1
Let l(w) = 70*w**3 - 855*w**2 + 1330*w - 715. Let m(s) = 5*s**3 - 61*s**2 + 95*s - 51. Let n(d) = 6*l(d) - 85*m(d). Determine r, given that n(r) = 0.
1, 9
Let y(r) be the first derivative of 2 + 0*r**3 - 1/5*r**5 + 0*r**2 + 0*r + 1/4*r**4. Factor y(l).
-l**3*(l - 1)
Let c(t) be the first derivative of 5 + 0*t**2 + 2/7*t - 32/21*t**3. Factor c(b).
-2*(4*b - 1)*(4*b + 1)/7
Suppose -5*h = -2*h + 6. Let a = h + 10. Determine z so that 5*z - 5*z - 14*z**3 + 14*z + 4 - 12*z**2 + a*z**4 = 0.
-1, -1/4, 1, 2
Let z be -2 - (21 + -3)/(-3). Suppose n = z*n. Find l such that n - 1/2*l**3 + 0*l - 1/2*l**2 = 0.
-1, 0
Let u(s) = 4*s**3 - 3*s**2 - s. Let m(n) = -n**3 + n. Let i(r) = -m(r) - u(r). Solve i(x) = 0.
0, 1
Let t(u) be the first derivative of u**6/75 + 3*u**5/50 + u**4/15 + u - 6. Let h(o) be the first derivative of t(o). Suppose h(y) = 0. Calculate y.
-2, -1, 0
Solve -3*w + 8 - 7 + 3*w**2 - 2*w**3 + 4*w**3 - 3*w**3 = 0 for w.
1
Let d(q) = -4*q - 24. Let u be d(-7). Determine k so that -k**u - 4/3 + 0*k + 7/3*k**2 + 1/3*k**3 - 1/3*k**5 = 0.
-2, -1, 1
What is x in 4/3*x**2 - 2/3*x**3 + 0 + 2*x = 0?
-1, 0, 3
Factor -12 - d**3 + 12.
-d**3
Let b = 3809/3420 - 1/380. Find l, given that -8/9*l - b*l**4 + 0 - 34/9*l**3 - 32/9*l**2 = 0.
-2, -1, -2/5, 0
Let g(a) be the third derivative of -a**6/120 + a**5/15 - a**4/6 + 11*a**2. Suppose g(w) = 0. Calculate w.
0, 2
Let d(f) be the second derivative of f**7/3360 - f**6/360 + f**5/160 + 5*f**3/6 - 4*f. Let q(g) be the second derivative of d(g). Let q(j) = 0. Calculate j.
0, 1, 3
Factor 0 + 6/7*s + 3/7*s**2.
3*s*(s + 2)/7
Let t be 2 + 5 + (-6)/2. Let w(i) be the second derivative of -1/12*i**t + 0 + 0*i**2 + i - 1/12*i**3 - 1/40*i**5. Factor w(k).
-k*(k + 1)**2/2
Factor 0*v + 0 - 9/7*v**2 - 1/7*v**3.
-v**2*(v + 9)/7
Let v be -6*6/9 - -6. Let h(x) be the first derivative of -4 + 0*x - 1/3*x**3 - 1/5*x**5 + 0*x**v + 1/2*x**4. Factor h(n).
-n**2*(n - 1)**2
Let u(k) = -7*k**2 + 0*k + k**2 + 6*k. Let d be (8/(-5))/(2/(-10)). Let s(m) = 2*m**2 - 2*m. Let l(b) = d*s(b) + 3*u(b). Factor l(t).
-2*t*(t - 1)
Factor 1 + 1/2*g**2 + 7/4*g - 1/4*g**3.
-(g - 4)*(g + 1)**2/4
Let z(d) be the third derivative of 2*d**6/105 + 2*d**5/15 + 11*d**4/42 + 5*d**3/21 - 16*d**2. Factor z(g).
2*(2*g + 1)**2*(2*g + 5)/7
Let c(d) be the third derivative of -d**9/98280 - d**8/21840 - d**7/16380 + d**4/6 + 8*d**2. Let p(u) be the second derivative of c(u). Factor p(x).
-2*x**2*(x + 1)**2/13
Suppose -a = 1 - 4. Let r(n) = -n**5 - 6*n**4 - 6*n**3 + 2*n**2 + 3*n. Let b(j) = -j**4 - j**3 + j**2 + j. Let x(w) = a*b(w) - r(w). Solve x(z) = 0 for z.
-1, 0
Let r(q) = q**4 - 2*q**3 + 6*q**2 + 2*q - 1. Let v(z) = -z**4 + 2*z**3 - 5*z**2 - 2*z + 1. Let k(l) = 5*r(l) + 6*v(l). Factor k(d).
