- 2)**2*(k + 1)
Let v be (-4)/(-14) + (-6)/21. Suppose -19*p + 24*p = 20. Factor v + 3/2*a**p - 1/2*a - 7/2*a**3 + 5/2*a**2.
a*(a - 1)**2*(3*a - 1)/2
Let x(l) be the third derivative of -l**7/630 - l**6/90 - l**5/60 + l**4/18 + 2*l**3/9 - 6*l**2. Factor x(t).
-(t - 1)*(t + 1)*(t + 2)**2/3
Let v(y) = 2*y**4 + 6*y**3 + 2*y**2 - 3*y - 1. Let b(c) = -8*c**4 - 24*c**3 - 8*c**2 + 11*c + 3. Let f(z) = -6*b(z) - 26*v(z). Let f(a) = 0. What is a?
-2, -1, 1
Let a(l) be the third derivative of -l**7/840 + 3*l**6/80 - 97*l**5/240 + 3*l**4/2 - 8*l**3/3 + 23*l**2. Let a(m) = 0. Calculate m.
1, 8
Solve -17 - 15*d - 190*d**2 + 70*d**3 + 143*d - 20*d**3 - 7 = 0 for d.
2/5, 3
Suppose -a - 6 = -2*b + 2, a + 2*b = 12. Let c = 4 - 2. Solve 4 - 5 - a*f + 0*f**c - f**2 = 0 for f.
-1
Let o be (2/(-3))/(4/(-18)). Let x be 2 - o - 14/(-10). Determine p, given that 2/5 + x*p**2 + 4/5*p = 0.
-1
Let a(n) be the first derivative of n**7/42 - n**5/20 + 2*n + 1. Let u(q) be the first derivative of a(q). Factor u(p).
p**3*(p - 1)*(p + 1)
Let a(t) be the second derivative of 0 - 4*t - 1/40*t**5 + 0*t**2 + 1/12*t**3 + 0*t**4. Factor a(y).
-y*(y - 1)*(y + 1)/2
Let z = 128 + -126. Let i be (3/9)/((-1)/(-2)). Factor -4/9 + 2/9*y**z - 2/3*y + 2/9*y**4 + i*y**3.
2*(y - 1)*(y + 1)**2*(y + 2)/9
Let m(t) = 10*t**3 + 11*t**2 + t - 9. Let a(c) = 5*c**3 + 6*c**2 + c - 4. Let i(p) = 9*a(p) - 4*m(p). Suppose i(d) = 0. Calculate d.
-1, 0
Let f = -5 - -2. Let k be ((6/2)/(-3))/f. Suppose -1/3*t + k*t**3 + 0 + 0*t**2 = 0. Calculate t.
-1, 0, 1
Let a = 101 + -99. Determine v, given that 15/4*v + 3/2 + 3/2*v**a = 0.
-2, -1/2
Let r be (6/(-40))/((-9)/(-42)). Let m = -1/5 - r. Factor -m*t**3 + 1/2*t**2 + 0*t + 0.
-t**2*(t - 1)/2
Let n(k) be the second derivative of k**6/120 + k**5/80 - k**4/48 - k**3/24 - 5*k. Factor n(g).
g*(g - 1)*(g + 1)**2/4
Let b(y) be the third derivative of 4*y**2 + 1/36*y**4 + 0 + 1/9*y**3 - 1/180*y**6 + 0*y - 1/120*y**5 - 1/1260*y**7. Factor b(l).
-(l - 1)*(l + 1)*(l + 2)**2/6
Let r(v) be the third derivative of -v**7/105 + v**6/15 - v**5/10 - 6*v**2. Factor r(s).
-2*s**2*(s - 3)*(s - 1)
Let k(i) be the second derivative of i**4/96 - 5*i**3/24 + 25*i**2/16 + 6*i. Find s, given that k(s) = 0.
5
Let d(p) = -p**3 + 6*p**2 - 5*p + 3. Suppose 5*g - 28 = -3. Let y be d(g). Factor 0 + 6*i**y + i + 9/2*i**2 + 5/2*i**4.
i*(i + 1)**2*(5*i + 2)/2
Let l(z) be the second derivative of z**7/420 - z**6/90 + 7*z**3/6 + 9*z. Let w(n) be the second derivative of l(n). Let w(f) = 0. Calculate f.
0, 2
Let j(i) be the third derivative of -i**9/10584 + i**7/2940 - i**3/2 + 2*i**2. Let u(g) be the first derivative of j(g). Factor u(o).
-2*o**3*(o - 1)*(o + 1)/7
Factor -15*b**2 + 50/3*b - 5/3*b**3 + 0.
-5*b*(b - 1)*(b + 10)/3
Factor 2/3*j**4 - 2*j**2 + 0 + 4/3*j**3 + 0*j.
