 a**5/360 + a**4/4 - 7*a. Let r(t) be the third derivative of q(t). Find h, given that r(h) = 0.
-1, 1
Let p(b) be the third derivative of -4*b**2 - 1/210*b**7 + 1/30*b**5 + 0 + 1/15*b**6 - 1/6*b**4 - 1/84*b**8 - 1/6*b**3 + 0*b. Determine r, given that p(r) = 0.
-1, -1/4, 1
Let o = 11 - 5. Let l(h) be the second derivative of 1/42*h**4 + 0*h**3 + 0*h**5 - 1/105*h**o - h + 0*h**2 + 0. Factor l(t).
-2*t**2*(t - 1)*(t + 1)/7
Let v(a) be the first derivative of -a**6/900 - a**5/100 - a**4/30 + 4*a**3/3 + 1. Let b(n) be the third derivative of v(n). Factor b(k).
-2*(k + 1)*(k + 2)/5
Let k(q) = -q**2 - 6*q + 4. Let b be k(-6). Let c(v) = v**2 - 4*v - 1. Let d(g) = -g - g + g + 0. Let a(i) = b*d(i) - c(i). What is x in a(x) = 0?
-1, 1
Let s(y) = y**3 - 7*y**2 - 8*y + 2. Let d be s(8). Determine c so that -c + 3*c**3 - 7*c**3 + 2*c**3 - c - 4*c**d = 0.
-1, 0
What is n in -80*n**3 + 57 - 6*n**4 + 80*n + 25 - 10*n**4 + 18 - 84*n**2 = 0?
-5/2, -1, 1
Let k(r) be the third derivative of r**5/360 - r**4/48 + r**3/18 + 7*r**2. Factor k(t).
(t - 2)*(t - 1)/6
Let h(o) be the first derivative of o**6/27 + 2*o**5/45 - o**4/18 - 2*o**3/27 - 9. Factor h(f).
2*f**2*(f - 1)*(f + 1)**2/9
Let l = 1441 + -1441. Factor 2/5*t**2 + 0*t + l.
2*t**2/5
Let l(p) be the second derivative of -p**7/3780 + p**6/540 - p**5/180 + p**4/12 - 4*p. Let s(z) be the third derivative of l(z). Factor s(b).
-2*(b - 1)**2/3
Factor -4/9*y - 5/3*y**3 - 13/9*y**2 + 0 - 1/9*y**5 - 7/9*y**4.
-y*(y + 1)**3*(y + 4)/9
Let i(c) = -368*c**4 + 880*c**3 - 664*c**2 + 146*c + 16. Let h(j) = -123*j**4 + 293*j**3 - 221*j**2 + 49*j + 5. Let s(m) = 16*h(m) - 5*i(m). Factor s(v).
-2*v*(4*v - 3)**3
Let w(z) be the second derivative of 0*z**2 - 1/18*z**3 + z + 0 + 2/45*z**6 - 1/126*z**7 - 1/10*z**5 + 1/9*z**4. Factor w(g).
-g*(g - 1)**4/3
Factor -15/8*a**3 + 0 + 0*a + 9/4*a**4 + 0*a**2 - 3/8*a**5.
-3*a**3*(a - 5)*(a - 1)/8
Suppose 6*r = 3*r + 2*j + 40, 2*r - 40 = -2*j. Let v = r + -14. Determine o, given that -1/4 - 1/2*o - 1/4*o**v = 0.
-1
Suppose -10*m = -4*a - 6*m + 88, 145 = 5*a + 2*m. Determine p so that 12*p**3 + 3/2*p**4 + 0*p + a*p**2 - 81/2 = 0.
-3, 1
Let f(t) = -4*t**4 - 6*t**2 + 4*t. Suppose 3*o = -0*o - 9. Let m(x) = -3*x**4 + x**3 - 5*x**2 + 3*x. Let b = -5 + 7. Let v(y) = b*f(y) + o*m(y). Factor v(z).
z*(z - 1)**3
Let k be 7/(-56) + (-2)/(-16). Find o such that 0*o - 1/4*o**2 + k + 1/4*o**3 = 0.
0, 1
Let y(p) be the second derivative of 1/30*p**5 + p + 2/9*p**4 + 5/9*p**3 + 2/3*p**2 + 0. Factor y(s).
2*(s + 1)**2*(s + 2)/3
Let a(j) = j**3 - j**2 - 2*j - 4. Let c be a(0). Let k be (24/c)/(1 + -4). Solve 4/5*t + 0 + 6/5*t**k + 2/5*t**3 = 0.
-2, -1, 0
Suppose 5*b = -0*b - 5. Let n be -4 - b - (4 - 10). Suppose 12/5*x**n + 8/5*x**2 + 2/5*x + 8/5*x**4 + 2/5*x**5 + 0 = 0. What is x?