-(d - 1)**3*(d + 1)
Suppose -4 = -5*r + 4*q, -2*r - 4*q - 3 = 1. Let c(p) be the second derivative of r*p**2 + 1/24*p**4 - 2*p + 1/6*p**3 + 0. What is j in c(j) = 0?
-2, 0
Let c be 6/24 + (-22)/(-8). Factor -3*s**c - s**3 - 17*s**3 + 6*s - 2*s**2 + 17*s**2.
-3*s*(s - 1)*(7*s + 2)
Let l(n) be the first derivative of 19*n**5/15 + 55*n**4/12 + 17*n**3/3 + 13*n**2/6 - 2*n/3 + 2. Determine g so that l(g) = 0.
-1, 2/19
Suppose -3*q + 9 = -3. Let r be (q + -2)*(-3)/(-3). Determine v so that 2*v**r + 0*v**2 - 3*v**2 + 3*v**2 = 0.
0
Let f(u) be the second derivative of -u**4/60 + 2*u**3/15 - 3*u**2/10 + u - 4. Factor f(x).
-(x - 3)*(x - 1)/5
Suppose 0 = 4*n - 3*n - 3. Let z = n + -3. Determine b so that 6*b**4 + 0*b**3 + 2*b**5 + 4*b**3 + 4 - 6 + z*b**3 - 6*b - 4*b**2 = 0.
-1, 1
Let x(a) be the third derivative of 0*a + 0*a**3 + 1/48*a**4 + 1/120*a**5 - 1/240*a**6 + 2*a**2 - 1/420*a**7 + 0. Let x(d) = 0. What is d?
-1, 0, 1
Let n(s) = 3*s - 25. Let p be n(10). Factor -3*b**4 + 6*b**p + 3*b**3 - 7*b**5 - 4*b**3 + b**4.
-b**3*(b + 1)**2
Let p(j) be the first derivative of -j**5/330 + j**4/44 - 2*j**3/33 + j**2 - 4. Let v(b) be the second derivative of p(b). Let v(i) = 0. Calculate i.
1, 2
Let n(p) = -2*p**2 - p + 2. Let z be n(0). Let i(m) be the first derivative of -m**z - 2/3*m**3 - 1/8*m**4 - 3 + 0*m. Determine q, given that i(q) = 0.
-2, 0
Let f be -3*(6/9 + -1). Let s be (f - (-3)/(-12))*4. Find u such that -2/7*u**s + 0 + 0*u - 2/7*u**2 + 2/7*u**4 + 2/7*u**5 = 0.
-1, 0, 1
Let f(v) = v. Let o be f(2). Suppose -3 = -4*c + 37. Let s(u) = 6*u**2 - 7*u + 6. Let b(j) = -j**2 + j - 1. Let q(g) = c*b(g) + o*s(g). Factor q(p).
2*(p - 1)**2
Let i be 2/((3 + -6)*(-80)/12). Let f(h) be the first derivative of 4 + i*h**5 - 1/3*h**3 + 1/2*h + 0*h**2 + 0*h**4. Factor f(a).
(a - 1)**2*(a + 1)**2/2
Let k be ((-78)/(-9))/(0 + 4). Let c = 8/3 - k. Determine x so that 0*x + 0 - 1/2*x**3 + c*x**2 = 0.
0, 1
Determine d, given that 9/7 + 3/7*d**3 + 15/7*d**2 + 3*d = 0.
-3, -1
Suppose k + 13 = 5*n + 3, 3*n - 6 = k. Let f be (2 + -2)/(k + 1). Factor -2/5*d**3 - 4/5*d**2 - 2/5*d + f.
-2*d*(d + 1)**2/5
Let q = 50 + -46. Find k such that -7/2*k**4 + 1/2 + k - k**5 - q*k**3 - k**2 = 0.
-1, 1/2
Let p(k) be the third derivative of -3/40*k**6 - 1/112*k**8 + 0*k**4 + 0*k + 3/70*k**7 + 0 - 3*k**2 + 1/20*k**5 + 0*k**3. Solve p(h) = 0.
0, 1
Suppose 0*b + 3/5*b**4 + 0 + 0*b**2 - 9/5*b**3 = 0. What is b?
0, 3
Let t(y) be the first derivative of -y**6/120 + y**5/60 + y**4/24 - y**3/6 + 5*y**2/2 + 5. Let f(o) be the second derivative of t(o). Factor f(a).
-(a - 1)**2*(a + 1)
Let s be ((-12)/5)/(21/(-140)). Let x = s + -16. Factor 0*v + 0*v**2 + 0*v**3 + 2/5*v**4 + x.
2*v**4/5
Let m(i) be the second derivative of 1/15*i**6 + 4/3*i**3 - 5*i + 0 + 2/5*i**5 + i**2 + i**4. Determine f, given that m(f) = 0.
