 1. Let d(v) = v**2 + v. Let s(r) = c*q(r) - 11*d(r). Find z, given that s(z) = 0.
-2, 1
Let b(h) be the first derivative of h**6/12 - 3*h**5/10 + 3*h**4/8 - h**3/6 - 23. Factor b(u).
u**2*(u - 1)**3/2
Let x(d) be the second derivative of -d**3/2 - 15*d**2/2 - 4*d. Let n be x(-6). Suppose -2/5*s**4 + 0*s + 0 + 4/5*s**n - 2/5*s**2 = 0. What is s?
0, 1
Let -2/15*k**3 + 2/15*k - 8/15 + 8/15*k**2 = 0. What is k?
-1, 1, 4
Let p(b) = b**2 + 3*b + 4. Let f be p(-3). Find c such that 6*c**2 - 3*c**5 - 8*c**4 + 2*c + 2*c**f + c + 0*c = 0.
-1, 0, 1
Let n(y) be the second derivative of 0*y**5 - 1/3*y**3 + 0*y**2 - 1/36*y**4 + y + 0 + 1/540*y**6. Let u(h) be the second derivative of n(h). Factor u(q).
2*(q - 1)*(q + 1)/3
Let f(k) = 4*k**2 + 3*k - 4. Let y(l) = -3*l**2 - 2*l + 3. Let o(i) = 2*f(i) + 3*y(i). Factor o(v).
-(v - 1)*(v + 1)
Solve -p**2 + 1/4*p**4 + 1/2*p**3 - 1/2*p + 3/4 = 0 for p.
-3, -1, 1
Let v = 497 - 495. Determine n, given that 1/2*n**v + 1 + 3/2*n = 0.
-2, -1
Let f(c) be the second derivative of -c**6/15 - 3*c**5/10 - c**4/2 - c**3/3 + 72*c. Determine b so that f(b) = 0.
-1, 0
Factor 1/3*p + 0 + 1/3*p**3 - 2/3*p**2.
p*(p - 1)**2/3
Let x(n) = n**2 - n - 3. Let u be x(3). Suppose -u*r + 4*r = 0. Factor r*f**2 + 0 + 0*f**4 + 2/11*f - 4/11*f**3 + 2/11*f**5.
2*f*(f - 1)**2*(f + 1)**2/11
Let g(l) be the first derivative of -l**7/40 - l**6/60 + 7*l**5/40 + l**4/4 - 2*l**3/3 - 1. Let u(j) be the third derivative of g(j). Factor u(x).
-3*(x - 1)*(x + 1)*(7*x + 2)
Let m be (-3)/15*-3 + 6/(-10). Factor -1/3*x**2 + 1/3*x + m.
-x*(x - 1)/3
Let n be 4/(-6)*(1 + (-55)/40). Factor 1/4 + n*d**2 + 1/2*d.
(d + 1)**2/4
Let s(b) = 10*b**2 - 18*b + b**2 - 4*b**2 + 11. Suppose -4 = n - 11. Let f(p) = 8*p**2 - 18*p + 10. Let i(x) = n*f(x) - 6*s(x). Factor i(a).
2*(a - 1)*(7*a - 2)
Let z(c) be the third derivative of -7*c**6/24 - c**5/3 + 13*c**2. Factor z(r).
-5*r**2*(7*r + 4)
Let x(k) be the first derivative of 2/5*k**2 + 1/5*k**3 - 6 + 1/25*k**5 - 1/5*k**4 - 4/5*k. Factor x(r).
(r - 2)**2*(r - 1)*(r + 1)/5
Let f(b) = 5*b - 6. Let n(z) = -11*z + 13. Let v(j) = 13*f(j) + 6*n(j). Let d be v(-2). Find l, given that -2/7*l + 0*l**d + 0 + 2/7*l**3 = 0.
-1, 0, 1
Let n(h) be the second derivative of -h**6/45 + h**5/30 + h**4/9 + 12*h. Factor n(o).
-2*o**2*(o - 2)*(o + 1)/3
Let k(h) be the first derivative of 1/6*h**4 + 0*h + 0*h**2 - 2 - 2/9*h**3. Determine c so that k(c) = 0.
0, 1
Let p(w) = 3*w**2 - 22*w - 169. Let f(i) = -4*i**2 + 21*i + 169. Let k(g) = 4*f(g) + 5*p(g). Factor k(b).
-(b + 13)**2
Let w = 201 - 134. Let s = w - 131/2. Find p such that 0*p + 1/2*p**4 + 0 - 1/2*p**2 + s*p**5 - 3/2*p**3 = 0.
-1, -1/3, 0, 1
Let d = -15 + 46/3. Let r(o) be the first derivative of 1/6*o**6 - 1/6*o**4 - 1/3*o + 3 - d*o**5 + 2/3*o**3 - 1/6*o**2. Factor r(i).