-1, 0
Let f(b) = 180*b**2 - 25*b - 35. Let h(u) = -15*u**2 + 2*u + 3. Let t(c) = -3*f(c) - 35*h(c). Solve t(j) = 0.
0, 1/3
Let b(z) be the second derivative of 0 - 1/10*z**4 - 1/50*z**5 - 1/5*z**3 + 2*z - 1/5*z**2. What is u in b(u) = 0?
-1
Factor 6 - 116*n + 0 - 3*n**2 + 113*n.
-3*(n - 1)*(n + 2)
Let u(o) be the third derivative of 0*o**5 + 0*o**4 + 0*o + 1/105*o**7 + 1/60*o**6 - 2*o**2 + 0*o**3 + 0. Let u(f) = 0. Calculate f.
-1, 0
Let m(s) = s**2 - 1. Let t(k) = 2*k**2 - 2*k - 4. Let u(l) = -4*m(l) + t(l). Factor u(o).
-2*o*(o + 1)
Let r(k) = 9*k**3 + 5*k**2 - 2. Let c(b) = -b - 11 + 0*b + 12 - b**3. Let z(x) = 2*c(x) + r(x). Find f such that z(f) = 0.
-1, 0, 2/7
Let g(b) be the first derivative of -3 + 1/8*b**2 + 1/4*b - 1/12*b**3 - 1/16*b**4. Solve g(x) = 0.
-1, 1
Let v(g) be the first derivative of 0*g**2 - 4/3*g**3 - 2 + 2*g + 0*g**4 + 2/5*g**5. Factor v(c).
2*(c - 1)**2*(c + 1)**2
Let f(d) = d**3 + 5*d**2 + d + 6. Let i be f(-5). Let m be (-236)/(-48) + i/(-4). Factor -m*x**4 + 0 - 4/3*x + 2*x**2 + 2*x**5 + 2*x**3.
2*x*(x - 1)**3*(3*x + 2)/3
Let m be ((-72)/243)/(6/(-9)). Let -2/3*o - m - 2/9*o**2 = 0. Calculate o.
-2, -1
Let k(r) = 11*r**3 - 11*r**2 - r + 6. Let p(i) = 39*i**3 - 39*i**2 - 3*i + 21. Let h(s) = 18*k(s) - 5*p(s). Factor h(x).
3*(x - 1)**2*(x + 1)
Let r be (-1)/2*(-1 + 1). Suppose r = -2*d - 2*d. Find j such that 5*j**5 + 8*j**2 - 2*j + d*j**5 + j**3 - 8*j**4 - 5*j**3 + j**5 = 0.
-1, 0, 1/3, 1
Find k, given that 1/2 - 1/2*k**2 + 0*k = 0.
-1, 1
Let b(q) be the second derivative of 6*q + 0 + 35/27*q**4 - 5/18*q**5 - 44/27*q**3 + 8/9*q**2. Find z such that b(z) = 0.
2/5, 2
Let n(h) = -h**2 + 9*h + 3. Let g be n(9). Let j(u) be the first derivative of -2 + 2*u - 4*u**2 + 4*u**g + 2/5*u**5 - 2*u**4. Factor j(o).
2*(o - 1)**4
Let j(g) = g**5 + 8*g**4 - 13*g**3 + 7*g**2 + 3*g + 3. Let y(s) = s + 2 + 8*s**4 - 12*s**3 + s**2 + 5*s**2 + s. Let d(u) = 2*j(u) - 3*y(u). Factor d(i).
2*i**2*(i - 2)*(i - 1)**2
Let k = 203/10 - 94/5. Factor 3/2*r**3 + 9/2*r + 9/2*r**2 + k.
3*(r + 1)**3/2
Let w be 2/5 - (-6)/10. Let m = 1 + w. Factor -2/3*o**m - 2/3*o + 2/3*o**3 + 2/3*o**4 + 0.
2*o*(o - 1)*(o + 1)**2/3
Let n(l) = 4*l**3 - 5*l**2 - 9. Let r(h) = h**3 - h**2 - 2. Let g(z) = -2*n(z) + 9*r(z). Factor g(c).
c**2*(c + 1)
Let p be (-6)/5*30/(-12). Let d(w) = w**5 + w**4 - w**3 - 6*w**2 - 5*w + 5. Let i(q) = 3*q**2 + 3*q - 3. Let t(h) = p*d(h) + 5*i(h). Solve t(l) = 0 for l.
-1, 0, 1
Let w(m) be the third derivative of -m**5/90 - 5*m**4/36 - 4*m**3/9 + 2*m**2 - 2. What is a in w(a) = 0?
-4, -1
Let n(r) = 4*r**3 - 12*r - 8. Let x(l) = 4*l**3 - 12*l - 8. Let k(i) = -3*n(i) + 2*x(i). Find j such that k(j) = 0.