-1
Let d = 9 + -89/10. Let c(j) be the third derivative of 1/6*j**4 + d*j**5 + 0*j + 1/6*j**3 + 1/210*j**7 + 0 - 3*j**2 + 1/30*j**6. Solve c(t) = 0 for t.
-1
Factor 0 + 2/7*w - 2/7*w**2.
-2*w*(w - 1)/7
Let t be (2/(-6))/(21/(-42)). Factor 1/3*x + 1/3*x**2 - t.
(x - 1)*(x + 2)/3
Let h(l) be the first derivative of l**6/15 + 8*l**5/75 - l**4/15 - 8*l**3/45 - l**2/15 - 6. Let h(s) = 0. Calculate s.
-1, -1/3, 0, 1
Let l(i) be the second derivative of 3/2*i**2 + 0 - 2*i + 0*i**3 - 1/4*i**4. Factor l(c).
-3*(c - 1)*(c + 1)
Let y(b) be the third derivative of -b**7/105 - b**6/30 + b**4/6 + b**3/3 - 3*b**2. Determine v so that y(v) = 0.
-1, 1
Let k(x) = x**3 + 4*x**2 - 6*x - 4. Let o be k(-5). Let f = 1 + o. What is m in 8*m**4 + f*m**2 + 10*m**3 + m**2 - m**2 = 0?
-1, -1/4, 0
Suppose 12*x + 6*x**2 + 17 - 13 + 3*x**2 = 0. What is x?
-2/3
Let c(s) be the first derivative of -s**4/10 + 2*s**3/5 - 2*s**2/5 + 8. Factor c(h).
-2*h*(h - 2)*(h - 1)/5
Let l be 2590/252 + 1/(-2). Factor 32/9 - l*m**3 - 160/9*m + 14/9*m**4 + 64/3*m**2.
2*(m - 2)**3*(7*m - 2)/9
Let r(z) = z**2 - 6*z + 2. Let p(v) = -7*v + 3. Suppose 2*u - 3*u = 4. Let i(a) = u*r(a) + 3*p(a). Factor i(j).
-(j - 1)*(4*j + 1)
Suppose -4*b = -4*g + 6 - 2, 5*g - 19 = -2*b. Let 2/9*a + 0 - 2/9*a**4 + 2/9*a**b - 2/9*a**3 = 0. What is a?
-1, 0, 1
Suppose 5*b = u, 0 = -8*b + 4*b + 4*u. Let o be ((-12)/(-90)*3)/((-2)/(-20)). Determine i so that b*i + 0 - 4/3*i**2 + 0*i**3 + 13*i**o + 35/3*i**5 = 0.
-1, -2/5, 0, 2/7
Let n(a) be the second derivative of -a**7/7560 + a**6/2160 + a**5/180 - 5*a**4/12 - 6*a. Let c(s) be the third derivative of n(s). Factor c(g).
-(g - 2)*(g + 1)/3
Let a be (5 - 3)*(0 + 2). Solve k**2 + k**2 - 2*k**a - k**3 + k**3 = 0.
-1, 0, 1
Let d = 5 - 2. Suppose d = 3*h - 2*h. Factor 2*g**2 - 3*g**2 - 2*g + 2 - h.
-(g + 1)**2
Let t(j) be the first derivative of -j**3/3 - 6*j**2 - 20*j - 23. Find s, given that t(s) = 0.
-10, -2
Let w = 369 + -2559/7. Let c = w - 58/21. Find y such that 0*y**3 - c*y**4 + 4/3*y**2 - 2/3 + 0*y = 0.
-1, 1
Let a(x) = x**2 - 5*x - 2. Let v(r) be the second derivative of -r**4/6 + r**3 + r**2 + 3*r. Let d(n) = 3*a(n) + 2*v(n). Factor d(l).
-(l + 1)*(l + 2)
Let o be (0/3)/(-4) - -5. Let l(b) be the third derivative of 0*b**3 + 0*b**4 + 0 + 0*b**o - b**2 + 0*b - 1/540*b**6. Suppose l(m) = 0. What is m?
0
Let p(u) be the third derivative of u**6/60 + 2*u**5/15 + u**4/3 - 11*u**2. Factor p(w).
2*w*(w + 2)**2
Let q be 15/30*(2 - -1*4). Let l(k) be the first derivative of 2/21*k**q + 3 + 1/7*k**2 + 0*k. Factor l(j).
2*j*(j + 1)/7
Suppose -2*t = 4*d - 2, -5*d - t - 2*t + 3 = 0. Suppose v - 4 = -d. Factor 4*h**3 + 2*h**4 + 2*h**2 + v*h**3 - 