i).
(i + 1)**2/4
Suppose 10*r + 5*r - 45 = 0. Factor 1/4 - 1/4*c**2 + 1/4*c - 1/4*c**r.
-(c - 1)*(c + 1)**2/4
Let f(a) be the second derivative of -a**5/20 + a**4/2 + 2*a**2 + a. Let j be f(6). Suppose -2*v**4 - 2*v**3 - v**2 - v**j + 2*v**4 = 0. Calculate v.
-1, 0
Factor -o - 3/2 + 1/2*o**2.
(o - 3)*(o + 1)/2
Let p(m) = -2*m + 3*m + 2 + 11 - 2. Let l be p(-8). Solve 0 + 2/7*f**4 + 0*f**l - 2/7*f**2 + 0*f = 0.
-1, 0, 1
Determine y so that 0 + 1/2*y**2 + 3/2*y = 0.
-3, 0
Let h(k) be the third derivative of -1/30*k**6 + 0*k**4 - 2/35*k**7 + 0 - 2*k**2 + 0*k**3 - 1/180*k**5 + 0*k. What is i in h(i) = 0?
-1/6, 0
Let p be 1/(-4) - ((-82)/(-56) - 2). What is h in -p*h**3 + 8/7*h**2 + 4/7 - 10/7*h = 0?
1, 2
Let g = 1046 - 1043. Factor -1/2*x**2 + 3/2*x**4 - 1 - 5/2*x**g + 5/2*x.
(x - 1)**2*(x + 1)*(3*x - 2)/2
Let w be (25/(-15) + 2)*0/2. What is f in -8/5*f**2 + 0 + 0*f**3 - 2/5*f**5 + w*f + 6/5*f**4 = 0?
-1, 0, 2
Let h(w) be the third derivative of w**6/1020 - w**5/510 - w**4/204 + w**3/51 + 6*w**2. Suppose h(y) = 0. What is y?
-1, 1
Let w(f) be the first derivative of 3*f**5/35 - 3*f**4/14 - 3*f**3/7 - 38. Let w(j) = 0. Calculate j.
-1, 0, 3
Let c(t) be the third derivative of 2*t**7/35 + 7*t**6/30 - 2*t**5/5 + 9*t**2 + 4*t. Determine a, given that c(a) = 0.
-3, 0, 2/3
Let t(x) = x**5 + 5*x**4 - x**3 + x**2 + 3*x - 3. Suppose 0 = 4*y - 3 - 5. Let c(u) = 6 + 0*u + 4*u**4 - 8 + 2*u. Let d(i) = y*t(i) - 3*c(i). Solve d(o) = 0.
-1, 0, 1
Let k(w) = -w - 7. Let m be k(-9). Let v be m/(-6)*(-6 - -5). Factor v*l**2 + 2/3*l + 1/3.
(l + 1)**2/3
Let h = -12/35 - -2207/6335. Let l = h - -721/543. Factor 0 + l*j**2 - 2/3*j**3 - 2/3*j.
-2*j*(j - 1)**2/3
Let i(j) be the third derivative of 0*j**4 - 1/720*j**6 + 0 - 1/180*j**5 + 0*j**3 + 4*j**2 + 0*j. Solve i(c) = 0 for c.
-2, 0
Suppose c = -5*p + 36 + 15, 0 = -5*c + 5. Suppose 0 = -4*x + 3*f + 15, 5 = -x - 3*f - p. Find h, given that 1/2*h**2 + x*h - 1/2 = 0.
-1, 1
Let i(f) be the third derivative of -5/168*f**4 + 1/210*f**6 + 1/2352*f**8 + 0*f + 1/210*f**5 + 1/21*f**3 - 2/735*f**7 - 8*f**2 + 0. What is r in i(r) = 0?
-1, 1, 2
Let y(m) be the second derivative of 0 - 1/24*m**4 - 6*m - 1/2*m**3 - 9/4*m**2. Factor y(n).
-(n + 3)**2/2
Let s(t) = t - 3. Let y be s(6). Let w be (-4)/2*y/(-2). Solve b**3 - 2*b**2 + b**2 - w*b**3 + 3*b**3 = 0 for b.
0, 1
Let t(s) = -41 - 9*s**2 + s**3 + 45 + 3*s**2 + 8*s. Let r(o) = o**2. Let h(m) = -22*r(m) - 2*t(m). Factor h(c).
-2*(c + 1)*(c + 2)**2
Let x(l) be the first derivative of 1/40*l**5 - l**3 + 1/16*l**4 - 1/80*l**6 + 0*l**2 + 0*l - 3. Let q(p) be the third derivative of x(p). Solve q(c) = 0.
-1/3, 1
Let i(x) = x - 1. Let k(s) = -5*s**2 + 8*s + 17. Let v(d) = 2*i(d) + k(d). Factor v(m).