2*j**2*(j - 1)*(j + 3)/3
Find g such that 0*g + 0 + 1/4*g**2 = 0.
0
Let k(j) = j + 12. Let z be k(-9). Solve 8 - 2 - i - z*i**2 - 2*i = 0 for i.
-2, 1
Let k = 4425/7 + -631. Solve 4/7*b**2 - k*b + 0 = 0 for b.
0, 2
Suppose 6 + 2 = 4*c. Factor c*q**2 + 0*q**2 + 10*q + 4 - 7*q**2 - 9*q**2.
-2*(q - 1)*(7*q + 2)
Let y be (-40)/(-30)*((-10)/(-4) + -1). Factor 3/5*n**y - 12/5*n + 12/5.
3*(n - 2)**2/5
Let t(d) be the third derivative of 0*d + 0 + 0*d**3 + 0*d**6 + d**2 + 0*d**4 - 1/30*d**5 + 1/105*d**7. Determine q so that t(q) = 0.
-1, 0, 1
Let y(h) be the third derivative of h**5/30 - h**4/3 + 4*h**3/3 - 46*h**2. Factor y(d).
2*(d - 2)**2
Let w be 2 + (0 + -9 - -9). Factor 2/3*z**3 + 0*z + 0 + 2/3*z**4 + 0*z**w.
2*z**3*(z + 1)/3
Let i = 4 + -2. Suppose -h - i*h + 12 = 0. Suppose 3*t**4 - 3*t**4 + t**2 - h*t**4 + 3*t**4 = 0. What is t?
-1, 0, 1
Let m(n) be the second derivative of 0*n**2 + 0 - 11*n - 1/4*n**3 - 1/6*n**4 - 1/40*n**5. Determine r, given that m(r) = 0.
-3, -1, 0
Let v(w) be the second derivative of -w**6/105 - w**5/70 + 2*w**4/21 + 4*w**3/21 - 11*w. Factor v(j).
-2*j*(j - 2)*(j + 1)*(j + 2)/7
Let m(o) = 4*o**3 - 4*o**2. Let h be (3 - (-48)/(-9)) + 3/9. Let w(l) = 3*l - 3*l - l - 4*l**2 + 5*l**3. Let r(u) = h*w(u) + 3*m(u). Factor r(g).
2*g*(g - 1)**2
Let z(n) be the third derivative of n**7/135 + n**6/60 + n**5/135 + 18*n**2. Factor z(c).
2*c**2*(c + 1)*(7*c + 2)/9
Let t(g) be the second derivative of 0*g**5 + 3*g + 1/105*g**7 + 0*g**2 - 1/15*g**3 + 0 + 1/15*g**4 - 2/75*g**6. Let t(d) = 0. What is d?
-1, 0, 1
Let x(c) be the second derivative of -c**6/135 + 2*c**5/45 - c**4/9 + 4*c**3/27 - c**2/9 - 4*c. Let x(i) = 0. Calculate i.
1
Let b(n) be the second derivative of -1/15*n**3 - 5*n + 0 - 1/5*n**2 + 1/50*n**5 + 1/30*n**4. Find k, given that b(k) = 0.
-1, 1
Let l = -2/141 - -292/705. Factor 0 - 2/5*v**2 + l*v.
-2*v*(v - 1)/5
Let z(m) be the third derivative of -m**5/450 + 28*m**2. Factor z(f).
-2*f**2/15
Let p(y) be the third derivative of -y**6/660 - y**5/165 - y**4/132 + 6*y**2. Determine m, given that p(m) = 0.
-1, 0
Let y(w) be the second derivative of -9*w**5/5 + 7*w**4/3 + 4*w**3/3 + 3*w. Factor y(i).
-4*i*(i - 1)*(9*i + 2)
Suppose 2*b = 3*i + 8 + 4, 0 = 4*b + i - 52. Let o be (-12)/(-9)*b/8. Solve -1/2*u**2 - o + 2*u = 0.
2
Let p(r) be the second derivative of r**5/5 + r**4 + 4*r**3/3 - 5*r. Suppose p(y) = 0. Calculate y.
-2, -1, 0
Let l(n) = n**2 - n - 4. Let v be l(3). Factor 1 + 13 - 8 + 4*z - 2*z**v.
-2*(z - 3)*(z + 1)
Let c = 12 + -10. Solve 3*x**c - 6*x**2 - 5*x**3 + 3*x**3 + x**2 = 0 for x.
-1, 0
Let z(q) = q - 9. Let b be z(9). Determine t, given that b*t**3 - 2*t**2 - 2*t + 3*t + 0*t**2 + t**3 = 0.
0, 1
Let k(m) be the third derivative of -m**5/270 + m**4/36 + 35*m**2. Find v such that k(v) = 0.