(i - 1)**3*(i + 1)*(3*i + 1)/3
Suppose -2*u = -4*u + 2. Let i(h) = 3*h**2 - h. Let s be i(u). Find q, given that 0 + 0 + s*q**3 = 0.
0
Let c(q) be the first derivative of q**3/3 - 10*q**2 + 100*q - 26. Suppose c(a) = 0. What is a?
10
Find n such that 0 + 0 - 38*n**3 + 6*n**2 + 2*n**5 + 40*n**3 - 6*n**4 - 4*n = 0.
-1, 0, 1, 2
Let i(g) be the first derivative of g**4/2 + 2*g**3/3 - 8. Solve i(b) = 0.
-1, 0
Let c(d) = -d**3 + 3*d**2 - 2. Let v(n) = 2*n**3 - 7*n**2 + 5. Let o(k) = 15*c(k) + 6*v(k). Determine a, given that o(a) = 0.
0, 1
Let p(x) be the third derivative of 0*x**3 + 0*x + 5*x**2 + 0 + 1/300*x**5 - 1/1050*x**7 - 1/120*x**4 + 1/600*x**6. Factor p(u).
-u*(u - 1)**2*(u + 1)/5
Suppose -2*r + 15 = r, -a - 3*r = -19. Factor -3*k + 1 - 2*k**3 + k**2 + k**5 + a*k - 3*k**2 + k**4.
(k - 1)**2*(k + 1)**3
Let l(m) be the third derivative of -m**7/105 - m**6/30 + m**4/6 + m**3/3 + 7*m**2. Factor l(y).
-2*(y - 1)*(y + 1)**3
Find o, given that 0 + 3/7*o**3 - 12/7*o - 9/7*o**2 = 0.
-1, 0, 4
Let o(l) be the first derivative of 5*l**4/8 + 4*l**3/3 + l**2/4 - l - 23. Factor o(n).
(n + 1)**2*(5*n - 2)/2
Let n = 33 + -29. Let k = 263/12 - 62/3. Find d such that -3/4*d**2 + 1/4*d**3 + 1/4*d**n - k*d - 1/2 = 0.
-1, 2
Factor -2/11 + 2/11*u**2 - 2/11*u + 2/11*u**3.
2*(u - 1)*(u + 1)**2/11
Let r(c) be the third derivative of c**8/2184 - c**7/273 + c**6/78 - c**5/39 + 5*c**4/156 - c**3/39 + 11*c**2. Solve r(z) = 0.
1
Let w(g) be the first derivative of -g**4/14 - 10*g**3/21 - 8*g**2/7 - 8*g/7 + 3. Factor w(c).
-2*(c + 1)*(c + 2)**2/7
Let j(w) be the first derivative of w**4/48 + w**3/12 + w**2/12 + 22. Factor j(u).
u*(u + 1)*(u + 2)/12
Let o(h) be the third derivative of h**5/210 + h**4/84 - 2*h**3/21 - 8*h**2. Factor o(w).
2*(w - 1)*(w + 2)/7
Let q(z) be the third derivative of z**5/30 - z**4/30 + 3*z**2. Factor q(b).
2*b*(5*b - 2)/5
Let v be (4/(-78))/((-4)/(-36)*-3). Factor -v*n**2 - 2/13*n**3 + 2/13*n**4 + 0 + 2/13*n.
2*n*(n - 1)**2*(n + 1)/13
Let r be 6/(-7)*-1 - (-520)/(-1456). Find v such that -1/2*v**3 + r*v + v**2 - 1 = 0.
-1, 1, 2
Let c(u) = -u - 15. Let x be c(-15). What is h in 8/5*h**4 + 2/5*h**5 + 2*h**3 + 4/5*h**2 + x + 0*h = 0?
-2, -1, 0
Let b(d) be the first derivative of -5*d**3/3 + 25*d**2/2 - 30*d + 22. Let b(p) = 0. Calculate p.
2, 3
Let f = 1334/4571 - 4/653. Factor -f*w - 4/7 + 2/7*w**2.
2*(w - 2)*(w + 1)/7
Suppose -3*z + 9 = 3*x, -3 = 3*z - 7*z + 5*x. Factor 3*a**2 - 11*a**2 - 3*a + 7*a**2 - z.
-(a + 1)*(a + 2)
Suppose -4*q = -2*q. Let t = -1 - -3. Let q*m**2 - t*m**2 + 3*m + 5*m**2 = 0. What is m?
-1, 0
Let h(n) be the first derivative of -n**6/12 - 3*n**5/10 - 3*n**4/8 - n**3/6 - 2. Factor h(w).
-w**2*(w + 1)**3/2
Let z be (-318)/(-48) + 2 - 8. Factor 1/4 - 3/8*h**3 + z*h - 1/2*h**2.