-5*(m - 3)*(m + 1)
Let a = 107/385 - -3/35. What is i in -14/11*i**2 + 10/11*i + a = 0?
-2/7, 1
Suppose 2*v = 7 - 3. Let o(h) be the third derivative of 0*h**3 + 2*h**v + 0*h + 1/12*h**4 - 1/30*h**5 + 0. Factor o(k).
-2*k*(k - 1)
Let p(y) be the second derivative of 2/15*y**4 - 1/5*y**2 - 1/20*y**5 + 0 - 1/30*y**3 + 2*y. Factor p(g).
-(g - 1)**2*(5*g + 2)/5
Let i = 9 + -5. Let u(o) be the third derivative of -1/6*o**3 + 0*o + 1/120*o**5 + 2*o**2 + 0 - 1/48*o**i. Factor u(x).
(x - 2)*(x + 1)/2
Let t(n) = -13 + 2*n**3 + 4*n**3 - 4*n**3 + n**2 + 10*n**2. Let x(g) = 2*g**3 + 10*g**2 - 12. Let o(w) = -4*t(w) + 5*x(w). Factor o(l).
2*(l - 1)*(l + 2)**2
Let i = 1 - 1. Let m = 138 - 135. Factor 4/9*w**2 + 2/9*w**5 - 4/9*w**4 + 0 - 2/9*w + i*w**m.
2*w*(w - 1)**3*(w + 1)/9
Let l(b) = 3*b**2 + 2*b - 1. Let i be l(1). Factor -3*o + 0*o**3 + 3*o - 2*o**i + 2*o**5 - 2*o**3 + 2*o**2.
2*o**2*(o - 1)**2*(o + 1)
Let m(b) = 56*b**2 + 28*b - 4. Let h(i) = 37*i**2 + 19*i - 3. Let o(z) = 8*h(z) - 5*m(z). Suppose o(y) = 0. Calculate y.
-1, 1/4
Let z = -1487/3 - -497. Solve -1/3*u**3 - 4/3*u + z*u**2 + 0 = 0 for u.
0, 2
Let h(k) = 7*k**2 + 4*k + 1. Let j(p) = 6*p**2 + 4*p + 1. Suppose 11 = 4*n - 1. Let w(s) = n*h(s) - 4*j(s). Factor w(a).
-(a + 1)*(3*a + 1)
Let n = 586/63 - 62/7. Let -n + 10/9*f + 2/9*f**3 - 8/9*f**2 = 0. What is f?
1, 2
Determine q so that 3/5*q**3 + 24/5*q + 21/5*q**2 - 48/5 = 0.
-4, 1
Let a(o) be the third derivative of 169*o**6/480 + 221*o**5/240 + 7*o**4/12 + o**3/6 + 9*o**2. Factor a(n).
(n + 1)*(13*n + 2)**2/4
Let n = 17 - 8. Solve -n + 2*f**2 - f + 7 - f**2 = 0.
-1, 2
Factor -12/17*o - 2/17*o**2 + 14/17.
-2*(o - 1)*(o + 7)/17
Let k(q) be the third derivative of 0*q - 1/30*q**5 - 2*q**2 - 1/336*q**8 + 1/24*q**4 + 0 + 0*q**3 + 1/105*q**7 + 0*q**6. Find u such that k(u) = 0.
-1, 0, 1
Let s(b) = b**4 + b**3 - b**2 + b. Let p(u) = -u**5 + 6*u**4 + u**3 - 3*u**2 + 3*u. Let r(t) = -2*p(t) + 6*s(t). Factor r(v).
2*v**3*(v - 2)*(v - 1)
Let s(b) be the first derivative of b**3/6 - 5*b**2/4 + 2*b - 2. Suppose s(a) = 0. What is a?
1, 4
Suppose -b - f - 1 = -5, 3*f = -b + 8. Let k be 0 + -2 + -2 + 5. What is g in 9/2*g**3 - 3*g**b - 5/2*g + k = 0?
-2/3, 1/3, 1
Let r(f) be the third derivative of f**7/1575 + f**6/225 - 11*f**5/450 + f**4/30 + 31*f**2. Factor r(j).
2*j*(j - 1)**2*(j + 6)/15
Let j(h) be the second derivative of h**7/168 - h**5/40 + h**3/24 - 3*h. Determine v so that j(v) = 0.
-1, 0, 1
Find u such that -14/9*u**3 + 0 + 2/9*u + 0*u**2 + 4/3*u**4 = 0.
-1/3, 0, 1/2, 1
Suppose -2*h = h + 15, -2*i + h = 13. Let w be 1 + 6/i + 0. What is g in -1/3*g**2 + 1/3*g**3 + 0 + 1/3*g**4 - w*g = 0?
-1, 0, 1
Let v be (-15)/(-2)*-2*3/(-18). Factor -v*a - 1/2 - 2*a**2.
