hat is z?
-1, 0
Let z(r) be the first derivative of 0*r + 1/3*r**2 + 0*r**4 + 4/15*r**5 - 1/9*r**6 + 2 - 4/9*r**3. Factor z(k).
-2*k*(k - 1)**3*(k + 1)/3
Let y(l) be the second derivative of l**6/30 + l**5/20 - 2*l. Determine v, given that y(v) = 0.
-1, 0
Let p(r) be the first derivative of 1/9*r**6 + 2/15*r**5 - 2/9*r**3 - 1/6*r**4 + 0*r + 0*r**2 + 1. What is w in p(w) = 0?
-1, 0, 1
Suppose 0 + 4/9*h + 2*h**2 = 0. What is h?
-2/9, 0
Let a = 170 + -100. Let u be 20/a - 0/(-3). Let u*l**3 + 2/7*l**4 + 0 - 2/7*l - 2/7*l**2 = 0. Calculate l.
-1, 0, 1
Let x(j) be the third derivative of -7/80*j**5 + 1/280*j**7 + 0 + 3/80*j**6 - 1/224*j**8 + 0*j - 2*j**2 + 1/16*j**4 + 0*j**3. Find g such that x(g) = 0.
-2, 0, 1/2, 1
Let w(d) be the third derivative of d**6/40 - d**5/10 + d**4/8 - 12*d**2. What is r in w(r) = 0?
0, 1
Solve 3*n**2 - 18*n**4 - 7*n**3 + 31*n**3 - 27*n**5 + 3*n + 15*n**2 = 0 for n.
-1, -1/3, 0, 1
Let d be 75/100*(2 - 22/12). What is q in -d + 3/8*q - 3/8*q**2 + 1/8*q**3 = 0?
1
Let b(a) be the first derivative of a**6/9 + 2*a**5/3 + 7*a**4/6 - 2*a**3/9 - 8*a**2/3 - 8*a/3 - 21. Let b(f) = 0. Calculate f.
-2, -1, 1
Let g(z) be the second derivative of -3*z**5/20 + 5*z**4/4 - 4*z**3 + 6*z**2 + 37*z. Factor g(o).
-3*(o - 2)**2*(o - 1)
Suppose -6 + 4*b - 2/3*b**2 = 0. Calculate b.
3
Let o be (0/1)/(-3 + 5). Suppose -g + 3*g - 4 = o. Factor -5*s**2 - 2*s + 0 - s + g.
-(s + 1)*(5*s - 2)
Let c(j) be the third derivative of -j**6/1080 + j**4/72 - j**3/27 + 4*j**2. Solve c(o) = 0 for o.
-2, 1
Find a such that 12/11*a**2 + 2/11 + 8/11*a**3 + 2/11*a**4 + 8/11*a = 0.
-1
Let v(j) be the third derivative of -j**8/168 + 2*j**7/105 - j**5/15 + j**4/12 - 3*j**2. Factor v(m).
-2*m*(m - 1)**3*(m + 1)
Suppose 0 = -5*c + 5*r - 0*r + 10, -5*c = 3*r + 6. Factor 0 - 1/5*i**4 + c*i**2 + 1/5*i**3 + 0*i.
-i**3*(i - 1)/5
Suppose 5*x + 34 = 3*j, 0*j + j = x + 8. Let n = 0 + j. Factor -2*l**2 + 4 + l**n - 4.
l**2*(l - 2)
Let y be 7/(-2) - (-10 + 6 + 0). Factor 1/2*m**2 - y*m + 0.
m*(m - 1)/2
Let b(s) = s**3 - 7*s**2 + 6*s + 2. Let o be b(6). Suppose -o*d - 4 = -3*y, 5*d = 5*y - 0*y. Factor 2*h**2 - 4*h**3 + 5*h**y - 3*h**4 + 0*h**2.
2*h**2*(h - 1)**2
Factor -63/8*z - 81/8 + 17/8*z**2 - 1/8*z**3.
-(z - 9)**2*(z + 1)/8
Let d be ((-2)/2)/((56/(-12))/7). Let j(i) be the first derivative of 0*i - 1 + i**3 - d*i**2. What is n in j(n) = 0?
0, 1
Find o, given that 7*o**3 + 10*o**3 - 2*o**5 - 15*o**3 = 0.
-1, 0, 1
Let q(p) = -5*p - 33. Let y be q(-7). Factor 0 + 2/3*f + 1/3*f**y.
f*(f + 2)/3
Let c(l) be the second derivative of 3/2*l**2 + 0 + 3*l - 1/3*l**4 - 11/6*l**3. Factor c(p).
-(p + 3)*(4*p - 1)
Let r(i) = i**2 + 3*i - 5. Let m be (-2)/(-1 + 1/2). Suppose 3*a = m*a - 1. Let u(b) = b - 1. Let y(j) = a*r(j) - 5*u(j). Find h such that y(h) = 0.