0, 3
Let v be ((-27)/6 + 4)/(-7 - -5). Factor v*x**2 + 0 - 1/4*x.
x*(x - 1)/4
Let r(k) be the first derivative of 0*k + 1/9*k**4 - 1/27*k**6 + 0*k**5 + 0*k**3 - 1/9*k**2 + 1. Solve r(u) = 0 for u.
-1, 0, 1
Let r = -6 - -6. Suppose 2*w - 5 - 1 = r. Factor 3*m**5 - m**3 + m**3 - w*m**4 + 3*m**2 - 3*m**3.
3*m**2*(m - 1)**2*(m + 1)
Let o(c) = 4*c**2 + 20*c + 16. Let t(x) = -4*x**2 - 21*x - 16. Let n(w) = -5*o(w) - 4*t(w). Factor n(j).
-4*(j + 2)**2
Let g(z) = -2*z + 16. Let j be g(6). Let p(y) be the first derivative of 2 + 0*y**2 - 9/14*y**j + 2/5*y**5 + 4/21*y**3 + 0*y. Suppose p(d) = 0. Calculate d.
0, 2/7, 1
Let w be (-2)/4 + 5/2. Let b(q) be the second derivative of 0 + q + 1/18*q**4 + 0*q**w + 1/18*q**3 + 1/60*q**5. Factor b(y).
y*(y + 1)**2/3
Let i(z) = -2*z - 8. Let s be i(6). Let n = s - -20. Factor 0*b**2 + 0*b + n - 1/6*b**4 + 1/6*b**3.
-b**3*(b - 1)/6
Factor 4/3*l**2 + 0*l + 0*l**3 - 2/3*l**4 - 2/3.
-2*(l - 1)**2*(l + 1)**2/3
Let 5/4 + 7/8*r**2 - 37/8*r = 0. Calculate r.
2/7, 5
Suppose -5*d + 10 = -2*q, 2*d = -d - q + 17. Factor 11*z - 3*z + 0*z - d*z**2.
-4*z*(z - 2)
Let i(l) be the first derivative of 0*l**2 + 0*l**3 + 1/5*l**4 - 2/25*l**5 + 0*l - 4. Determine d so that i(d) = 0.
0, 2
Let q(l) be the first derivative of -2*l - 19/3*l**3 - 13/4*l**4 + 5 - 11/2*l**2 - 3/5*l**5. Let q(x) = 0. Calculate x.
-2, -1, -1/3
Let h(c) be the third derivative of 1/504*c**8 + 1/36*c**4 - 1/45*c**5 + 0*c + 0 + 1/315*c**7 + 1/9*c**3 - 1/90*c**6 + 3*c**2. Suppose h(r) = 0. What is r?
-1, 1
Let v(t) be the first derivative of t**6/90 + t**5/60 + 6*t + 1. Let d(p) be the first derivative of v(p). Let d(i) = 0. Calculate i.
-1, 0
Let w(i) be the first derivative of 1/20*i**4 + 2 - 4/5*i + 0*i**2 + 1/5*i**3. Factor w(h).
(h - 1)*(h + 2)**2/5
Let s(m) = -m. Let b be s(-9). Factor -5*l**3 - b*l**2 - 5*l**2 + 12*l**2.
-l**2*(5*l + 2)
Let u be 6/((2 - 5)/(-1)). Suppose 6 = u*z - 0. Find q such that 3/2*q**z - 3/2*q - 1/2*q**2 + 1 - 1/2*q**4 = 0.
-1, 1, 2
Factor -10 - 159*g**2 + 85*g + 80*g**3 - 127*g**2 + 86*g**2.
5*(g - 2)*(4*g - 1)**2
Let m(t) be the third derivative of t**7/140 - t**6/40 + t**5/40 - 9*t**2. Determine d, given that m(d) = 0.
0, 1
Let g(o) = -o**3 - 12*o**2 + 4. Let u be (-2 + 0)*(-2 - 0). Let z(d) = d**3 - d**2 - d + 1. Let i(y) = u*z(y) - g(y). Find m such that i(m) = 0.
-2, 0, 2/5
Let q(v) = -2*v - 6. Let h be q(-6). Suppose c + 4*z + h = 0, 0*c = c + 3*z + 4. Factor -2*g + c*g**3 - 2*g**4 + 0*g**3 + 2*g**2 + 0*g**4.
-2*g*(g - 1)**2*(g + 1)
Suppose i - 5 + 1 = 0. Factor -3*y**2 + 5*y**3 + 2*y**2 - 5*y**4 + 3*y**5 + 2*y**2 - i*y**3.
y**2*(y - 1)**2*(3*y + 1)
Find t such that 0*t**2 - 4/9*t**4 - 4/9*t*