3*(-20)/(-12)*1. Let r(s) = s**4 - s**3 + 9*s**2 - 3*s + 2. Let k(b) = b**4 + 9*b**2 - 2*b + 2. Let o(p) = u*r(p) - 4*k(p). Let o(n) = 0. What is n?
1, 2
Factor -5*j**3 - 6*j**2 + 8*j + j**3 + 2*j**4 + 0*j**3 + 8.
2*(j - 2)**2*(j + 1)**2
Let i(r) be the first derivative of 2*r**5/45 + r**4/6 + 4*r**3/27 + 7. Determine m so that i(m) = 0.
-2, -1, 0
Factor -a + 2*a**3 - 167 + 170 + 2*a - 7*a**2 + a.
(a - 3)*(a - 1)*(2*a + 1)
Let p(b) be the second derivative of b**9/5040 + b**8/2240 - b**7/420 - b**4/4 + 4*b. Let i(u) be the third derivative of p(u). Factor i(o).
3*o**2*(o - 1)*(o + 2)
Let i(p) = 10*p**2 - 3 + 4 + 3 + 9*p + 2. Let o(x) = -3*x**2 - 3*x - 2. Suppose -12 + 4 = -2*f. Let m(c) = f*i(c) + 14*o(c). Factor m(r).
-2*(r + 1)*(r + 2)
Let m(u) be the third derivative of u**2 + 1/540*u**6 - 1/135*u**5 + 0*u**3 + 0 + 0*u + 1/108*u**4. Find x, given that m(x) = 0.
0, 1
Let d(u) = -u**3 - 2*u**2 + 1. Let m be d(-1). Suppose -5*z + 7 = -3. Factor 0*f - 1/3*f**3 + 0*f**z + m + 0*f**4 + 1/3*f**5.
f**3*(f - 1)*(f + 1)/3
Let n be (-2)/3*-9 - (-8 + 7). Let d(l) be the third derivative of -1/240*l**6 - 3*l**2 + 0*l**3 + 0 - 1/840*l**n + 1/240*l**5 + 0*l + 1/48*l**4. Factor d(s).
-s*(s - 1)*(s + 1)*(s + 2)/4
Solve 2*b**2 + 4*b**3 - b**4 - 2*b**4 + 5*b**4 = 0 for b.
-1, 0
Let p = -23 + 28. Suppose 0 = p*c - 10 - 10. Factor 13/3*s**2 + 4/3*s**c - 2*s + 1/3 - 4*s**3.
(s - 1)**2*(2*s - 1)**2/3
Let x be (-10 + 16)*1*4. Let i be (-1 + -11)*(-8)/x. Suppose 13/3*t**3 - 4/3*t + 0 + 4/3*t**2 + 5/3*t**i = 0. Calculate t.
-2, -1, 0, 2/5
Let o(m) = -m**2 - m + 7. Suppose a = 8 - 3. Let l(j) = -1. Let u(q) = a*l(q) + o(q). Find b such that u(b) = 0.
-2, 1
Suppose 41 + 43 - m**2 + 4*m - 84 = 0. Calculate m.
0, 4
Suppose 0 = j + 3*p + 14, 3*j - 2*p - 7 = 6. Let m(i) = i**2 + i + 1. Let t(z) = -2. Let d(q) = j*t(q) + 2*m(q). Let d(s) = 0. What is s?
-1, 0
Let a(c) be the second derivative of -c**6/75 - 3*c**5/25 - 2*c**4/5 - 2*c**3/3 - 3*c**2/5 - c. Find y such that a(y) = 0.
-3, -1
Let p(g) = g - 4. Let y(i) = -8*i**3 + 2*i + 1. Let d be y(-1). Let r be p(d). Determine k so that -3*k**3 + k - r*k - 4*k**2 + k**3 = 0.
-1, 0
Let q(n) = 4 - n**3 - 6*n**2 - 2*n**2 + 2*n**2. Let m be q(-6). What is s in -4*s**2 + 3*s**2 + 4*s**4 - 3*s**m = 0?
-1, 0, 1
Let n(f) be the first derivative of 2*f**5/25 - f**4/5 + 2*f**2/5 - 2*f/5 + 5. Find d, given that n(d) = 0.
-1, 1
Let c be 4/14 - 130/(-35). Let h(p) be the third derivative of 1/24*p**c - 2*p**2 + 0*p + 0*p**3 - 1/60*p**5 + 0. Factor h(q).
-q*(q - 1)
Let x(r) be the first derivative of 3/4*r**4 - 1 + 0*r**2 - 6/5*r**5 + 0*r + 1/2*r**6 + 0*r**3. Suppose x(s) = 0. Calculate s.