0, 2
Let j(b) be the second derivative of -5*b + 1/10*b**5 - 1/3*b**3 - b**2 + 1/6*b**4 + 0. Factor j(p).
2*(p - 1)*(p + 1)**2
Determine v, given that -8*v - 16 + 34*v**2 - 2*v**3 + 4*v**3 - 30*v**2 = 0.
-2, 2
Let l = -49/144 + 9/16. Factor 2/9*t - l*t**3 + 0 + 0*t**2.
-2*t*(t - 1)*(t + 1)/9
Suppose 9*f - 10 = 4*f. Let i be 0 - (-1)/6*f. Factor -1/3 - 1/3*w**3 + 1/3*w**2 + i*w.
-(w - 1)**2*(w + 1)/3
Let m(x) be the second derivative of -1/4*x**4 - 5*x + 0*x**2 + 1/6*x**3 - 1/4*x**5 + 0 + 1/10*x**6 + 2/21*x**7. Factor m(p).
p*(p - 1)*(p + 1)**2*(4*p - 1)
Factor -8/15*x**4 + 0*x + 0 + 2/3*x**3 - 2/15*x**2.
-2*x**2*(x - 1)*(4*x - 1)/15
Let y = 22 + -22. Let z(c) be the third derivative of -1/15*c**5 + 1/60*c**6 + c**2 + 1/12*c**4 + y + 0*c**3 + 0*c. Factor z(w).
2*w*(w - 1)**2
Let h(l) = -l - 9. Let t be h(-7). Let u be ((-18)/t)/3 - 0. Find w such that 0*w + 0 + 0*w**2 + 2/3*w**u = 0.
0
Let t be -5 + 3 + 3 + -1. Factor t + 18/7*m**2 - 4/7*m.
2*m*(9*m - 2)/7
Let i(v) be the third derivative of 0*v**3 + 0*v**7 + 0*v**4 - 3*v**2 + 0*v**5 + 1/1344*v**8 - 1/480*v**6 + 0 + 0*v. Factor i(t).
t**3*(t - 1)*(t + 1)/4
Let n(y) be the first derivative of -y**6/60 - y**5/30 + y**4/12 + y**3/3 + y**2 + 1. Let u(f) be the second derivative of n(f). Determine b so that u(b) = 0.
-1, 1
Let a(i) = 2*i**2 + 16*i + 18. Let x be a(-7). Let n(p) be the second derivative of 0 - 1/6*p**3 + 0*p**2 - 2*p - 1/12*p**x. Find v, given that n(v) = 0.
-1, 0
Let g(m) = 4*m**2 - 9*m - 1. Let v(j) = 20*j**2 - 44*j - 4. Let f(p) = 28*g(p) - 6*v(p). Find l such that f(l) = 0.
1/2, 1
Let k be 3/(-6)*-2 + 3. Suppose -k*l + 4 = -12, -4*z - 12 = -5*l. Factor -4*t**2 - 3*t**2 + 2*t**4 + t**z + 4*t.
2*t*(t - 1)**2*(t + 2)
Let w(j) = j**2 - j - 4. Let c be w(0). Let b = c + 8. Suppose -2*q**4 + 5*q**b + 1 - 4*q**4 + 2*q**3 - 2*q = 0. What is q?
-1, 1
Suppose 26*t - 4*t**2 - 16*t - 16 - 26*t = 0. What is t?
-2
Let t(j) be the third derivative of j**8/1176 + 2*j**7/735 - j**5/105 - j**4/84 - 4*j**2. Factor t(q).
2*q*(q - 1)*(q + 1)**3/7
Let h(s) be the second derivative of s**6/135 - s**5/9 - 23*s**4/54 - 4*s**3/9 - 17*s. Factor h(m).
2*m*(m - 12)*(m + 1)**2/9
Let s(j) = -j**4 + 24*j**3 - 16*j**2 + 7*j + 7. Let l(p) = -12*p**3 + 8*p**2 - 4*p - 4. Let v(g) = -7*l(g) - 4*s(g). What is d in v(d) = 0?
0, 1, 2
Let m(z) = -9*z**3 + 12*z**2 - 13*z + 6. Let q(r) = -26*r**3 + 36*r**2 - 38*r + 17. Let i(h) = 11*m(h) - 4*q(h). Factor i(d).
(d - 1)**2*(5*d - 2)
Let y(b) be the third derivative of b**5/135 - 2*b**4/27 + 2*b**2 + 5. Factor y(v).
4*v*(v - 4)/9
Let z be (1 + -4 + (-6)/(-2))*1. Let h = -21/85 + 11/17. Factor h*y**4 + z*y + 2/5*y**2 + 4/5*y**3 + 0.
2*y**2*(y + 1)**2/5
Suppose 5*f - f = 0. Solve -2*t**3 + f + 5 - 2 + 6*t + 1 = 0 for t.
