 0*n**3 + 1/24*n**4 - 1/120*n**6 - 7/120*n**5 - n**2 + 0*n + 1/60*n**7. Factor o(q).
q*(q - 1)*(q + 1)*(7*q - 2)/2
Let n(k) be the third derivative of -k**8/336 + k**7/70 - k**6/120 - k**5/20 + k**4/12 + 11*k**2. Let n(r) = 0. Calculate r.
-1, 0, 1, 2
Let b be 1/(-8)*-6*(-24)/(-3). Let f(q) be the second derivative of 1/105*q**b + q - 1/21*q**4 + 1/70*q**5 + 0 + 0*q**2 + 0*q**3. Suppose f(i) = 0. Calculate i.
-2, 0, 1
Determine j, given that 4/5*j**2 - 4/5*j**4 - 8/5*j + 8/5*j**3 + 0 = 0.
-1, 0, 1, 2
Suppose -u - 2 = -2*u. Factor 10*h**2 - 6*h**3 - 4*h - 4*h**2 + 4*h**u.
-2*h*(h - 1)*(3*h - 2)
Factor -34*n**2 + 16*n**3 - n + 34*n**2.
n*(4*n - 1)*(4*n + 1)
Suppose -4*p + 9*p = 0. Let l = -5 - -9. Factor -m**3 - m**4 + 2*m**2 + p*m**l - m**2 + m**5.
m**2*(m - 1)**2*(m + 1)
Let s be (-2)/(-17) - 94/(-68). Let z = 0 + s. Suppose 1/6 + z*t**2 - t = 0. Calculate t.
1/3
Let z(i) be the second derivative of 4/35*i**5 - 4/21*i**4 + 0*i**3 - 2/105*i**6 + 0 + i + 0*i**2. Find p, given that z(p) = 0.
0, 2
Let v(g) be the third derivative of 0*g**3 + 0 + 1/660*g**6 + 5*g**2 + 0*g + 2/165*g**5 + 1/33*g**4. Factor v(r).
2*r*(r + 2)**2/11
Let w(k) be the first derivative of k**4/36 - k**3/9 - 3*k - 1. Let h(x) be the first derivative of w(x). Factor h(z).
z*(z - 2)/3
Let q(r) be the second derivative of r**6/105 + r**5/35 - 2*r**3/21 - r**2/7 - 2*r + 15. Determine m so that q(m) = 0.
-1, 1
Let y = -94 + 99. Let u(q) be the second derivative of 1/12*q**4 + q - 1/60*q**6 - 1/4*q**2 + 0 - 1/20*q**y + 1/84*q**7 + 1/12*q**3. Factor u(k).
(k - 1)**3*(k + 1)**2/2
Let b = -52 + 52. Let l(w) be the second derivative of 1/21*w**3 + 0*w**4 + b - 1/70*w**5 + 0*w**2 + w. Suppose l(s) = 0. Calculate s.
-1, 0, 1
Find p, given that 20*p + 15*p**2 + 20/3 = 0.
-2/3
Let c = 4 - 14. Let j = c + 14. Suppose 0*k**2 - 10/3*k**j + 0 - 4/3*k**3 + 0*k = 0. Calculate k.
-2/5, 0
Let p(n) be the second derivative of -n**5/5 + 2*n**3/3 + n. Solve p(v) = 0.
-1, 0, 1
Let h be 2/(-9) + (-4)/(-18). Let t = 1 - h. Find f, given that 4 - 4 + 