-(h - 1)*(h + 2)*(3*h + 1)/8
Let b(u) = -1 + 8*u**2 - 9*u + 8*u**2 - 6*u**2 + 7. Let d(r) = -3*r**2 + 3*r - 2. Let y(g) = 2*b(g) + 7*d(g). What is v in y(v) = 0?
1, 2
Let g(z) be the second derivative of 1/9*z**3 - 2*z + z**2 + 0 + 1/180*z**5 - 1/24*z**4. Let n(t) be the first derivative of g(t). Solve n(j) = 0 for j.
1, 2
Let g(o) be the first derivative of -1/4*o**2 - 1 - 1/8*o**3 - 1/48*o**4 + 3*o. Let j(y) be the first derivative of g(y). Factor j(l).
-(l + 1)*(l + 2)/4
Let s(t) be the third derivative of -t**6/40 + 17*t**5/140 - 13*t**4/56 + 3*t**3/14 - 6*t**2. Factor s(j).
-3*(j - 1)**2*(7*j - 3)/7
Let b be (-2)/8 - (-148)/720. Let n = 152/45 + b. Factor 2/3 + n*l + 8/3*l**2.
2*(l + 1)*(4*l + 1)/3
Suppose 16*r**3 - 32/5*r**5 - 18/5 - 32/5*r**2 - 66/5*r + 32/5*r**4 = 0. What is r?
-1, -1/2, 3/2
Let a(c) = -c**3 - 5*c**2 + 5*c - 2. Let k be a(-6). Suppose -24 = -2*r + 2*l, -22 = -r + k*l - l. Factor r*z + 13*z - 8*z + z**3 + 3*z**2 - 9*z**2 - 8.
(z - 2)**3
Factor -18/11*o + 14/11*o**2 + 4/11.
2*(o - 1)*(7*o - 2)/11
Let -7*l**4 - l**2 + 9*l**2 + 3*l**4 - 4 = 0. What is l?
-1, 1
Let f = 73/582 + 4/97. Factor -1/6*k**3 + 0*k**2 + f*k + 0.
-k*(k - 1)*(k + 1)/6
Let k(d) be the second derivative of 3*d + 0*d**2 + 1/2*d**4 + 0 - 1/6*d**3 - 9/20*d**5 + 2/15*d**6. Determine p, given that k(p) = 0.
0, 1/4, 1
Let c = -21 - -23. Suppose -c*v + 13 = 5*w - 12, 0 = -4*v - 4*w + 20. Factor v - 1/4*m**2 + 0*m.
-m**2/4
Determine l so that 3/4*l**2 + 2*l**3 - 3*l - 1 - 3/4*l**4 = 0.
-1, -1/3, 2
Let a be (-13)/(-10) + 1/(-2). Let x = -2/95 - -8/19. Let -x*g**4 + 4/5*g + 2/5 - a*g**3 + 0*g**2 = 0. Calculate g.
-1, 1
Let k(l) = -l**2 + l. Let y(b) = b + 5. Let z be y(-7). Let a be 2 + z*1 + 6. Let r(m) = -3*m**4 + 8*m**3 - m**2 - 4*m. Let c(w) = a*k(w) + r(w). Factor c(j).
-j*(j - 1)**2*(3*j - 2)
Let u be (-77)/(-98) + (-2)/4. Let j(z) = -3*z**3 + 2*z**2 + z. Let l be j(-1). Factor -4/7*b**2 + 0*b + 2/7 + 0*b**3 + u*b**l.
2*(b - 1)**2*(b + 1)**2/7
Determine p, given that -4/3*p + 1/3*p**2 + 4/3 = 0.
2
Let h(z) be the second derivative of 1/20*z**5 + 0*z**4 + 0 + 4*z - 1/15*z**6 + 0*z**3 + 1/42*z**7 + 0*z**2. Factor h(w).
w**3*(w - 1)**2
Let h(i) be the second derivative of -i**5/60 - i**4/18 - i**3/18 + 13*i. Suppose h(z) = 0. What is z?
-1, 0
Suppose 0 + 3*x**4 - 2*x - 13/2*x**3 + 6*x**2 - 1/2*x**5 = 0. Calculate x.
0, 1, 2
Suppose 8*b = 3*b + 10. Let x = -2 + b. Factor x*h**3 + 0*h - 4/3*h**2 + 2/3 + 2/3*h**4.
2*(h - 1)**2*(h + 1)**2/3
Suppose 0 = 3*a - 2*a. Let a - h**2 + 1/2*h + 1/2*h**3 = 0. What is h?
0, 1
Let k(n) = 16*n**3 + 4*n**2 + 10*n. Let m(o) = -3*o**3 - o**2 - 2*o. Let t(x) = 4*k(x) + 22*m(x). What is l in t(l) = 0?
-2, -1, 0
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