0, 1
Let f(j) = 3*j**2 + 6*j + 1 - j - 2*j + 3*j**3. Let u(k) = 16*k**3 + 15*k**2 + 15*k + 5. Let b(r) = -11*f(r) + 2*u(r). Factor b(n).
-(n + 1)**3
Suppose -3*x + 13 = -2. Determine q, given that -q**2 + 0 - 1/2*q**3 + q**4 + 3/4*q**x - 1/4*q = 0.
-1, -1/3, 0, 1
Let a(z) be the third derivative of 1/48*z**4 - 1/240*z**6 + 1/12*z**3 - 1/120*z**5 + 0 + 0*z + 4*z**2. Solve a(f) = 0 for f.
-1, 1
Let 0 + 0*z + 1/5*z**5 + 0*z**3 - 1/5*z**4 + 0*z**2 = 0. What is z?
0, 1
Let x(s) = -2*s - 2. Let u(i) = i**2 - 1. Let a(v) = -u(v) - x(v). Let k be a(3). Find z such that 1/4*z + 3/2*z**2 + z**4 + k + 9/4*z**3 = 0.
-1, -1/4, 0
Let j = -2787/4 - -699. Factor j*y + 3/8*y**2 + 27/8.
3*(y + 3)**2/8
Let o = -1 + 5. Suppose o*m + 2*g - 20 - 8 = 0, -5*g = 4*m - 34. Solve -4*f**2 - 2*f - 2*f**4 + 3*f**2 - m*f**3 - 5*f**2 = 0.
-1, 0
Factor 12*c + 23*c**2 - 10*c**2 - 10*c**2 - 36.
3*(c - 2)*(c + 6)
Let t(i) = i - 1. Let y be 9/3 + 2 + -4. Let q be t(y). Determine n, given that 0*n**2 + 1/2*n - 1/2*n**3 + q = 0.
-1, 0, 1
Let u be 32/14 - 2/7. Determine n, given that n**u + 1/3*n**4 + 0 - n**3 - 1/3*n = 0.
0, 1
Let r = -124/171 + 18/19. Factor 2/9*z**2 + 2/9*z**3 - 2/9 - r*z.
2*(z - 1)*(z + 1)**2/9
Let r = 7 + -2. Suppose -r*w = i + i - 12, -5*i + 3 = -w. What is j in 2*j**2 - 2*j**3 + 3*j**w - 3*j**4 - 1 - j**2 + 2*j**5 = 0?
-1, -1/2, 1
Let n(r) be the second derivative of -3*r**5/50 - 7*r**4/20 - 2*r**3/5 + 6*r**2/5 - 14*r. Find d such that n(d) = 0.
-2, 1/2
Let w(d) be the third derivative of d**9/15120 - d**5/20 + 2*d**2. Let x(q) be the third derivative of w(q). Let x(f) = 0. Calculate f.
0
Let w(u) be the second derivative of u**7/840 + u**6/120 + u**5/40 + u**4/24 - u**3/6 + 6*u. Let t(x) be the second derivative of w(x). Solve t(j) = 0.
-1
Let k(u) be the third derivative of -u**5/420 - 5*u**4/168 - u**3/7 + 18*u**2. Factor k(t).
-(t + 2)*(t + 3)/7
Let w(o) be the first derivative of -5*o**4/4 - 20*o**3/3 + 55*o**2/2 - 30*o + 16. Determine f, given that w(f) = 0.
-6, 1
Let o be (-4)/(-8)*4*2. Suppose o*q + 137 - 2*q**2 - 141 + q**2 = 0. What is q?
2
Let l(n) be the first derivative of -n**6/2520 - 5*n**3/3 + 1. Let s(a) be the third derivative of l(a). Factor s(r).
-r**2/7
Let n be ((-28)/(-21))/(4 - (-55)/(-15)). Factor 2*k**5 + 0*k + 2/5*k**3 - 4/5*k**2 + 16/5*k**n + 0.
2*k**2*(k + 1)**2*(5*k - 2)/5
Suppose 0*y**3 + 0 + 0*y - 1/2*y**4 + 1/2*y**2 = 0. Calculate y.
-1, 0, 1
Factor 0 - 6/7*x + 9/7*x**3 - 3/7*x**2.
3*x*(x - 1)*(3*x + 2)/7
Suppose 0*u**2 + 0*u + 0 + 1/4*u**3 = 0. Calculate u.
0
Let d(l) = -l**3 - 11*l**2 - 11*l - 8. Let n be d(-10). Suppose -n*y = -5*m - 14, -2*m = 4*y - 3*m - 10. Let -2*o - 1/2*o**2 - y = 0. What is o?
-2
Let c = -729/2 + 365. What is s in c*s + 0 + 1/4*s**2 = 0?
-2, 0
Let o be -3 - 3/(12/(-20)). Factor 0 - 1/3*b**o + 0*b - 1/3*b**3.
