Here are the solutions to the math problems: a) Expand: (2x+3)(4−3x) b) Factorize completely: x2 - 7x + 10 c)…

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Here are the solutions to the math problems: a) Expand: (2x+3)(4−3x) b) Factorize completely: x2 - 7x + 10 c) Solve the quadratic equation: x2 - 5x − 6 = 0

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here are the solutions to the math problems: 21. a) Expand: (2x+3)(4−3x) Step 1: Use the distributive property (FOIL method). (2x+3)(4−3x) = 2x(4) + 2x(−3x) + 3(4) + 3(−3x) Step 2: Multiply the terms. = 8x − 6x² + 12 − 9x Step 3: Combine like terms. = −6x² + (8x − 9x) + 12; = −6x² − x + 12 The expanded expression is −6x² − x + 12. b) Factorize completely: x² − 7x + 10 Step 1: Find two numbers that multiply to 10 and add up to −7. The numbers are −2 and −5. Step 2: Rewrite the middle term using these numbers. x² − 2x − 5x + 10 Step 3: Factor by grouping. x(x−2) − 5(x−2) Step 4: Factor out the common binomial. (x−2)(x−5) The completely factorized expression is (x−2)(x−5). c) Solve the quadratic equation: x² − 5x − 6 = 0 Step 1: Find two numbers that multiply to −6 and add up to −5. The numbers are −6 and 1. Step 2: Rewrite the middle term using these numbers. x² − 6x + x − 6 = 0 Step 3: Factor by grouping. x(x−6) + 1(x−6) = 0 Step 4: Factor out the common binomial. (x+1)(x−6) = 0 Step 5: Set each factor equal to zero and solve for x. x+1 = 0 or x−6 = 0; x = −1 or x = 6; The solutions to the quadratic equation are x = −1 or x = 6.

Here are the solutions to the math problems: a) Expand: (2x+3)(4-3x) b) Factorize completely: x2 - 7x + 10 c) Solve the quadratic equation: x2 − 5x − 6 = 0

Answers

Step-by-step solution

Part b· 4 steps

Find two numbers that multiply to 10 and add up to $-7$ .

Rewrite the middle term using these numbers.

Factor by grouping.

Factor out the common binomial.

Part c· 5 steps
$x = -1 \text{ or } x = 6$

Find two numbers that multiply to $-6$ and add up to $-5$ .

Rewrite the middle term using these numbers.

Factor by grouping.

Factor out the common binomial.

Set each factor equal to zero and solve for $x$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions

Here are the solutions to the math problems: a) Expand: (2x+3)(4-3x) b) Factorize completely: x2 - 7x + 10 c) Solve the quadratic equation: x2 − 5x − 6 = 0

Answers

Step-by-step solution

Part b· 4 steps

Find two numbers that multiply to 10 and add up to −7-7−7.

Rewrite the middle term using these numbers.

Factor by grouping.

Factor out the common binomial.

Part c· 5 stepsx=−1 or x=6x = -1 \text{ or } x = 6x=−1 or x=6

Find two numbers that multiply to −6-6−6 and add up to −5-5−5.

Rewrite the middle term using these numbers.

Factor by grouping.

Factor out the common binomial.

Set each factor equal to zero and solve for xxx.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Find two numbers that multiply to 10 and add up to $-7$ .

Part c· 5 steps
$x = -1 \text{ or } x = 6$

Find two numbers that multiply to $-6$ and add up to $-5$ .

Set each factor equal to zero and solve for $x$ .