-1, 2
Let v(f) = f**3 - f + 4. Let j be v(0). Let g(u) be the second derivative of 1/15*u**5 + 0*u**j - 3*u - 1/9*u**3 + 0 + 0*u**2 + 0*u**6 - 1/63*u**7. Factor g(x).
-2*x*(x - 1)**2*(x + 1)**2/3
Factor 3/8*v**3 + 0*v + 0 - 3/8*v**2.
3*v**2*(v - 1)/8
Let x(f) be the first derivative of 0*f**2 + 15/4*f**4 - 5/2*f**6 - 2 + 6/5*f**5 - 2*f**3 + 0*f. Determine u, given that x(u) = 0.
-1, 0, 2/5, 1
Suppose -3*j + 0*j + 6 = 0. Let k = 0 + j. Factor 5*b + 2*b - 5*b + 7*b**k.
b*(7*b + 2)
Let j(a) be the second derivative of a**6/6 - a**5/4 - 5*a**4/12 + 5*a**3/6 + 4*a. Find l, given that j(l) = 0.
-1, 0, 1
Let u(f) be the first derivative of 4*f + 2 + 0*f**2 - 1/3*f**3. Suppose u(v) = 0. What is v?
-2, 2
Let x(m) = 4 + 2*m**2 - 2 - m**2 - m. Let r(z) = -2*z**2 + 3*z - 5. Let q(g) = -2*r(g) - 5*x(g). Let q(i) = 0. What is i?
-1, 0
Let j = 28 - 21. Let t(n) be the third derivative of 1/90*n**5 + 2*n**2 + 0 + 0*n + 1/63*n**j - 2/45*n**6 + 0*n**3 + 1/18*n**4. Factor t(l).
2*l*(l - 1)**2*(5*l + 2)/3
Let i(x) be the first derivative of x**7/5040 - x**5/720 + 4*x**3/3 + 4. Let v(a) be the third derivative of i(a). Factor v(z).
z*(z - 1)*(z + 1)/6
Let t(h) = -h**2 - h - 1. Let z(u) = 1. Let a(j) = t(j) + 3*z(j). Let a(s) = 0. Calculate s.
-2, 1
Let w(d) be the first derivative of 0*d + 0*d**2 + 1/6*d**5 - 1/18*d**3 - 1/12*d**6 - 1/24*d**4 - 3. What is a in w(a) = 0?
-1/3, 0, 1
Solve -3/5*u**4 + 0*u**2 + 0 + 0*u - 3/5*u**3 = 0.
-1, 0
Suppose 0 = 5*g - 4*f - 50, -3 = -3*g - 3*f - 0*f. Let -x - 4*x**2 + g*x**2 + x**2 + 3*x = 0. What is x?
-2/3, 0
Let m(z) be the first derivative of z**6/780 - z**5/390 - z**4/156 + z**3/39 - z**2 - 5. Let a(b) be the second derivative of m(b). Factor a(n).
2*(n - 1)**2*(n + 1)/13
Let y be 1/(-2) - (-28)/8. Suppose -5*c - 3*a = -2*a - 7, 2*a = -y*c. Factor 1/3*f**3 + 0 + 0*f - 1/3*f**c.
f**2*(f - 1)/3
Suppose 4*t + 2 = 14. Suppose 6*x = x. Solve x*q**t + 1/4*q**5 - 1/4*q + 0 - 1/2*q**2 + 1/2*q**4 = 0 for q.
-1, 0, 1
Suppose -2*h = -3*h. Suppose h = 4*t - 3*t + 2, -4*t = -3*a + 17. Find s, given that -2*s - s**5 + 5*s**3 - s**5 - s**a = 0.
-1, 0, 1
Suppose 4*i - 6 = -0*i + v, -5*i = v - 12. Factor -8/9*g**2 + 0*g + 0 + 0*g**3 + i*g**4.
2*g**2*(3*g - 2)*(3*g + 2)/9
Suppose -3*c + 1 + 8 = 0. Find z such that -4*z - 2 + z + c*z + 2*z**2 = 0.
-1, 1
Let z(j) = -j**5 + 6*j**4 + 4*j**3 - 8*j**2 - j + 4. Let p(m) = 3*m**5 - 19*m**4 - 13*m**3 + 24*m**2 + 3*m - 12. Let o(g) = -2*p(g) - 7*z(g). Factor o(a).
(a - 4)*(a - 1)**2*(a + 1)**2
Let p = 9/11 + -41/77. Solve 0 - 2/7*n**2 + p*n = 0 for n.
0, 1
Suppose -2*o - o + 15 = 0. Let k = -3 + o. Solve 3*r**4 - 4 - r**k - 2*r**5 + 4 = 0.
-1/2, 0, 1
Let v(w) be the third derivative of 0*w - 3*w**2 + 0 