-b**2*(b + 1)/3
Factor 1/9*g - 1/9 - 1/9*g**3 + 1/9*g**2.
-(g - 1)**2*(g + 1)/9
Let p(q) = 3*q**3 + 5*q - 4. Let x(f) = -8*f**3 - f**2 - 15*f + 11. Let u(m) = -11*p(m) - 4*x(m). Factor u(n).
-n*(n - 5)*(n + 1)
Let m(y) be the second derivative of y**4/15 + 4*y**3/15 - 6*y**2/5 - 10*y. Determine d so that m(d) = 0.
-3, 1
Let o(p) be the third derivative of p**5/40 + p**4/8 + p**3/4 + 12*p**2. Factor o(l).
3*(l + 1)**2/2
Factor -2/9*i**2 - 2/9*i + 0.
-2*i*(i + 1)/9
Let a be (1/14)/(114/(-24) + 5). Factor a*q + 2/7*q**2 + 0.
2*q*(q + 1)/7
Let k(q) be the first derivative of q**6/2 - 9*q**4/2 + 8*q**3 - 9*q**2/2 + 13. Find v, given that k(v) = 0.
-3, 0, 1
Let h(l) be the first derivative of l**4/18 + 4*l**3/9 + 4*l**2/3 - l + 7. Let t(k) be the first derivative of h(k). Solve t(j) = 0 for j.
-2
Let o be (6/(-4))/((-3)/4). Suppose 2*i**3 + 2*i**3 + o*i**2 + 2*i**2 - 10*i**2 - 4*i = 0. What is i?
-1/2, 0, 2
Let i(f) = -9*f**5 - 3*f**4 + f**3 - 5*f - 5. Let h = 4 - 7. Let n(x) = -5*x**5 - x**4 + x**3 - 3*x - 3. Let z(p) = h*i(p) + 5*n(p). Solve z(q) = 0 for q.
-1, 0
Let n = -16 + 19. Let m(f) be the first derivative of 16*f - 88*f**2 - 91*f**5 + 1225/6*f**6 + 664/3*f**3 - n - 206*f**4. Suppose m(i) = 0. What is i?
-1, 2/7, 2/5
Let j(z) = 2 + z**2 - 7*z - 5 + 8*z**2 - z**3 - 1. Let n be j(8). Factor 2*g**3 + 0 + 4 + 6*g + n + 10*g**2 + 10*g.
2*(g + 1)*(g + 2)**2
Let l(s) = s**2 - 2*s + 1. Let h(y) = -3*y**2 + 6*y - 3. Let j = 9 - 12. Let k(g) = j*h(g) - 8*l(g). Factor k(b).
(b - 1)**2
Suppose -15*p + 6*p = 0. Let j(y) be the third derivative of p*y + 0 - 3*y**2 - 1/24*y**4 - 1/60*y**5 + 0*y**3. Solve j(a) = 0 for a.
-1, 0
Let q be (24/110 - 0) + (-64)/(-352). Solve 2/5*b**3 + 0*b - q*b**4 + 0 + 0*b**2 = 0.
0, 1
Let j(i) be the third derivative of i**8/13440 - i**7/1120 + i**6/240 + i**5/15 + 7*i**2. Let n(z) be the third derivative of j(z). What is q in n(q) = 0?
1, 2
Let c(a) = a - a**2 + 2 + 1 - 4. Let b be (-1)/((-2)/3 - -1). Let g(v) = -2*v**2 + 2*v - 5. Let w(h) = b*c(h) + g(h). Factor w(p).
(p - 2)*(p + 1)
Let v(f) be the second derivative of -f**7/378 - 7*f**6/270 - f**5/10 - 5*f**4/27 - 4*f**3/27 - 59*f. Factor v(w).
-w*(w + 1)*(w + 2)**3/9
Factor 6/7*b - 2/7*b**2 - 4/7.
-2*(b - 2)*(b - 1)/7
Let h(k) be the third derivative of k**7/1260 - k**6/180 + k**5/60 - k**4/8 + 2*k**2. Let m(f) be the second derivative of h(f). Let m(o) = 0. Calculate o.
1
Let h(k) be the third derivative of -k**8/3528 - k**7/2205 + k**6/252 - k**5/210 - 36*k**2. Factor h(i).
-2*i**2*(i - 1)**2*(i + 3)/21
Let f(t) be the first derivative of -1 + 0*t + 2/5*t**2 - 2/15*t**3. Factor f(o).
-2*o*(o - 2)/5
Let z(h) be the first derivative of h**5/35 - h**4/28 - 2*h**3/7 + 2*h**2/7 + 8*h/7 - 15. Factor z(w).
(w - 2)**2*(w + 1)*(w + 2)/7