-(a + 1)*(4*a + 1)/2
Let t(f) = f**2 - 3*f - 2. Let o be t(4). Let x be o/7 + 52/14. Factor b**2 - 3*b**3 + b**5 - x*b**4 + 7*b**4 - 2*b**5.
-b**2*(b - 1)**3
Let q be (-20)/10 + (-4)/1. Let d be (-8 - (-4 + 0))/q. Let -2/3*t + d*t**2 + 0 = 0. What is t?
0, 1
Let r(c) be the second derivative of 0 + 0*c**2 + 1/30*c**3 + c + 1/100*c**5 - 1/30*c**4. Factor r(g).
g*(g - 1)**2/5
Let l(k) be the second derivative of 2/5*k**2 + 11/15*k**3 + 3/10*k**4 + 0 + 4*k. Find z such that l(z) = 0.
-1, -2/9
Let c = -11 + -42. Let q = c - -213/4. Factor q*j**3 - 1/4*j**2 + 1/4*j**4 - 1/4*j + 0.
j*(j - 1)*(j + 1)**2/4
Let h(a) be the second derivative of a**4/4 + 5*a**3/2 + 9*a**2 - 2*a. Determine o so that h(o) = 0.
-3, -2
Let x(s) be the first derivative of -s**6/21 - 8*s**5/35 - 5*s**4/14 - 4*s**3/21 + 39. Solve x(t) = 0 for t.
-2, -1, 0
Let h(w) be the second derivative of w**6/60 - w**4/12 + w**2/4 - 3*w. Determine p, given that h(p) = 0.
-1, 1
Let r(b) = b**3 + 4*b**2 - b - 4. Let h = 32 - 23. Let z(l) = -2*l**3 - 9*l**2 + 2*l + 9. Let d(i) = h*r(i) + 4*z(i). Factor d(y).
y*(y - 1)*(y + 1)
Let l = -17 - -23. Let a be (1 - 1)/(-10 + l). Determine m so that -3/2*m**2 - 3*m**3 + 0 - 3/2*m**4 + a*m = 0.
-1, 0
Let v(u) be the third derivative of u**7/105 - u**6/12 + 7*u**5/30 - u**4/4 - 2*u**2. Find b such that v(b) = 0.
0, 1, 3
Let n(u) be the second derivative of u**7/84 - u**6/30 - u**5/40 + u**4/12 + 2*u. Find x, given that n(x) = 0.
-1, 0, 1, 2
Let o(w) be the first derivative of 0*w - w**3 + 3/2*w**2 - 4. Factor o(r).
-3*r*(r - 1)
Let q(d) = -d**2. Let f(h) = h**2 + 7*h - 6. Let j be f(-7). Let v(w) = 8 - 48*w + 64*w**2 + 2 - 2. Let l(p) = j*q(p) + v(p). Solve l(c) = 0 for c.
2/7, 2/5
Let p(w) be the first derivative of -2*w**7/105 - 13*w**6/120 - 11*w**5/60 - w**4/12 + 3*w**2 - 6. Let o(y) be the second derivative of p(y). Factor o(s).
-s*(s + 1)*(s + 2)*(4*s + 1)
Let 9/5 + 1/5*x**2 + 6/5*x = 0. Calculate x.
-3
Suppose -4*b + 28 = -20. Factor 6*n**3 + b*n**3 + 2*n**2 - 16*n**3.
2*n**2*(n + 1)
Let h be (-82)/(-91) + (-28)/98. Factor 154/13*n**2 - 64/13*n + h - 98/13*n**3.
-2*(n - 1)*(7*n - 2)**2/13
Suppose 2 = b + 3. Let x = b + 3. Find l such that 16/9*l**x + 2/9*l**4 - 8/9*l - 10/9*l**3 + 0 = 0.
0, 1, 2
Suppose -15*g**5 + 10*g**3 + 1087 - 5*g**4 - 1087 = 0. What is g?
-1, 0, 2/3
Let a = -3 + 4. Let c be 4 + a + (3 - 5). Find d, given that 4*d**2 + 3*d**c - 3*d**2 - 2*d**2 - 2*d**3 = 0.
0, 1
Let f(y) = y**3 + y**4 - 1 + 4*y**4 - 6*y**4 + y. Let s(h) = 3*h**3 - h - 2. Let b(t) = -f(t) + s(t). Suppose b(q) = 0. What is q?
-1, 1
Let h be 1 + (26 - 4/2). Let b = -123/5 + h. Factor 2/5*f**3 - b*f**2 - 2/5*f + 2/5.
2*(f - 1)**2*(f + 1)/5
Let 7/4*q**5 - 1/2*q - 5/4*q**3 - 9/4*q**2 + 9/4*q**4 + 0 = 0. Calculate q.
-1, -2/7, 0, 1
Let m = -1 + 1. Suppose m*x - 2