-1, 2
Suppose -60/11*p**4 - 30/11*p - 14/11*p**5 - 4/11 - 100/11*p**3 - 80/11*p**2 = 0. What is p?
-1, -2/7
Factor -9*v + 4*v**4 + 9*v**3 + v**4 - 2*v**4 - 3*v.
3*v*(v - 1)*(v + 2)**2
Factor 4/17*j**2 + 0 - 2/17*j**3 - 2/17*j.
-2*j*(j - 1)**2/17
Let n = -4 + 8. Determine v so that -2*v**3 + 2*v - 2*v**4 + n*v**3 - 6*v**2 + 4*v**3 = 0.
0, 1
Factor -3*a**2 + 0*a**2 + 0*a + 2*a + 0*a**2 + a**3.
a*(a - 2)*(a - 1)
Let j(y) = -y - 3. Let q be j(-5). Let r be (15/6 - -4) + 4/(-1). Factor 0 + r*k**q - k - 5/2*k**4 + k**3.
-k*(k - 1)*(k + 1)*(5*k - 2)/2
Let n(b) be the third derivative of b**7/2520 - b**5/120 + 5*b**4/24 + 3*b**2. Let l(m) be the second derivative of n(m). Factor l(a).
(a - 1)*(a + 1)
Let m = 27/5 - 5. Let r be 2/(-90) + 8/36. What is j in r*j**2 + 1/5 - m*j = 0?
1
Let j(h) be the third derivative of 0 - 2*h**3 - 1/20*h**5 - 1/2*h**4 + 5*h**2 + 0*h. Factor j(x).
-3*(x + 2)**2
Let x(o) = -o**2 + o. Let u(b) = -3*b**2 + 2*b + 1. Let c(v) = 4*u(v) - 10*x(v). Determine y, given that c(y) = 0.
-2, 1
Let b(k) be the third derivative of 2*k**2 - 1/168*k**8 + 0*k**3 + 0*k**4 + 1/30*k**5 + 0 - 1/20*k**6 + 0*k + 1/35*k**7. Determine v so that b(v) = 0.
0, 1
Let t be 4/18 + 10/(-45). Let j be (1 + 1)*(-9)/(-6). Factor j*u + 2*u**2 - u + t*u.
2*u*(u + 1)
Suppose 5*z = -15, 5 - 18 = -2*t + 3*z. Suppose t*m + 0 = 3*r - 4, -m = -r + 1. Factor -2 + 2 - r*q**3 + 0*q**3 + 2*q.
-2*q*(q - 1)*(q + 1)
Factor 0 + 0*l - 9/2*l**5 - 3*l**4 - 1/2*l**3 + 0*l**2.
-l**3*(3*l + 1)**2/2
Let m = -5 + -1. Let t be 4/6 - 8/m. Solve -15*h**t - 2*h**4 - 2 - h**4 + 11*h**3 + 9*h + 0*h**3 = 0 for h.
2/3, 1
Let x(g) be the second derivative of -g**4/24 + g**3/12 + g**2/2 + 6*g. Let x(p) = 0. Calculate p.
-1, 2
Determine j, given that 2/5*j**2 + 0*j + 0 = 0.
0
Let p(s) be the third derivative of 5*s**8/112 + s**7/42 - s**6/8 - s**5/12 - 20*s**2. Solve p(q) = 0 for q.
-1, -1/3, 0, 1
Let f(a) be the third derivative of -a**7/1050 + a**6/200 - a**4/30 + 11*a**2. Find j, given that f(j) = 0.
-1, 0, 2
Let r(g) be the first derivative of -7*g**3/27 + 5*g**2/18 + 2*g/9 + 7. Determine n so that r(n) = 0.
-2/7, 1
Let g(l) be the second derivative of -l**4/18 + l**3/3 + 4*l**2/3 + 24*l. Factor g(j).
-2*(j - 4)*(j + 1)/3
Solve -1/6*n**4 + 1/6*n**5 + 1/6*n**2 + 0 + 0*n - 1/6*n**3 = 0 for n.
-1, 0, 1
Let b = -24009/13 + 1849. Determine l so that 12/13*l**4 + 4/13 - 2/13*l**5 + 32/13*l**2 - b*l**3 - 18/13*l = 0.
1, 2
Let v(l) be the third derivative of 7*l**8/7200 - l**7/450 + l**6/450 + l**5/30 + l**2. Let i(j) be the third derivative of v(j). Factor i(k).
2*(7*k - 2)**2/5
Let z(d) be the first derivative of 0*d**4 + 0*d**3 - 2/25*d**5 - 1/15*d**6 + 6 + 0*d + 0*d**2. Solve z(v) = 0.
-1, 0
Factor 2/3*o**3 + 2/3*o**2 - 1/3*o - 1/3*o**5 - 1/3 - 1/3*o**4.
-(o - 1)**2*(o